Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions
Linander, Hampus; Nilsson, Bengt E. W.
2016-07-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F = 0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.
The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
Linander, Hampus
2016-01-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using $F=0$ to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this n...
Madsen, Niels K; Godtliebsen, Ian H; Christiansen, Ove
2017-04-07
Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
Post, U.; Kunz, J.; Mosel, U.
1987-01-01
We present a new method for the solution of the coupled differential equations which have to be solved in various field-theory models. For the solution of the eigenvalue problem a modified version of the imaginary time-step method is applied. Using this new scheme we prevent the solution from running into the negative-energy sea. For the boson fields we carry out a time integration with an additional damping term which forces the field to converge against the static solution. Some results are given for the Walecka model and the Friedberg-Lee model.
Energy Technology Data Exchange (ETDEWEB)
Valat, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1960-12-15
Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
The tanh-coth method combined with the Riccati equation for solving non-linear equation
Energy Technology Data Exchange (ETDEWEB)
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
Ahlkrona, Josefin; Kirchner, Nina; Zwinger, Thomas
2015-01-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains under long time-intervals. The method couples the exact, full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem where the number of degrees of freedom is comparable to a real world application, ISCAL performs almost an order of magnitude faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
Ahlkrona, Josefin; Lötstedt, Per; Kirchner, Nina; Zwinger, Thomas
2016-03-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical......Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Fitting and forecasting non-linear coupled dark energy
Casas, Santiago; Baldi, Marco; Pettorino, Valeria; Vollmer, Adrian
2015-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range $z=0-1.6$ and wave modes below $k=10 \\text{h/Mpc}$. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and w...
Non-linear equation: energy conservation and impact parameter dependence
Kormilitzin, Andrey
2010-01-01
In this paper we address two questions: how energy conservation affects the solution to the non-linear equation, and how impact parameter dependence influences the inclusive production. Answering the first question we solve the modified BK equation which takes into account energy conservation. In spite of the fact that we used the simplified kernel, we believe that the main result of the paper: the small ($\\leq 40%$) suppression of the inclusive productiondue to energy conservation, reflects a general feature. This result leads us to believe that the small value of the nuclear modification factor is of a non-perturbative nature. In the solution a new scale appears $Q_{fr} = Q_s \\exp(-1/(2 \\bas))$ and the production of dipoles with the size larger than $2/Q_{fr}$ is suppressed. Therefore, we can expect that the typical temperature for hadron production is about $Q_{fr}$ ($ T \\approx Q_{fr}$). The simplified equation allows us to obtain a solution to Balitsky-Kovchegov equation taking into account the impact pa...
Estimation of saturation and coherence effects in the KGBJS equation - a non-linear CCFM equation
Deak, Michal
2012-01-01
We solve the modified non-linear extension of the CCFM equation - KGBJS equation - numerically for certain initial conditions and compare the resulting gluon Green functions with those obtained from solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.
A method for solving systems of non-linear differential equations with moving singularities
Gousheh, S S; Ghafoori-Tabrizi, K
2003-01-01
We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution.
A Master Equation for Multi-Dimensional Non-Linear Field Theories
Park, Q H
1992-01-01
A master equation ( $n$ dimensional non--Abelian current conservation law with mutually commuting current components ) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras
Zinn-Justin, P
1998-01-01
A set of coupled non-linear integral equations is derived for a class of models connected with the quantum group $U_q(\\hat g)$ ($q=e^{i\\gamma}$ and $g$ simply laced Lie algebra), which are solvable using the Bethe Ansatz; these equations describe arbitrary excited states of a system with finite spatial length $L$. They generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring model to affine Toda field theory with imaginary coupling constant. As an application, the central charge and all the conformal weights of the UV conformal field theory are extracted in a straightforward manner. The quantum group truncation for rational values of $\\gamma/\\pi$ is discussed in detail; in the UV limit we recover through this procedure the RCFTs with extended $W(g)$ conformal symmetry.
Mártin, Daniel A; 10.1103/PhysRevE.80.056601
2012-01-01
We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative refraction index material with third order effective electric and magnetic non-linearities. Two coupled non-linear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik
2004-01-01
The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Bifurcation for non linear ordinary differential equations with singular perturbation
Directory of Open Access Journals (Sweden)
Safia Acher Spitalier
2016-10-01
Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.
Institute of Scientific and Technical Information of China (English)
陈化; 罗壮初
2002-01-01
In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct × Cnx. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct × Cnx.
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
A scalar hyperbolic equation with GR-type non-linearity
Khokhlov, A M
2003-01-01
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate balance between linear and non-linear terms. We formulate two classes of second-order accurate central-difference schemes, CFLN and MOL, for numerical integration of this equation. Solutions produced by the schemes converge to exact solutions at any fixed time $t$ when numerical resolution is increased. However, in certain cases integration becomes asymptotically unstable when $t$ is increased and resolution is kept fixed. This behavior is caused by subtle changes in the balance between linear and non-linear terms when the equation is discretized. Changes in the balance occur without violating second-order accuracy of discretization. We thus demonstrate that a second-order accuracy, althoug necessary for convergence at finite $t$, does not guarantee a correct asymptotic behavior...
Application of homotopy-perturbation to non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cveticanin, L. [Faculty of Technical Sciences, 21000 Novi Sad, Trg D. Obradovica 6 (Serbia)], E-mail: cveticanin@uns.ns.ac.yu
2009-04-15
In this paper He's homotopy perturbation method has been adopted for solving non-linear partial differential equations. An approximate solution of the differential equation which describes the longitudinal vibration of a beam is obtained. The solution is compared with that found using the variational iteration method introduced by He. The difference between the two solutions is negligible.
Non-local investigation of bifurcations of solutions of non-linear elliptic equations
Energy Technology Data Exchange (ETDEWEB)
Il' yasov, Ya Sh
2002-12-31
We justify the projective fibration procedure for functionals defined on Banach spaces. Using this procedure and a dynamical approach to the study with respect to parameters, we prove that there are branches of positive solutions of non-linear elliptic equations with indefinite non-linearities. We investigate the asymptotic behaviour of these branches at bifurcation points. In the general case of equations with p-Laplacian we prove that there are upper bounds of branches of positive solutions with respect to the parameter.
GDTM-Padé technique for the non-linear differential-difference equation
Directory of Open Access Journals (Sweden)
Lu Jun-Feng
2013-01-01
Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.
Institute of Scientific and Technical Information of China (English)
Pascale KULISA; Cédric DANO
2006-01-01
Three linear two-equation turbulence models k- ε, k- ω and k- 1 and a non-linear k- l model are used for aerodynamic and thermal turbine flow prediction. The pressure profile in the wake and the heat transfer coefficient on the blade are compared with experimental data. Good agreement is obtained with the linear k- l model. No significant modifications are observed with the non-linear model. The balance of transport equation terms in the blade wake is also presented. Linear and non-linear k- l models are evaluated to predict the threedimensional vortices characterising the turbine flows. The simulations show that the passage vortex is the main origin of the losses.
Series solutions of non-linear Riccati differential equations with fractional order
Energy Technology Data Exchange (ETDEWEB)
Cang Jie; Tan Yue; Xu Hang [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China); Liao Shijun [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: sjliao@sjtu.edu.cn
2009-04-15
In this paper, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h. Besides, it is proved that well-known Adomian's decomposition method is a special case of the homotopy analysis method when h = -1. This work illustrates the validity and great potential of the homotopy analysis method for the non-linear differential equations with fractional order. The basic ideas of this approach can be widely employed to solve other strongly non-linear problems in fractional calculus.
Non-linear Matter Spectra in Coupled Quintessence
Saracco, F; Tetradis, N; Pettorino, V; Robbers, G
2010-01-01
We consider cosmologies in which a dark-energy scalar field interacts with cold dark matter. The growth of perturbations is followed beyond the linear level by means of the time-renormalization-group method, which is extended to describe a multi-component matter sector. Even in the absence of the extra interaction, a scale-dependent bias is generated as a consequence of the different initial conditions for baryons and dark matter after decoupling. The effect is greatly enhanced by the extra coupling and can be at the percent level in the range of scales of baryonic acoustic oscillations. We compare our results with N-body simulations, finding very good agreement.
Asymptotic theory for weakly non-linear wave equations in semi-infinite domains
Directory of Open Access Journals (Sweden)
Chirakkal V. Easwaran
2004-01-01
Full Text Available We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Lipschitz Operators and the Solvability of Non-linear Operator Equations
Institute of Scientific and Technical Information of China (English)
Huai Xin CAO; Zong Ben XU
2004-01-01
Let U and V be Banach spaces, L and N be non-linear operators from U into V. L is some basic properties of Lipschitz operators and then discuss the unique solvability, exact solvability,approximate solvability of the operator equations Lx = y and Lx + Nx = y. Under some conditions we prove the equivalence of these solvabilities. We also give an estimation for the relative-errors of the solutions of these two systems and an application of our method to a non-linear control system.
A solution to the non-linear equations of D=10 super Yang-Mills theory
Mafra, Carlos R
2015-01-01
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.
Canonical structure of evolution equations with non-linear dispersive terms
Indian Academy of Sciences (India)
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
A Bohmian approach to the perturbations of non-linear Klein--Gordon equation
Indian Academy of Sciences (India)
FARAMARZ RAHMANI; MEHDI GOLSHANI; MOHSEN SARBISHEI
2016-08-01
In the framework of Bohmian quantum mechanics, the Klein--Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave $\\phi(x)$ in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein--Gordon equation? We examine this approach for $\\phi_{4}(x)$ and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.
A computerized implementation of a non-linear equation to predict barrier shielding requirements.
Chamberlain, A C; Strydom, W J
1997-04-01
A non-linear equation to predict barrier shielding thickness from the work function of x- and gamma-ray generators is presented. This equation is incorporated into a model that takes into account primary, scatter, and leakage radiation components to determine the amount of shielding necessary. The case of multiple wall materials is also considered. The equation accurately models the radiation attenuation curves given in NCRP 49 for concrete and lead, thus eliminating the necessity to use graphical or tabular methods to calculate shielding thickness, which can be inaccurate.
Superdiffusions and positive solutions of non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Dynkin, E B [Cornell University, New York (United States)
2004-02-28
By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.
High order explicit symplectic integrators for the Discrete Non Linear Schr\\"odinger equation
Boreux, Jehan; Hubaux, Charles
2010-01-01
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes, that result to be explicit methods and thus very fast. The performances of the integrators are discussed, studied as functions of the integration time step and compared with some non symplectic methods.
On the non-linearity of the master equation describing spin-selective radical-ion-pair reactions
Kominis, I. K.
2010-01-01
We elaborate on the physical meaning of the non-linear master equation that was recently derived to account for spin-selective radical-ion-pair reactions. Based on quite general arguments, we show that such a non-linear master equation is indeed to be expected.
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Variational principle and a perturbative solution of non-linear string equations in curved space
Roshchupkin, S N
1999-01-01
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H
A discrete homotopy perturbation method for non-linear Schrodinger equation
Directory of Open Access Journals (Sweden)
H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
Murrell, J K J
2001-01-01
previously unexplored regions of parameter space. We show that these calculations predict a range of previously unreported dynamical I-V characterises for SQUID rings in the strongly hysteretic regime. Finally, we present the successful realisation of a novel experimental technique that permits the weak link of a SQUID to be probed independently of the associated ring structure by mechanically opening and closing the ring. We demonstrate that this process can be completed during the same experimental run without the need for warming and re-cooling of the sample. This thesis is concerned with the investigation of the non-linear behaviour of a Superconducting Quantum Interference Device (SQUID) coupled to a RF tank circuit. We consider two regimes, one where the underlying SQUID behaviour is non-hysteretic with respect to an externally applied magnetic flux, and the other where hysteretic (dissipative) behaviour is observed. We show that, by following non-linearities induced in the tank circuit response, the un...
Zia, Haider
2017-06-01
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.
KPP reaction-diffusion equations with a non-linear loss inside a cylinder
Giletti, Thomas
2010-01-01
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Experimental characterization and modeling of non-linear coupling of the LHCD power on Tore Supra
Preynas, M.; Goniche, M.; Hillairet, J.; Litaudon, X.; Ekedahl, A.
2014-02-01
To achieve steady state operation on future tokamaks, in particular on ITER, the unique capability of a LHCD system to efficiently drive off-axis non-inductive current is needed. In this context, it is of prime importance to study and master the coupling of LH wave to the core plasma at high power density (tens of MW/m2). In some specific conditions, deleterious effects on the LHCD coupling are sometimes observed on Tore Supra. At high power the waves may modify the edge parameters that change the wave coupling properties in a non-linear manner. In this way, dedicated LHCD experiments have been performed using the LHCD system of Tore Supra, composed of two different conceptual designs of launcher: the Fully Active Multijunction (FAM) and the new Passive Active Multijunction (PAM) antennas. A nonlinear interaction between the electron density and the electric field has been characterized in a thin plasma layer in front of the two LHCD antennas. The resulting dependence of the power reflection coefficient with the LHCD power, leading occasionally to trips in the output power, is not predicted by the standard linear theory of the LH wave coupling. Therefore, it is important to investigate and understand the possible origin of such non-linear effects in order to avoid their possible deleterious consequences. The PICCOLO-2D code, which self-consistently treats the wave propagation in the antenna vicinity and its interaction with the local edge plasma density, is used to simulate Tore Supra discharges. The simulation reproduces very well the occurrence of a non-linear behavior in the coupling observed in the LHCD experiments. The important differences and trends between the FAM and the PAM antennas, especially a larger increase in RC for the FAM, are also reproduced by the PICCOLO-2D simulation. The working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling is therefore validated through this comprehensive modeling
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...... the computational performance, it is applied to the analysis of a compliant foil bearing modelled using the simple elastic foundation model. The model is derived and perturbed using complex notation. Top foil sagging effect is added to the bump foil compliance in terms of a close-form periodic function. For a foil...... bearing utilized in an industrial turbo compressor, the influence of boundary conditions and sagging on the pressure profile, shaft equilibrium position and dynamic coefficients is numerically simulated. The proposed scheme is faster, leading to the conclusion that it is suitable, not only for steady...
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Performance prediction of gas turbines by solving a system of non-linear equations
Energy Technology Data Exchange (ETDEWEB)
Kaikko, J.
1998-09-01
This study presents a novel method for implementing the performance prediction of gas turbines from the component models. It is based on solving the non-linear set of equations that corresponds to the process equations, and the mass and energy balances for the engine. General models have been presented for determining the steady state operation of single components. Single and multiple shad arrangements have been examined with consideration also being given to heat regeneration and intercooling. Emphasis has been placed upon axial gas turbines of an industrial scale. Applying the models requires no information of the structural dimensions of the gas turbines. On comparison with the commonly applied component matching procedures, this method incorporates several advantages. The application of the models for providing results is facilitated as less attention needs to be paid to calculation sequences and routines. Solving the set of equations is based on zeroing co-ordinate functions that are directly derived from the modelling equations. Therefore, controlling the accuracy of the results is easy. This method gives more freedom for the selection of the modelling parameters since, unlike for the matching procedures, exchanging these criteria does not itself affect the algorithms. Implicit relationships between the variables are of no significance, thus increasing the freedom for the modelling equations as well. The mathematical models developed in this thesis will provide facilities to optimise the operation of any major gas turbine configuration with respect to the desired process parameters. The computational methods used in this study may also be adapted to any other modelling problems arising in industry. (orig.) 36 refs.
A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-05-15
In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.
A Non-Hermitian Approach to Non-Linear Switching Dynamics in Coupled Cavity-Waveguide Systems
DEFF Research Database (Denmark)
Heuck, Mikkel; Kristensen, Philip Trøst; Mørk, Jesper
2012-01-01
We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations.......We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations....
Directory of Open Access Journals (Sweden)
Kim Gaik Tay
2010-04-01
Full Text Available In the present work, by considering the artery as a prestressed thin-walled elastic tube with a symmetrical stenosis and the blood as an incompressible viscous fluid, we have studied the amplitude modulation of nonlinear waves in such a composite medium through the use of the reductive perturbation method [23]. The governing evolutions can be reduced to the dissipative non-linear Schrodinger (NLS equation with variable coefficient. The progressive wave solution to the above non-linear evolution equation is then sought.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
Energy Technology Data Exchange (ETDEWEB)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato.minamitsuji@ist.utl.pt, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Imbert, Cyril
2009-01-01
The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic i...
Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations
Directory of Open Access Journals (Sweden)
Javier Zamora
2016-12-01
Full Text Available Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601. There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrödinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q − values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27. It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which q = 1 or with its NRT non-linear q-generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ∼ 1 instance via a perturbative analysis of the NRT equations.
DIFFERENCE METHODS FOR A NON-LINEAR ELLIPTIC SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS,
DIFFERENCE EQUATIONS, ITERATIONS), (*ITERATIONS, DIFFERENCE EQUATIONS), (* PARTIAL DIFFERENTIAL EQUATIONS , BOUNDARY VALUE PROBLEMS), EQUATIONS, FUNCTIONS(MATHEMATICS), SEQUENCES(MATHEMATICS), NONLINEAR DIFFERENTIAL EQUATIONS
Energy Technology Data Exchange (ETDEWEB)
Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation
Kiessling, A; Heavens, A F
2011-01-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Eucl...
Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles
Shakra, Farah Abou
2012-01-01
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2014-01-01
The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second...... or the first order differential equation (or a set of equations) for electrical system, depending on properties of the electrical circuit. For the sake of brevity, we assume a 1DOF mechanical system, coupled to 1 or 1/2DOF electrical system (depending whether the capacitance is, or is not considered......). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications...
Marschler, Christian
2014-01-01
Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential growth of lifetime as a function of a control parameter, the Reynolds number for pipe flow, and with transitions from bounded chaotic patches to an invasion of space of irregular motion. Dynamical systems models are unique tools in this respect because they can provide insight into the origin of the very long life time of puffs, and the dynamical mechanism leading to the transition from puffs to slugs in pipe flow. The present paper contributes to this enterprise by introducing a unidirectionally coupled map lattice. It mimics three of the salient features of pipe-flow turbulence: (i) the transition from laminar flow to puffs, (ii) a super-exponential scaling of puff lifetime, and (iii) the transition from puffs to slugs by an unbinding transition in an intermittency scenario. ...
Offrein, B.J.; Offrein, B.J.; van Schoot, J.B.P.; van Schoot, J.B.P.; Driessen, A.; Hoekstra, Hugo; Popma, T.J.A.
1993-01-01
Materials with an intensity dependent index of refraction and absorption coefficient¿third-order optical non-linear (ONL) effects¿offer the possibility of all-optical signal processing. Prism coupling is a well-known tool to investigate the intensity dependent refractive index, however, such experim
Anderson, Johan; Johansson, Jonas
2016-12-01
An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to \\exp ≤ft(-cw23/2\\right) , where w 2 is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Energy Technology Data Exchange (ETDEWEB)
Aminov, G. [ITEP, Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation); Mironov, A. [ITEP, Moscow (Russian Federation); Lebedev Physics Institute, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation)
2016-08-15
Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N = 3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter. (orig.)
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Aminov, G; Morozov, A
2016-01-01
Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta-functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N=3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.
Classical Field-Theoretical approach to the non-linear q-Klein-Gordon Equation
Plastino, A
2016-01-01
In the wake of efforts made in [EPL {\\bf 97}, 41001 (2012)], we extend them here by developing a classical field theory (FT)to the q-Klein-Gordon equation advanced in [Phys. Rev. Lett. {\\bf 106}, 140601 (2011)]. This makes it possible to generate a hipotetical conjecture regarding black matter. We also develop the classical field theory for a q-Schrodinger equation, different from the one in [EPL {\\bf 97}, 41001 (2012)], that was deduced in [Phys. Lett. A {\\bf 379}, 2690 (2015)] from the hypergeometric differential equation. Our two classical theories reduce to the usual quantum FT for $q\\rightarrow 1$.
Khachatryan, Kh A.
2015-04-01
We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate non-linear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
Chapline, George
2015-01-01
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations fo...
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Askari, Amir R.; Tahani, Masoud
2017-02-01
This paper focuses on the size-dependent dynamic pull-in instability in rectangular micro-plates actuated by step-input DC voltage. The present model accounts for the effects of in-plane displacements and their non-classical higher-order boundary conditions, von Kármán geometric non-linearity, non-classical couple stress components and the inherent non-linearity of distributed electrostatic pressure on the micro-plate motion. The governing equations of motion, which are clearly derived using Hamilton's principle, are solved through a novel computationally very efficient Galerkin-based reduced order model (ROM) in which all higher-order non-classical boundary conditions are completely satisfied. The present findings are compared and successfully validated by available results in the literature as well as those obtained by three-dimensional finite element simulations carried out using COMSOL Multyphysics. A detailed parametric study is also conducted to illustrate the effects of in-plane displacements, plate aspect ratio, couple stress components and geometric non-linearity on the dynamic instability threshold of the system.
Perturbative treatment of the non-linear q-Schr\\"odinger and q-Klein-Gordon equations
Zamora, D J; Plastino, A; Ferri, G L
2016-01-01
Interesting nonlinear generalization of both Schr\\"odinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\\bf 106}, 140601 (2011)]. There is much current activity going on in this area. The non-linearity is governed by a real parameter $q$. It is a fact that the ensuing non linear q-Schr\\"odinger and q-Klein-Gordon equations are natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for $q-$values close to unity [Nucl. Phys. A {\\bf 955}, 16 (2016), Nucl. Phys. A {\\bf 948}, 19 (2016)]. It is also well known that q-exponential behavior is found in quite different settings. An explanation for such phenomenon was given in [Physica A {\\bf 388}, 601 (2009)] with reference to empirical scenarios in which data are collected via set-ups that effect a normalization plus data's pre-processing. Precisely, the ensuing normalized output was there shown to be q-exponentially distributed if the input dat...
Progress in solutions of the non-linear Boussinesq groundwater equation (Invited)
Dias, N. L.; Chor, T. L.; de Zarate, A. R.
2013-12-01
An existing truncated series solution, previously obtained from inversion techniques from the solution for the Blasius boundary-layer equation, is obtained directly for the Boussinesq equation in terms of a recurrence relation. The series is found to have a finite radius of convergence, which also explains why previous approximations to the solution of the Boussinesq equation had to resort to a combination of series/Padé expressions for small values of the independent variable and asymptotic approximations for large ones. The radius of convergence is obtained numerically to a high accuracy by means of path integration techniques that are able to identify the complex-plane singularities which determine that radius. New variable transformations are proposed for numerical integration of the equation that avoid singularities at the origin, and further asymptotic approximations, which remain necessary due to the finite radius of convergence, are also obtained. The approach can be extended to non-homogeneous boundary conditions at the origin, which is important in realistic scenarios where an aquifer discharges into a channel of finite-depth. Further recurrence relations are found for series solutions of the non-homogeneous case, as well as their radii of convergence and corresponding asymptotic approximations. Results obtained by joining ten terms of the series solution and the asymptotic approximation obtained by Heaslet and Alksne (1961).
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Explosive Solutions of Elliptic Equations with Absorption and Non-Linear Gradient Term
Indian Academy of Sciences (India)
Marius Ghergu; Constantin Niculescu; Vicenţiu Rădulescu
2002-08-01
Let be a non-decreasing $C^1$-function such that $f > 0$ on $(0, ∞), f(0) = 0, \\int_1^∞ 1/\\sqrt{F(t)}dt < ∞$ and $F(t)/f^{2/a}(t)→ 0$ as $t →∞$, where $F(t) = \\int_0^t f(s)ds$ and $a \\in (0,2]$. We prove the existence of positive large solutions to the equation $ u + q(x)|\
Spectral coupling issues in a two-degree-of-freedom system with clearance non-linearities
Padmanabhan, C.; Singh, R.
1992-06-01
In an earlier study [14], the frequency response characteristics of a multi-degree-of-freedom system with clearance non-linearities were presented. The current study is an extension of this prior work and deals specifically with the issue of dynamic interactions between resonances. The harmonic balance method, digital solutions and analog computer simulation are used to investigate a two-degree-of-freedom system under a mean load, when subjected to sinusoidal excitations. The existence of harmonic, periodic and chaotic solutions is demonstrated using digital simulation. The method of harmonic balance is employed to construct approximate solutions at the excitation frequency which are then used to classify weak, moderate and strong non-linear spectral interactions. The effects of parameters such as damping ratio, mean load, alternating load and frequency spacing between the resonances have been quantified. The applicability of the methodology is demonstrated through the following practical examples: (i) neutral gear rattle in an automotive transmission system; and (ii) steady state characteristics of a spur gear pair with backlash. In the second case, measured dynamic transmission error data at the gear mesh frequency are used to investigate spectral interactions. Limitations associated with solution methods and interaction classification schemes are also discussed.
A General Method for Solving Systems of Non-Linear Equations
Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)
1995-01-01
The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.
Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities
Directory of Open Access Journals (Sweden)
Ana M. Martín-Caraballo
2015-08-01
Full Text Available but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position method and the tangent (or Newton-Raphson method, this last as example of fixed-point methods.
Stahl, A.; Landreman, M.; Embréus, O.; Fülöp, T.
2017-03-01
Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modeling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Stahl, A; Embréus, O; Fülöp, T
2016-01-01
Energetic electrons are of interest in many types of plasmas, however previous modelling of their properties have been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modelling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Directory of Open Access Journals (Sweden)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2013-01-01
An electro-magneto-mechanical system combines three physical domains - a mechanical structure, a magnetic field and an electric circuit. The interaction between these domains is analysed for a structure with two degrees of freedom (translational and rotational) and two electrical circuits. Each...... electrical circuit is described by a differential equation of the 1st order, which is considered to contribute to the coupled system by 0.5 DOF. The electrical and mechanical systems are coupled via a magnetic circuit, which is inherently non-linear, due to a non-linear nature of the electro-magnetic force...
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2013-01-01
An electro-magneto-mechanical system combines three physical domains - a mechanical structure, a magnetic field and an electric circuit. The interaction between these domains is analysed for a structure with two degrees of freedom (translational and rotational) and two electrical circuits. Each...... electrical circuit is described by a differential equation of the 1st order, which is considered to contribute to the coupled system by 0.5 DOF. The electrical and mechanical systems are coupled via a magnetic circuit, which is inherently non-linear, due to a non-linear nature of the electro-magnetic force....... To study the non-linear behaviour of the coupled problem analytically, the classical multiple scale method is applied. The response at each mode in resonant as well as in sub-harmonic excitation conditions is analysed in the cases of internal resonance and internal parametric resonance....
Energy Technology Data Exchange (ETDEWEB)
Fike, Jeffrey A.
2013-08-01
The construction of stable reduced order models using Galerkin projection for the Euler or Navier-Stokes equations requires a suitable choice for the inner product. The standard L2 inner product is expected to produce unstable ROMs. For the non-linear Navier-Stokes equations this means the use of an energy inner product. In this report, Galerkin projection for the non-linear Navier-Stokes equations using the L2 inner product is implemented as a first step toward constructing stable ROMs for this set of physics.
Energy Technology Data Exchange (ETDEWEB)
Jan Hesthaven
2012-02-06
Final report for DOE Contract DE-FG02-98ER25346 entitled Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Principal Investigator Jan S. Hesthaven Division of Applied Mathematics Brown University, Box F Providence, RI 02912 Jan.Hesthaven@Brown.edu February 6, 2012 Note: This grant was originally awarded to Professor David Gottlieb and the majority of the work envisioned reflects his original ideas. However, when Prof Gottlieb passed away in December 2008, Professor Hesthaven took over as PI to ensure proper mentoring of students and postdoctoral researchers already involved in the project. This unusual circumstance has naturally impacted the project and its timeline. However, as the report reflects, the planned work has been accomplished and some activities beyond the original scope have been pursued with success. Project overview and main results The effort in this project focuses on the development of high order accurate computational methods for the solution of hyperbolic equations with application to problems with strong shocks. While the methods are general, emphasis is on applications to gas dynamics with strong shocks.
Non-Linear Integral Equation and excited-states scaling functions in the sine-Gordon model
Destri, C
1997-01-01
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six vertex model.
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
The vector Maxwell equations of nonlinear optics coupled to a single Lorentz oscillator and with instantaneous Kerr nonlinearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...... to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether's theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including...
Non-linear dynamics, entanglement and the quantum-classical crossover of two coupled SQUID rings
Everitt, M J
2009-01-01
We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Oscillatons formed by non linear gravity
Obregón, O; Schunck, F E; Obregon, Octavio; Schunck, Franz E.
2004-01-01
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.
Fukuda, Hiroki; Suwa, Hideaki; Nakano, Atsushi; Sakamoto, Mari; Imazu, Miki; Hasegawa, Takuya; Takahama, Hiroyuki; Amaki, Makoto; Kanzaki, Hideaki; Anzai, Toshihisa; Mochizuki, Naoki; Ishii, Akira; Asanuma, Hiroshi; Asakura, Masanori; Washio, Takashi; Kitakaze, Masafumi
2016-11-01
Brain natriuretic peptide (BNP) is the most effective predictor of outcomes in chronic heart failure (CHF). This study sought to determine the qualitative relationship between the BNP levels at discharge and on the day of cardiovascular events in CHF patients. We devised a mathematical probabilistic model between the BNP levels at discharge (y) and on the day (t) of cardiovascular events after discharge for 113 CHF patients (Protocol I). We then prospectively evaluated this model on another set of 60 CHF patients who were readmitted (Protocol II). P(t|y) was the probability of cardiovascular events occurring after >t, the probability on t was given as p(t|y) = -dP(t|y)/dt, and p(t|y) = pP(t|y) = αyβP(t|y), along with p = αyβ (α and β were constant); the solution was p(t|y) = αyβ exp(-αyβt). We fitted this equation to the data set of Protocol I using the maximum likelihood principle, and we obtained the model p(t|y) = 0.000485y0.24788 exp(-0.000485y0.24788t). The cardiovascular event-free rate was computed as P(t) = 1/60Σi=1,…,60 exp(-0.000485yi0.24788t), based on this model and the BNP levels yi in a data set of Protocol II. We confirmed no difference between this model-based result and the actual event-free rate. In conclusion, the BNP levels showed a non-linear relationship with the day of occurrence of cardiovascular events in CHF patients.
Ender, I A; Flegontova, E Yu; Gerasimenko, A B
2016-01-01
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.;
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the non-linear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local non-linear analysis. The various methods of analysis combine to provide significant...
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
Bachelard, Nicolas; Sebbah, Patrick; Vanneste, Christian
2014-01-01
We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
Carlen, Eric A.; Fröhlich, Jürg; Lebowitz, Joel
2016-02-01
We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrödinger equation with a focusing nonlinearity of order p transitions" and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein-Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to ∞. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and "chemical potential" determined by the stochastic noise term.
Directory of Open Access Journals (Sweden)
Kesavan.E
2013-04-01
Full Text Available This paper suggests an idea to design an adaptive PID controller for Non-linear liquid tank System and is implemented in PLC. Online estimation of linear parameters (Time constant and Gain brings an exact model of the process to take perfect control action. Based on these estimated values, the controller parameters will be well tuned by internal model control. Internal model control is an unremarkably used technique and provides well tuned controller in order to have a good controlling process. PLC with its ability to have both continues control for PID Control and digital control for fault diagnosis which ascertains faults in the system and provides alerts about the status of the entire process.
Non-linear dynamics of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
by the rotation of the aerodynamic load and the curvature, as well as inertial induced non-linearities caused by the support point motion. The non-linear partial differential equations of motion in the moving frame of reference have been discretized, using the fixed base eigenmodes as a functional basis......The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced....... Important non-linear couplings between the fundamental blade mode and edgewise modes have been identified based on a resonance excitation of the wing, caused by a harmonically varying support point motion with the circular frequency omega. Assuming that the fundamental blade and edgewise eigenfrequencies...
Coupling and reduction of the HAWC equations
Energy Technology Data Exchange (ETDEWEB)
Nim, Erik
2001-09-01
This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies for more than the ten years. The principal aim of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict enomena caused by geometric non-linear effects. However, the method can also be applied to model the nacelle/shaft structure of a turbine more detailed than the present HAWC model. In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve the condition of the system. (au)
Coupling and reduction of the HAWC equations
DEFF Research Database (Denmark)
Nim, E.
2001-01-01
This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system....
Energy Technology Data Exchange (ETDEWEB)
Zhu Shundong [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)], E-mail: zhusd1965@sina.com
2008-09-15
The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by the generalizing Riccati equation mapping method and picking up its new solutions. In order to test the validity of this approach, the (2 + 1)-dimensional Boiti-Leon-Pempinelle equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.
Energy Technology Data Exchange (ETDEWEB)
Merton, S. R.; Smedley-Stevenson, R. P. [Computational Physics Group, AWE Aldermaston, Reading, Berkshire RG7 4PR (United Kingdom); Pain, C. C. [Dept. of Earth Science and Engineering, Imperial College London, London SW7 2AZ (United Kingdom)
2012-07-01
This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)
EXACT EXPLICIT SOLUTIONS OF THE NONLINEAR SCHR(O)DINGER EQUATION COUPLED TO THE BOUSSINESQ EQUATION
Institute of Scientific and Technical Information of China (English)
姚若侠; 李忠斌
2003-01-01
A system comprised of the nonlinear Schrodinger equation coupled to theBoussinesq equation (S-B equations) which dealing with the stationary propagation of cou-pled non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed.To examine its solitary wave solutions, a reduced set of ordinary differential equations areconsidered by a simple traveling wave transformation. It is then shown that several newsolutions (either functional or parametrical) can be obtained systematically, in addition torederiving all known ones by means of our simple and direct algebra method with the helpof the computer algebra system Maple.
Directory of Open Access Journals (Sweden)
Briti Sundar Sil
2016-01-01
Full Text Available Flood routing is of utmost importance to water resources engineers and hydrologist. Muskingum model is one of the popular methods for river flood routing which often require a huge computational work. To solve the routing parameters, most of the established methods require knowledge about different computer programmes and sophisticated models. So, it is beneficial to have a tool which is comfortable to users having more knowledge about everyday decision making problems rather than the development of computational models as the programmes. The use of micro-soft excel and its relevant tool like solver by the practicing engineers for normal modeling tasks has become common over the last few decades. In excel environment, tools are based on graphical user interface which are very comfortable for the users for handling database, modeling, data analysis and programming. GANetXL is an add-in for Microsoft Excel, a leading commercial spreadsheet application for Windows and MAC operating systems. GANetXL is a program that uses a Genetic Algorithm to solve a wide range of single and multi-objective problems. In this study, non-linear Muskingum routing parameters are solved using GANetXL. Statistical Model performances are compared with the earlier results and found satisfactory.
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Panda, Nishant; Dawson, Clint; Zhang, Yao; Kennedy, Andrew B.; Westerink, Joannes J.; Donahue, Aaron S.
2014-09-01
A local discontinuous Galerkin method for Boussinesq-Green-Naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal. Currently Green-Naghdi equations have many variants. In this paper a numerical method in one dimension is presented for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations for both the analytical problem and the numerical method. Verification is done against a linearized standing wave problem in flat bathymetry and h, p (denoted by K in this paper) error rates are plotted. Validation plots show good agreement of the numerical results with the experimental ones.
Coupled Ito equations of continuous quantum state measurement, and estimation
Diósi, L; Konrad, T; Scherer, A; Audretsch, Juergen; Diosi, Lajos; Konrad, Thomas; Scherer, Artur
2006-01-01
We discuss a non-linear stochastic master equation that governs the time-evolution of the estimated quantum state. Its differential evolution corresponds to the infinitesimal updates that depend on the time-continuous measurement of the true quantum state. The new stochastic master equation couples to the two standard stochastic differential equations of time-continuous quantum measurement. For the first time, we can prove that the calculated estimate almost always converges to the true state, also at low-efficiency measurements. We show that our single-state theory can be adapted to weak continuous ensemble measurements as well.
Cherevko, A. A.; Bord, E. E.; Khe, A. K.; Panarin, V. A.; Orlov, K. J.; Chupakhin, A. P.
2016-06-01
This article considers method of describing the behaviour of hemodynamic parameters near vascular pathologies. We study the influence of arterial aneurysms and arteriovenous malformations on the vascular system. The proposed method involves using generalized model of Van der Pol-Duffing to find out the characteristic behaviour of blood flow parameters. These parameters are blood velocity and pressure in the vessel. The velocity and pressure are obtained during the neurosurgery measurements. It is noted that substituting velocity on the right side of the equation gives good pressure approximation. Thus, the model reproduces clinical data well enough. In regard to the right side of the equation, it means external impact on the system. The harmonic functions with various frequencies and amplitudes are substituted on the right side of the equation to investigate its properties. Besides, variation of the right side parameters provides additional information about pressure. Non-linear analogue of Nyquist diagrams is used to find out how the properties of solution depend on the parameter values. We have analysed 60 cases with aneurysms and 14 cases with arteriovenous malformations. It is shown that the diagrams are divided into classes. Also, the classes are replaced by another one in the definite order with increasing of the right side amplitude.
Molini, A.; Casagrande, E.; Mueller, B.
2013-12-01
Land-Atmosphere (L-A) interactions, their strength and directionality, are one of the main sources of uncertainty in current climate modeling, with strong implications on the accurate assessment of future climate variability and climate change impacts. Beside from the scarcity of direct observations, major uncertainties derive from the inherent complexity and nonlinearity of these interactions, and from their multi-scale character. Statistical analysis of L-A couplings is traditionally based on linear correlation methods and metrics. However, these approaches are not designed to detect causal connections or non-linear couplings and they poorly perform in presence of non-stationarities. Additionally these methods assess L-A couplings essentially in the time domain, despite the fact that L-A dynamical drivers can act simultaneously over a wide range of different space and time scales. This talk explores the multi-scale nature of L-A interactions, through the example of soil moisture-temperature couplings and soil-moisture memory effects. In several regions of the world, soil moisture can have a dampening effect on temperature due to evaporative cooling. By using spectral decomposition techniques and both newly developed satellite based products and re-analysis, we analyze the contribution of different time scales to the build-up of global soil moisture-temperature coupling hot spots, addressing at the same time the role of seasonality, causation and non-linear feedbacks in land-atmosphere interactions. Finally we focus on the role of fine (sub-monthly) time scales and their interplay with the seasonal scales.
DEFF Research Database (Denmark)
Kim, Taeseong; Natarajan, Anand
2013-01-01
The design driving loads on offshore wind turbine monopile support structures at water depths of 35m, which are beyond current monopile installation depths, are derived based on fully coupled aerohydroelastic simulations of the wind turbine in normal operation and in storm conditions in the prese...
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption....
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt
2012-12-01
Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.
Directory of Open Access Journals (Sweden)
G. Wollenberg
2004-01-01
Full Text Available An interconnection system whose loads protected by a voltage suppressor and a low-pass filter against overvoltages caused by coupling pulse-shaped electromagnetic waves is analyzed. The external wave influencing the system is assumed as a plane wave with HPM form. The computation is provided by a full-wave PEEC model for the interconnection structure incorporated in the SPICE code. Thus, nonlinear elements of the protection circuit can be included in the calculation. The analysis shows intermodulation distortions and penetrations of low frequency interferences caused by intermodulations through the protection circuits. The example examined shows the necessity of using full-wave models for interconnections together with non-linear circuit solvers for simulation of noise immunity in systems protected by nonlinear devices.
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption.......Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Non-linear states of a positive or negative refraction index material in a cavity with feedback
Mártin, D. A.; Hoyuelos, M.
2010-06-01
We study a system composed by a cavity with plane mirrors containing a positive or negative refraction index material with third order effective electric and magnetic non-linearities. The aim of the work is to present a general picture of possible non-linear states in terms of the relevant parameters of the system. The parameters are the ones that appear in a reduced description that has the form of the Lugiato-Lefever equation. This equation is obtained from two coupled non-linear Schrödinger equations for the electric and magnetic field amplitudes.
New Exact Solutions to NLS Equation and Coupled NLS Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2004-01-01
A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrodinger (NLS) equation and coupled NLS equations. Many kinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some are found for the first time.
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
Açıkyıldız, Metin; Gürses, Ahmet; Güneş, Kübra; Yalvaç, Duygu
2015-11-01
The present study was designed to compare the linear and non-linear methods used to check the compliance of the experimental data corresponding to the isotherm models (Langmuir, Freundlich, and Redlich-Peterson) and kinetics equations (pseudo-first order and pseudo-second order). In this context, adsorption experiments were carried out to remove an anionic dye, Remazol Brillant Yellow 3GL (RBY), from its aqueous solutions using a commercial activated carbon as a sorbent. The effects of contact time, initial RBY concentration, and temperature onto adsorbed amount were investigated. The amount of dye adsorbed increased with increased adsorption time and the adsorption equilibrium was attained after 240 min. The amount of dye adsorbed enhanced with increased temperature, suggesting that the adsorption process is endothermic. The experimental data was analyzed using the Langmuir, Freundlich, and Redlich-Peterson isotherm equations in order to predict adsorption isotherm. It was determined that the isotherm data were fitted to the Langmuir and Redlich-Peterson isotherms. The adsorption process was also found to follow a pseudo second-order kinetic model. According to the kinetic and isotherm data, it was found that the determination coefficients obtained from linear method were higher than those obtained from non-linear method.
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
Institute of Scientific and Technical Information of China (English)
Shu-hua Zhang; Tao Lin; Yan-ping Lin; Ming Rao
2001-01-01
In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
Generalized Ghost Dark Energy with Non-Linear Interaction
Ebrahimi, E; Mehrabi, A; Movahed, S M S
2016-01-01
In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...
Energy Technology Data Exchange (ETDEWEB)
Pastor, J
2004-07-01
We have determined the equation of state of nuclear matter according to relativistic non-linear models. In particular, we are interested in regions of high density and/or high temperature, in which the thermodynamic functions have very different behaviours depending on which model one uses. The high-density behaviour is, for example, a fundamental ingredient for the determination of the maximum mass of neutron stars. As an application, we have studied the process of two-pion annihilation into e{sup +}e{sup -} pairs in dense and hot matter. Accordingly, we have determined the way in which the non-linear terms modify the meson propagators occurring in this process. Our results have been compared with those obtained for the meson propagators in free space. We have found models that give an enhancement of the dilepton production rate in the low invariant mass region. Such an enhancement is in good agreement with the invariant mass dependence of the data obtained in heavy ions collisions at CERN/SPS energies. (author)
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Gravitationally Coupled Dirac Equation for Antimatter
Jentschura, U D
2013-01-01
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously in [D.R. Brill and J.A. Wheeler, Rev. Mod. Phys., vol. 29, p. 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion the curved-space Dirac equation from East-Coast to West-Coast conventions, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes anti-particles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particl...
Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation
Rana, S.; Mehmood, R.; Narayana, PV S.; Akbar, N. S.
2016-12-01
The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10-5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.
Proposal for a running coupling JIMWLK equation
Lappi, T
2014-01-01
In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.
Analytic Solution of Strongly Coupling Schroedinger Equation
Liao, J Y; Liao, Jinfeng; Zhuang, Pengfei
2002-01-01
The recently developed expansion method for ground states of strongly coupling Schr\\"odinger equations by Friedberg, Lee and Zhao is extended to excited states. The coupling constant dependence of bound states for power-law central forces $V(r) \\propto g^k r^n$ is particularly studied. With the extended method all the excited states of the Hydrogen atom problem are resolved and the low-lying states for Yukawa potential are approximately obtained.
Solutions of the coupled Higgs field equations.
Talukdar, Benoy; Ghosh, Swapan K; Saha, Aparna; Pal, Debabrata
2013-07-01
By an appropriate choice for the phase of the complex nucleonic field and going over to the traveling coordinate, we reduce the coupled Higgs equations to the Hamiltonian form and treat the resulting equation using the dynamical system theory. We present a phase-space analysis of its stable points. The results of our study demonstrate that the equation can support both traveling- and standing-wave solutions. The traveling-wave solution appears in the form of a soliton and resides in the midst of doubly periodic standing-wave solutions.
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
Yamada, Hirofumi
2012-01-01
Based on the strong coupling expansion, we reinvestigate the scaling behavior of the susceptibility chi of two-dimensional O(N) sigma model on the square lattice by the use of Pade-Borel approximants. To exploit the Borel transform, we express the bare coupling g in series expansion in chi. At large N, Pade-Borel approximants exhibit the scaling behavior at the four-loop level. Then, the estimation of the non-perturbative constant associated with the susceptibility is performed for N>=3 and the results are compared with the available theoretical results and Monte Carlo data.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
Breathers and rogue waves: Demonstration with coupled nonlinear Schrödinger family of equations
Indian Academy of Sciences (India)
N Vishnu Priya; M Senthilvelan; M Lakshmanan
2015-03-01
Different types of breathers and rogue waves (RWs) are some of the important coherent structures which have been recently realized in several physical phenomena in hydrodynamics, nonlinear optics, Bose–Einstein condensates, etc. Mathematically, they have been deduced in non-linear Schrödinger (NLS) equations. Here we show the existence of general breathers, Akhmediev breathers, Ma soliton and rogue wave solutions in coupled Manakov-type NLS equations and coupled generalized NLS equations representing four-wave mixing. We deduce their explicit forms using Hirota bilinearization procedure and bring out their exact structures and important properties. We also show the method to deduce the various breather solutions from rogue wave solutions using factorization form and the so-called imbricate series.
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Coupled Nonlinear Schr\\"{o}dinger equation and Toda equation (the Root of Integrability)
Hisakado, Masato
1997-01-01
We consider the relation between the discrete coupled nonlinear Schr\\"{o}dinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\\"{o}dinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.
Energy Technology Data Exchange (ETDEWEB)
Longuemare, P.
1996-11-28
The aim of this study is to provide a better description of the rock contribution to fluid flows in sedimentary basins and petroleum reservoirs. After a study of the mechanical behaviour of high porosity chalks and shales, we present the elaboration of an elastoplastic constitutive model for the description of their behaviour under various strain and stress paths. This model is introduced in a coupled poro-mechanical approach and used to study the advantages of a good description of strain and stress paths in petroleum reservoirs and sedimentary basins studies. Hydro-mechanical modelling of the behaviour of petroleum reservoir allowed us to analyse the influence of boundary limit conditions on stress paths recovery rates. The study of sedimentary basins showed the importance of the consideration of the evolution of the porosity with time due to the time-scale difference between the laboratory and the field data. (author) 58 refs.
Bouchiat, Marie-Anne
2010-01-01
We derive the general formula giving the Berry phase for an arbitrary spin, having both magnetic-dipole and electric-quadrupole couplings with external time-dependent fields. We assume that the effective E and B fields remain orthogonal during the quantum cycles. This mild restriction has many advantages. It provides simple symmetries leading to selection rules and the Hamiltonian-parameter and density-matrix spaces coincide for S=1. This implies the identity of the Berry and Aharonov-Anandan phases, which is lost for S>1. We have found that new features of Berry phases emerge for integer spins>2. We provide explicit numerical results of Berry phases for S=2,3,4. We give a precise analysis of the non-adiabatic corrections. The accuracy for satisfying adiabaticity is greatly improved if one chooses for the time derivatives of the parameters a time-dependence having a Blackman pulse shape. This has the effect of taming the non-adiabatic oscillation corrections which could be generated by a linear ramping. For r...
Institute of Scientific and Technical Information of China (English)
M·T·穆斯塔法; K·玛苏德
2009-01-01
应用Lie对称法,当弹性能具有三阶非调和修正项时,分析纵向变形的非线性弹性波动方程.通过不同对称下的恒等条件,寻找对称代数,并将它简化为二阶常微分方程.对该简化的常微分方程作进一步分析后,获得若干个显式的精确解.分析Apostol的研究成果(Apostol B F.on a non-linear wave equation in elasticity.Phys Lett A,2003,318(6):545-552)发现,非调和修正项通常导致解在有限时间内具有时间相关奇异性.除了得到时间相关奇异性的解外,还得到无法显示时间相关奇异性的解.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Charged relativistic fluids and non-linear electrodynamics
Dereli, T.; Tucker, R. W.
2010-01-01
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.
Non-linear Oscillations of Compact Stars and Gravitational Waves
Passamonti, A
2006-01-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative or...
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Unpolarized coupled DGLAP evolution equation at small-
Indian Academy of Sciences (India)
Saurav Bhattacharjee; Ranjit Baishya; Jayanata Kumar Sarma
2013-01-01
In this paper, we have obtained the solution of the unpolarized coupled Dokshitzer–Gribove–Lipatov–Alterelli–Parisi (DGLAP) evolution equation in leading order at the small- limit. Here, we have used a Taylor series expansion, separation of functions and then the method of characteristics to solve the evolution equations. We have also calculated -evolution of singlet and gluon distribution functions and the results are compared with E665 and NNPDF data for singlet structure function and GRV1998 and MRST2004 gluon parametrizations. It is shown that our results are in good agreement with the parametrizations especially at small-x and high-2 region. From global parametrizations and our results, we have seen that the singlet and gluon distribution functions increase when 2 increases for fixed values of .
Upper bounds on the solution of coupled algebraic riccati equation
Directory of Open Access Journals (Sweden)
Czornik Adam
2001-01-01
Full Text Available Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE and discrete time coupled algebraic Riccati equation (DCARE are developed as special cases of bounds for the unified coupled algebraic Riccati equation (UCARE. They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.
Integrability of two coupled Kadomtsev–Petviashvili equations
Indian Academy of Sciences (India)
Abdul-Majid Wazwaz
2011-08-01
The integrability of two coupled KP equations is studied. The simpliﬁed Hereman form of Hirota’s bilinear method is used to examine the integrability of each coupled equation. Multiplesoliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation.
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Institute of Scientific and Technical Information of China (English)
张洪生; 洪广文; 丁平兴; 曹振轶
2001-01-01
In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.
Fluid flow of incompressible viscous fluid through a non-linear elastic tube
Energy Technology Data Exchange (ETDEWEB)
Lazopoulos, A.; Tsangaris, S. [National Technical University of Athens, Fluids Section, School of Mechanical Engineering, Zografou, Athens (Greece)
2008-11-15
The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung's (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain-energy density function. The fluid is described through a Navier-Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response. (orig.)
Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system
Kahraman, A.; Singh, R.
1991-04-01
Frequency response characteristics of a non-linear geared rotor-bearing system with time-varying mesh stiffness k h( overlinet) are examined in this paper. First, the single-degree-of-freedom spur gear pair model with backlash is extended to include sinusoidal or periodic mesh stiffness k h( overlinet) . Second, a three-degree-of-freedom model with k h( overlinet) and clearance non-lineariries associated with gear backlash and rolling element bearings, as excited by the static transmission error overlinee( overlinet) under a mean torque load, is developed. The governing equations are solved using digital simulation technique and only the primary resonances are studied. Resonances of the corresponding linear time-varying system associated with parametric and external excitations are identified using the method of multiple scales and digital simulation. Interactions between the mesh stiffness variation and clearance non-linearities have been investigated; a strong interaction between time-varying mesh stiffness k h( overlinet) and gear backlash is found, whereas the coupling between k h( overlinet) and bearing non-linearities is weak. Finally, our time-varying non-linear formulations yield reasonably good predictions when compared with the benchmark experimental results available in the literature.
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Higher order effects in non-linear evolution from a veto in rapidities
Chachamis, G.; Lublinsky, M.; Sabio Vera, A.
2005-02-01
Higher order corrections to the Balitsky-Kovchegov equation have been estimated by introducing a rapidity veto which forbids subsequent emissions to be very close in rapidity and is known to mimic higher order corrections to the linear BFKL equation. The rapidity veto constraint has been first introduced using analytical arguments obtaining a power growth with energy, Q(Y)˜e, of the saturation scale of λ˜0.45. Then a numerical analysis for the non-linear Balitsky-Kovchegov equation has been carried out for phenomenological rapidities: when a veto of about two units of rapidity is introduced for a fixed value of the coupling constant of α=0.2 the saturation scale λ decreases from ˜0.6 to ˜0.3, and when running coupling effects are taken into account it decreases from ˜0.4 to ˜0.3.
Non-linear Dynamics in $QED_{3}$ and Non-trivial Infrared Structure
Mavromatos, Nikolaos E
1999-01-01
In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated consistently. The non-linearity of the equations gives rise to highly non-trivial constraints among the mass and effective (`running') gauge coupling, which impose lower and upper bounds on the latter for dynamical mass generation to occur. Possible implications of this to the theory of high-temperature superconductivity are...
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
The Importance of Non-Linearity on Turbulent Fluxes
DEFF Research Database (Denmark)
Rokni, Masoud
2007-01-01
Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...
Reciprocal link for a coupled Camassa-Holm type equation
Li, Nianhua; Zhang, Jinshun; Wu, Lihua
2016-04-01
A coupled Camassa-Holm type equation is linked to the first negative flow in a modified Drinfeld-Sokolov III hierarchy by a transformation of reciprocal type. Meanwhile the Lax pair and bi-Hamiltonian structure behaviors of this coupled Camassa-Holm type equation under the reciprocal transformation are analyzed.
Attractor for a Viscous Coupled Camassa-Holm Equation
Directory of Open Access Journals (Sweden)
Tian Lixin
2010-01-01
Full Text Available The global existence of solution to a viscous coupled Camassa-Holm equation with the periodic boundary condition is investigated. We obtain the compact and bounded absorbing set and the existence of the global attractor for the viscous coupled Camassa-Holm equation in by uniform prior estimate.
DEFF Research Database (Denmark)
Schmidt, Johan Albrecht
The isotopic fractionation associated with photodissociation of N2O, OCS and CO2, at different altitudes in Earth’s atmosphere, is investigated theoretically using constructed quantum mechanical models of the dissociation processes (i.e. potential energy surfaces and relevant coupling elements...... or moderate, and overall sulfur fractionation in the stratosphere is very weak which does not exclude OCS from being an acceptable background the Stratospheric Sulfate Aerosol layer. (iii) CO2 photolysis in the upper stratosphere and lower mesosphere is highly fractionating in both isotopes, enriching...
Non-linearity parameter / of binary liquid mixtures at elevated pressures
Indian Academy of Sciences (India)
J D Pandey; J Chhabra; R Dey; V Sanguri; R Verma
2000-09-01
When sound waves of high amplitude propagate, several non-linear effects occur. Ultrasonic studies in liquid mixtures provide valuable information about structure and interaction in such systems. The present investigation comprises of theoretical evaluation of the acoustic non-linearity parameter / of four binary liquid mixtures using Tong and Dong equation at high pressures and = 303.15 K. Thermodynamic method has also been used to calculate the non-linearity parameter after making certain approximations.
Reciprocal link for a coupled Camassa–Holm type equation
Energy Technology Data Exchange (ETDEWEB)
Li, Nianhua, E-mail: linianh@hqu.edu.cn; Zhang, Jinshun; Wu, Lihua
2016-04-08
Highlights: • We construct a reciprocal transformation for a coupled Camassa–Holm type equation proposed by Geng and Xue. • The transformed coupled Camassa–Holm type system is a reduction of the first negative flow in a modified Drinfeld–Sokolov III hierarchy. • The Lax pair and bi-Hamiltonian structure behaviors of the coupled Camassa–Holm type equation under the reciprocal transformation are analyzed. - Abstract: A coupled Camassa–Holm type equation is linked to the first negative flow in a modified Drinfeld–Sokolov III hierarchy by a transformation of reciprocal type. Meanwhile the Lax pair and bi-Hamiltonian structure behaviors of this coupled Camassa–Holm type equation under the reciprocal transformation are analyzed.
Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators
Alpomishev, E X
2016-01-01
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
Indian Academy of Sciences (India)
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
Institute of Scientific and Technical Information of China (English)
WANG Zhongmin; GAO Jingbo; LI Huixia; LIU Hongzhao
2008-01-01
The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.
Directory of Open Access Journals (Sweden)
Yan Li-Mei
2013-01-01
Full Text Available The purpose of this paper is to extend the homotopy perturbation method to fractional heat transfer and porous media equations with the help of the Laplace transform. The fractional derivatives described in this paper are in the Caputo sense. The algorithm is demonstrated to be direct and straightforward, and can be used for many other non-linear fractional differential equations.
Global coupled equations for dynamic analysis of planishing mill
Institute of Scientific and Technical Information of China (English)
蔡敢为; 钟掘
2003-01-01
The dynamic properties of rolling mill are significantly influenced by many coupling factors. Accordingto the coupled mechanical and electric dynamics theory, the global coupled equations for the dynamic analysis ofplanishing mill CM04 of Shanghai Baosteel Group Corporation were derived, by using finite element methods. Theseelasto-dynamic equations establish the coupling relations among the stand vibration system, torsional vibration sys-tem, driving motors, etc. It provides theoretical basis to a certain extent for globally dynamic simulation, analysis ofstability of motion, prediction of abnormal operating mode, globally optimum design and control, etc.
Travelling and standing envelope solitons in discrete non-linear cyclic structures
Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph
2016-12-01
Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.
Exact Solutions of Bogoyavlenskii Coupled KdV Equations
Institute of Scientific and Technical Information of China (English)
HUHeng-Chun; LOUSen-Yue
2004-01-01
The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor -Carnvale Painleve' truncation expansion and the nonstandard truncation of a modified Conte's invariant Painlevé expansion.
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.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Likelihood inference for discretely observed non-linear diffusions
1998-01-01
This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the lat...
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
Faddeev equations for the coupled NN-πNN system
Afnan, I. R.; Stelbovics, A. T.
1981-04-01
We show that the two different formulations of the NN-πNN system proposed by Afnan-Blankleider and Stingl-Stelbovics lead to a set of three linear coupled operator equations which are identical in form to the Faddeev equations. The resulting equations include the fact that both nucleons are identical and either can emit a pion. They also have dressing for the πNN vertex and NN and πNN propagators. The final equations are shown to satisfy two-and three-body unitarity. NUCLEAR REACTIONS Feddeev-type equation for NN-πNN system, proof of two- and three-body unitarity.
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations
Khusnutdinova, K R
2011-01-01
We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying right- and left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scales expansions and averaging with respect to the fast time, we obtain a hierarchy of asymptotically exact coupled and uncoupled Ostrovsky equations for unidirectional waves. We then construct a weakly nonlinear solution of the initial-value problem in terms of solutions of the derived Ostrovsky equations within the accuracy of the governing equations, and show that there are no secular terms. When coupling parameters are equal to zero, our results yield a weakly nonlinear solution of the initial-value problem for the Boussinesq equation in terms of solutions of the initial-value problems for two Korteweg-de Vries equations, integrable by the Inverse Scattering Transform. We also perform relev...
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FUZun-Tao; LIUShi-Da; LIUShi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
On complexly coupled modified KdV equations
Indian Academy of Sciences (India)
Amitava Choudhuri
2010-10-01
We introduced complexly coupled modified KdV (ccmKdV) equations, which could be derived from a two-layer fluid model [Yang and Mao, Chin. Phys. Lett. 25, 1527 (2008); Hu, J. Phys. A: Math. Theor. 43, 185207 (2009)], and used the Miura transformation to construct expressions for their alternative Lax pair representations. We derived a Lagrangian-based approach to study the Hamiltonian structures of the ccmKdV equations and observed that the complexly coupled mKdV equations have an additional analytic structure. The coupled equations were characterized by two alternative Lagrangians not connected by a gauge term. We examined how the alternative Lagrangian descriptions of the system affect the bi-Hamiltonian structures.
Non-Linear Relativity in Position Space
Kimberly, D; Medeiros-Neto, J F; Kimberly, Dagny; Magueijo, João; Medeiros, João
2003-01-01
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.
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....
Strong Coulomb Coupling in the Todorov Equation
Bawin, M.; Cugnon, J.; Sazdjian, H.
A positronium-like system with strong Coulomb coupling, considered in its pseudoscalar sector, is studied in the framework of relativistic quantum constraint dynamics with the Todorov choice for the potential. Case’s method of self-adjoint extension of singular potentials, which avoids explicit introduction of regularization cut-offs, is adopted. It is found that, as the coupling constant α increases, the bound state spectrum undergoes an abrupt change at the critical value α=αc=1/2. For α>αc, the mass spectrum displays, in addition to the existing states for α<αc, a new set of an infinite number of bound states concentrated in a narrow band starting at mass W=0; all the states have indefinitely oscillating wave functions near the origin. In the limit α→αc from above, the oscillations disappear and the narrow band of low-lying states shrinks to a single massless state with a mass gap with the rest of the spectrum. This state has the required properties to represent a Goldstone boson and to signal spontaneous breakdown of chiral symmetry.
A Discrete Lax-Integrable Coupled System Related to Coupled KdV and Coupled mKdV Equations
Institute of Scientific and Technical Information of China (English)
LIU Ping; JIA Ma; LOU Sen-Yue
2007-01-01
A modified Korteweg-de Vries (mKdV) lattice is found to be also a discrete Korteweg-de Vries (KdV) equation.A discrete coupled system is derived from the single lattice equation and its Lax pair is proposed. The coupled system is shown to be related to the coupled KdV and coupled mKdV systems which are widely used in physics.
Faddeev equations for the coupled NN-. pi. NN system
Energy Technology Data Exchange (ETDEWEB)
Afnan, I.R.; Stelbovics, A.T.
1981-04-01
We show that the two different formulations of the NN-..pi..NN system proposed by Afnan-Blankleider and Stingl-Stelbovics lead to a set of three linear coupled operator equations which are identical in form to the Faddeev equations. The resulting equations include the fact that both nucleons are identical and either can emit a pion. They also have dressing for the ..pi..NN vertex and NN and ..pi..NN propagators. The final equations are shown to satisfy two- and three-body unitarity.
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
Non-linear irreversible thermodynamics of single-molecule experiments
Santamaria-Holek, I; Hidalgo-Soria, M; Perez-Madrid, A
2015-01-01
Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between di?erent con?gurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2016-07-01
Full Text Available In this paper, we improve the extended trial equation method to construct the exact solutions for nonlinear coupled system of partial differential equations in mathematical physics. We use the extended trial equation method to find some different types of exact solutions such as the Jacobi elliptic function solutions, soliton solutions, trigonometric function solutions and rational, exact solutions to the nonlinear coupled Schrodinger Boussinesq equations when the balance number is a positive integer. The performance of this method is reliable, effective and powerful for solving more complicated nonlinear partial differential equations in mathematical physics. The balance number of this method is not constant as we have in other methods. This method allows us to construct many new types of exact solutions. By using the Maple software package we show that all obtained solutions satisfy the original partial differential equations.
Institute of Scientific and Technical Information of China (English)
郝世峰; 楼茂园; 杨诗芳; 李超; 孔照林; 裘薇
2015-01-01
To solve atmospheric primitive equations, the finite difference approach would result in numerous problems, com-pared to the differential equations. Taking the semi-Lagrange model as an example, there exist two diﬃcult prob-lems——the particle trajectory computation and the solutions of the Helmholtz equations. In this study, based on the substitution of atmosphere pressure, the atmospheric primitive equations are linearized within an integral time step, which are broadly seen as ordinary differential equations and can be derived as semi-analytical solutions (SASs). The variables of SASs are continuous functions of time and discretized in a special direction, so the gradient and divergence terms are solved by the difference method. Since the numerical solution of the SASs can be calculated via a highly pre-cise numerical computational method of exponential matrix——the precise integration method, the numerical solution of SASs at any time in the future can be obtained via step-by-step integration procedure. For the SAS methodology, the pressure, as well as the wind vector and displacement, can be obtained without solving the Helmholtz formulations. Compared to the extrapolated method, the SAS is more reasonable as the displacements of the particle are solved via time integration. In order to test the validity of the algorithms, the SAS model is constructed and the same experi-ment of a non-linear density current as reported by Straka in 1993 is implemented, which contains non-linear dynamics, transient features and fine-scale structures of the fluid flow. The results of the experiment with 50 m spatial resolution show that the SAS model can capture the characters of generation and development process of the Kelvin-Helmholtz shear instability vortex; the structures of the perturbation potential temperature field are very close to the benchmark solutions given by Straka, as well as the structures of the simulated atmosphere pressure and wind field. To further
Various equations for gap probabilities of coupled Gaussian matrices
Energy Technology Data Exchange (ETDEWEB)
Rumanov, Igor, E-mail: igorrumanov@math.ucdavis.edu [Department of Mathematics, UC Davis, 1 Shields Avenue, CA 95616 (United States)
2011-04-08
Versions of Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) approaches are applied to derive various partial differential equations (PDE) satisfied by joint eigenvalue spacing probabilities of two coupled Gaussian Hermitian matrices (coupled GUE). All the lowest (third)-order PDE satisfied by the probabilities for the largest eigenvalues of two coupled GUE are found, and the results of both approaches are compared. The TW approach allows us to derive all PDE at once, while in the ASvM one starting with different bilinear identities leads to different subsets of the full set of equations. An interesting result is that the joint probability for the largest eigenvalues of coupled Gaussian matrices satisfies a number of different PDE, and the previously known Adler-van Moerbeke equation (AvM) (1999 Ann. Math. 149 921-76) is only one of them. Some of the new equations appear like 'coupled Painleve IV' and have the usual Painleve IV equation as the one-matrix limit, i.e. when the spectral endpoint of one of the matrices goes to infinity. This is in contrast to the AvM equation, which becomes trivial in this limit. Moreover, the new PDE, which stem from the matrix kernel approach of Tracy and Widom (2004 Commun. Math. Phys. 252 7-41), do not contain derivatives w.r.t. the strength of coupling, unlike the AvM equation. In other words, they contain fewer independent variables and in this sense are simpler.
Exact solution of the space-time fractional coupled EW and coupled MEW equations
Raslan, K. R.; S. EL-Danaf, Talaat; K. Ali, Khalid
2017-07-01
In this paper, we obtained a traveling wave solution by using the Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations, such as the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEWE), which are the important soliton equations. Both equations are reduced to ordinary differential equations by use of the fractional complex transform and of the properties of the modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
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 betwee...... 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.......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...... 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...
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media
Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo
2013-04-01
A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M B; Machado, P A N; Saa, S
2016-01-01
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic compl...
Non-linear dendrites can tune neurons
Directory of Open Access Journals (Sweden)
Romain Daniel Cazé
2014-03-01
Full Text Available A signature of visual, auditory, and motor cortices is the presence of neurons tuned to distinct features of the environment. While neuronal tuning can be observed in most brain areas, its origin remains enigmatic, and new calcium imaging data complicate this problem. Dendritic calcium signals, in a L2/3 neuron from the mouse visual cortex, display a wide range of tunings that could be different from the neuronal tuning (Jia et al 2010. To elucidate this observation we use multi-compartmental models of increasing complexity, from a binary to a realistic biophysical model of L2/3 neuron. These models possess non-linear dendritic subunits inside which the result of multiple excitatory inputs is smaller than their arithmetic sum. While dendritic non-linear subunits are ad-hoc in the binary model, non-linearities in the realistic model come from the passive saturation of synaptic currents. Because of these non-linearities our neuron models are scatter sensitive: the somatic membrane voltage is higher when presynaptic inputs target different dendrites than when they target a single dendrite. This spatial bias in synaptic integration is, in our models, the origin of neuronal tuning. Indeed, assemblies of presynaptic inputs encode the stimulus property through an increase in correlation or activity, and only the assembly that encodes the preferred stimulus targets different dendrites. Assemblies coding for the non-preferred stimuli target single dendrites, explaining the wide range of observed tunings and the possible difference between dendritic and somatic tuning. We thus propose, in accordance with the latest experimental observations, that non-linear integration in dendrites can generate neuronal tuning independently of the coding regime.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Jørgen Arendt
2013-01-01
. The accuracy of the nonlinear ASA is compared to the non-linear simulation program – Abersim, which is a numerical solution to the Burgers equation based on the OSM. Simulations are performed for a linear array transducer with 64 active elements, focus at 40 mm, and excitation by a 2-cycle sine wave......A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly...... increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated...
Fabrication and characterization of non-linear parabolic microporous membranes.
Rajasekaran, Pradeep Ramiah; Sharifi, Payam; Wolff, Justin; Kohli, Punit
2015-01-01
Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L - t(1/2). Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric "off-centered PMS" and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.
Non-linear aeroelastic prediction for aircraft applications
de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.
2007-05-01
in this domain. This is set within the context of a generic industrial process and the requirements of UK and US aeroelastic qualification. A range of test cases, from simple small DOF cases to full aircraft, have been used to evaluate and validate the non-linear methods developed and to make comparison with the linear methods in everyday use. These have focused mainly on aerodynamic non-linearity, although some results for structural non-linearity are also presented. The challenges associated with time domain (coupled computational fluid dynamics-computational structural model (CFD-CSM)) methods have been addressed through the development of grid movement, fluid-structure coupling, and control surface movement technologies. Conclusions regarding the accuracy and computational cost of these are presented. The computational cost of time-domain methods, despite substantial improvements in efficiency, remains high. However, significant advances have been made in reduced order methods, that allow non-linear behaviour to be modelled, but at a cost comparable with that of the regular linear methods. Of particular note is a method based on Hopf bifurcation that has reached an appropriate maturity for deployment on real aircraft configurations, though only limited results are presented herein. Results are also presented for dynamically linearised CFD approaches that hold out the possibility of non-linear results at a fraction of the cost of time coupled CFD-CSM methods. Local linearisation approaches (higher order harmonic balance and continuation method) are also presented; these have the advantage that no prior assumption of the nature of the aeroelastic instability is required, but currently these methods are limited to low DOF problems and it is thought that these will not reach a level of maturity appropriate to real aircraft problems for some years to come. Nevertheless, guidance on the most likely approaches has been derived and this forms the basis for ongoing
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Fliess, Michel; Join, Cédric; Sira-Ramirez, Hebertt
2008-01-01
International audience; Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line ...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Fliess, Michel; Sira-Ramirez, Hebertt
2007-01-01
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
Parametrization of the QCD coupling in the evolution equations
Energy Technology Data Exchange (ETDEWEB)
Ermolaev, B.I. [H. Niewodniczanski Nuclear Physics Institute PAN, 31-342 Krakow (Poland); Ioffe Physico-Technical Institute, 194021 St. Petersburg (Russian Federation)], E-mail: boris.ermolaev@cern.ch; Troyan, S.I. [St. Petersburg Institute of Nuclear Physics, 188300 Gatchina (Russian Federation)
2008-08-21
We examine the parametrization of the QCD coupling in the evolution equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k{sub perpendicular}{sup 2}/{beta} or just k{sub perpendicular}{sup 2}, stands only if the lowest integration limit in the transverse momentum space (the starting point {mu}{sup 2} of the Q{sup 2}-evolution) obeys the relation {mu}>>{lambda}{sub QCD}exp({pi}/2), otherwise the coupling should be replaced by the more complicated expression presented in Eq. (29)
Parametrization of the QCD coupling in the Evolution Equations
Ermolaev, B I
2008-01-01
We examine the parametrization of the QCD coupling in the Evolution Equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k^2_{\\perp}/\\beta or just k^2_{\\perp}, stands only if the lowest integration limit in the transverse momentum space (the starting point mu^2 of the Q^2 -evolution) obeys the relation mu >> Lambda_{QCD} \\exp {(\\pi/2)}, otherwise the coupling should be replaced by the more complicated expression presented in Eq. (37).
Energy Technology Data Exchange (ETDEWEB)
Khan, Masood [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hashim, E-mail: hashim_alik@yahoo.com [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan); Hussain, M. [Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad 44000 (Pakistan); Azam, M. [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan)
2016-08-15
This paper presents a study of the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Carreau fluid over a convectively heated surface. The analysis of heat transfer is further performed in the presence of non-linear thermal radiation. The appropriate transformations are employed to bring the governing equations into dimensionless form. The numerical solutions of the partially coupled non-linear ordinary differential equations are obtained by using the Runge-Kutta Fehlberg integration scheme. The influence of non-dimensional governing parameters on the velocity, temperature, local skin friction coefficient and local Nusselt number is studied and discussed with the help of graphs and tables. Results proved that there is significant decrease in the velocity and the corresponding momentum boundary layer thickness with the growth in the magnetic parameter. However, a quite the opposite is true for the temperature and the corresponding thermal boundary layer thickness. - Highlights: • We investigated the Magnetohydrodynamic flow of Carreau constitutive fluid model. • Impact of non-linear thermal radiation is further taken into account. • Runge-Kutta Fehlberg method is employed to obtain the numerical solutions. • Fluid velocity is higher in case of hydromagnetic flow in comparison with hydrodynamic flow. • The local Nusselt number is a decreasing function of the thermal radiation parameter.
Indian Academy of Sciences (India)
Sachin Kumar; K Singh; R K Gupta
2012-07-01
In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (′/)-expansion methodc, where = () satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.
Exact periodic solution in coupled nonlinear Schrodinger equations
Institute of Scientific and Technical Information of China (English)
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
Solution of fractional differential equations via coupled fixed point
Directory of Open Access Journals (Sweden)
Hojjat Afshari
2015-11-01
Full Text Available In this article, we investigate the existence and uniqueness of a solution for the fractional differential equation by introducing some new coupled fixed point theorems for the class of mixed monotone operators with perturbations in the context of partially ordered complete metric space.
Coupling conditions for the shallow water equations on a network
Caputo, Jean-Guy; Gleyse, Bernard
2015-01-01
We study numerically and analytically how nonlinear shallow water waves propagate in a fork. Using a homothetic reduction procedure, conservation laws and numerical analysis in a 2D domain, we obtain angle dependent coupling conditions for the water height and the velocity. We compare these to the ones for a class of scalar nonlinear wave equations for which the angle plays no role.
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Non-linear diffusion of cosmic rays escaping from supernova remnants I: the effect of neutrals
Nava, Lara; Marcowith, Alexandre; Morlino, Giovanni; Ptuskin, Vladimir S
2016-01-01
Supernova remnants are believed to be the main sources of galactic Cosmic Rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disk volume, where most supernovae explode, and are characterised by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that stream...
Non Linear Behaviour in Learning Processes
Manfredi, Paolo; Manfredi, Vicenzo Rosario
2003-01-01
This article is mainly based on R. E. Kahn's contribution to the book Non Linear Dynamics in Human Behavior. As stressed by Bronowski, both in art and in science, a person becomes creative by finding "a new unity" that is a link between things which were not thought alike before. Indeed the creative mind is a mind that looks for unexpected likeness finding a more profound unity, a pattern behind chaotic phenomena. In the context of scientific discovery, it can also be argued that creativi...
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Limits on Non-Linear Electrodynamics
Fouché, M; Rizzo, C
2016-01-01
In this paper we set a framework in which experiments whose goal is to test QED predictions can be used in a more general way to test non-linear electrodynamics (NLED) which contains low-energy QED as a special case. We review some of these experiments and we establish limits on the different free parameters by generalizing QED predictions in the framework of NLED. We finally discuss the implications of these limits on bound systems and isolated charged particles for which QED has been widely and successfully tested.
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
Identification of parameters in amplitude equations describing coupled wakes
Fullana, J M; Zaleski, S; Le Gal, P; Fullana, Jose Maria; Rossi, Maurice; Zaleski, Stephane; Le Gal, Patrice
1996-01-01
We study the flow behind an array of equally spaced parallel cylinders. A system of Stuart-Landau equations with complex parameters is used to model the oscillating wakes. Our purpose is to identify the 6 scalar parameters which most accurately reproduce the experimental data of Chauve and Le Gal [{Physica D {\\bf 58}}, pp 407--413, (1992)]. To do so, we perform a computational search for the minimum of a distance \\calj. We define \\calj as the sum-square difference of the data and amplitudes reconstructed using coupled equations. The search algorithm is made more efficient through the use of a partially analytical expression for the gradient \
A Non-linear Stochastic Model for an Office Building with Air Infiltration
DEFF Research Database (Denmark)
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model param...... heat load reduction during peak load hours, control of indoor air temperature and for generating forecasts of power consumption from space heating....
Global non-linear effect of temperature on economic production.
Burke, Marshall; Hsiang, Solomon M; Miguel, Edward
2015-11-12
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Global non-linear effect of temperature on economic production
Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward
2015-11-01
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe;
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...
Non-linear absorption for concentrated solar energy transport
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, O. A; Del Rio, J.A; Huelsz, G [Centro de Investigacion de Energia, UNAM, Temixco, Morelos (Mexico)
2000-07-01
In order to determine the maximum solar energy that can be transported using SiO{sub 2} optical fibers, analysis of non-linear absorption is required. In this work, we model the interaction between solar radiation and the SiO{sub 2} optical fiber core to determine the dependence of the absorption of the radioactive intensity. Using Maxwell's equations we obtain the relation between the refractive index and the electric susceptibility up to second order in terms of the electric field intensity. This is not enough to obtain an explicit expression for the non-linear absorption. Thus, to obtain the non-linear optical response, we develop a microscopic model of an harmonic driven oscillators with damp ing, based on the Drude-Lorentz theory. We solve this model using experimental information for the SiO{sub 2} optical fiber, and we determine the frequency-dependence of the non-linear absorption and the non-linear extinction of SiO{sub 2} optical fibers. Our results estimate that the average value over the solar spectrum for the non-linear extinction coefficient for SiO{sub 2} is k{sub 2}=10{sup -}29m{sup 2}V{sup -}2. With this result we conclude that the non-linear part of the absorption coefficient of SiO{sub 2} optical fibers during the transport of concentrated solar energy achieved by a circular concentrator is negligible, and therefore the use of optical fibers for solar applications is an actual option. [Spanish] Con el objeto de determinar la maxima energia solar que puede transportarse usando fibras opticas de SiO{sub 2} se requiere el analisis de absorcion no linear. En este trabajo modelamos la interaccion entre la radiacion solar y el nucleo de la fibra optica de SiO{sub 2} para determinar la dependencia de la absorcion de la intensidad radioactiva. Mediante el uso de las ecuaciones de Maxwell obtenemos la relacion entre el indice de refraccion y la susceptibilidad electrica hasta el segundo orden en terminos de intensidad del campo electrico. Esto no es
Non-Linear Dynamics of Saturn’s Rings
Esposito, Larry W.
2015-11-01
Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects
Existence of a coupled system of fractional differential equations
Energy Technology Data Exchange (ETDEWEB)
Ibrahim, Rabha W. [Multimedia unit, Department of Computer System and Technology Faculty of Computer Science & IT, University of Malaya, 50603 Kuala Lumpur (Malaysia); Siri, Zailan [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-10-22
We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.
Analytic Solution of Strongly Coupling Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
LIAO Jin-Feng; ZHUANG Peng-Fei
2004-01-01
A recently developed expansion method for analytically solving the ground states of strongly coupling Schrodinger equations by Friedberg,Lee,and Zhao is extended to excited states and applied to power-law central forces for which scaling properties are proposed.As examples for application of the extended method,the Hydrogen atom problem is resolved and the low-lying states of Yukawa potential are approximately obtained.
Global Solutions to the Coupled Chemotaxis-Fluid Equations
Duan, Renjun
2010-08-10
In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the Chemotaxis-Navier-Stokes system over three space dimensions, we obtain global existence and rates of convergence on classical solutions near constant states. When the fluid motion is described by the simpler Stokes equations, we prove global existence of weak solutions in two space dimensions for cell density with finite mass, first-order spatial moment and entropy provided that the external forcing is weak or the substrate concentration is small. © Taylor & Francis Group, LLC.
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Application of non-linear discretetime feedback regulators with assignable closed-loop dynamics
Directory of Open Access Journals (Sweden)
Dubljević Stevan
2003-01-01
Full Text Available In the present work the application of a new approach is demonstrated to a discrete-time state feedback regulator synthesis with feedback linearization and pole-placement for non-linear discrete-time systems. Under the simultaneous implementation of a non-linear coordinate transformation and a non-linear state feedback law computed through the solution of a system of non-linear functional equations, both the feedback linearization and pole-placement design objectives were accomplished. The non-linear state feedback regulator synthesis method was applied to a continuous stirred tank reactor (CSTR under non-isothermal operating conditions that exhibits steady-state multiplicity. The control objective was to regulate the reactor at the middle unstable steady state by manipulating the rate of input heat in the reactor. Simulation studies were performed to evaluate the performance of the proposed non-linear state feedback regulator, as it was shown a non-linear state feedback regulator clearly outperformed a standard linear one, especially in the presence of adverse disturbance under which linear regulation at the unstable steady state was not feasible.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time
Norman, M. R.
2013-12-01
derivatives to time and space-time derivatives, given a set of known spatial derivatives, one can use DTs analytically compute time and space-time derivatives cheaply. Then, integrating directly in time over these space-time expansions of the PDE terms creates a time discretization method of the same philosophy as ADER methods but with significantly less expense than the explicit Cauchy-Kowalewski procedure, which can be exponential in complexity with respect to temporal order of accuracy. Because DTs compute mixed-dimension spatial derivatives and mixed space-time derivatives, over a single time step, all terms of the PDE are fully coupled to arbitrarily high-order accuracy in all spatial dimensions and time over a time step. DT-based ADER time discretizations lead to fully coupled, non-linear, accurate time stepping without resorting to multiple stages such as Runge-Kutta methods. This is advantageous in massively parallel computing environments because communication frequency and volume are reduced, leading to greater parallel efficiency. Results in two and three dimensions for linear transport and non-linear compressible Euler equations will be presented as well as accuracy and timing measurements to assess the efficiency for atmospheric models of applying DTs at various levels within Finite-Volume and Finite-Element discretizations of the underlying PDEs.
Optimal non-linear health insurance.
Blomqvist, A
1997-06-01
Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Risks of non-linear climate change
Energy Technology Data Exchange (ETDEWEB)
Van Ham, J.; Van Beers, R.J.; Builtjes, P.J.H.; Koennen, G.P.; Oerlemans, J.; Roemer, M.G.M. [TNO-SCMO, Delft (Netherlands)
1995-12-31
Climate forcing as a result of increased concentrations of greenhouse gases has been primarily addressed as a problem of a possibly warmer climate. So far, such change has been obscured in observations, possibly as a result of natural climate variability and masking by aerosols. Consequently, projections of the effect of climate forcing have to be based on modelling, more specifically by applying Global Circulation Models GCMs. These GCMs do not cover all possible feedbacks; neither do they address all specific possible effects of climate forcing. The investigation reviews possible non-linear climate change which does not fall within the coverage of present GCMs. The review includes the potential relevance of changes in biogeochemical cycles, aerosol and cloud feedback, albedo instability, ice-flow instability, changes in the thermohaline circulation and changes resulting from stratospheric cooling. It is noted that these changes may have different time horizons. Three from the investigated issues provide indications for a possible non-linear change. On the decadal scale stratospheric cooling, which is the result of the enhanced greenhouse effect, in combination with a depleted ozone layer, could provide a positive feedback to further ozone depletion, in particular in the Arctic. Decreasing albedo on the Greenland ice sheet may enhance the runoff from this ice sheet significantly in case of warming on a timescale of a few centuries. Changes in ocean circulation in the North Atlantic could seasonally more than compensate a global warming of 3C in North-West Europe on a timescale of centuries to a millennium. 263 refs.
Multifrequency parametric resonance in a non-linear wave equation
Energy Technology Data Exchange (ETDEWEB)
Kolesov, Andrei Yu [Yaroslavl Demidov State University (Russian Federation); Rozov, Nikolai Kh [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
2002-12-31
We consider the boundary-value problem u{sub tt}+{epsilon}u{sub t}+(1+{epsilon}{sigma}{sub k=1}{sup m}{alpha}{sub k}cos 2{phi}{sub k})u = a{sup 2}u{sub xx}-u{sup 2}u{sub t}, u|{sub x=0}=u|{sub x={pi}}=0, where 0<{epsilon}<<1, a>0, {phi}{sub k}={sigma}{sub k}t+c{sub k}, k=1,...,m. We show that a suitable choice of a positive integer m and real parameters {alpha}{sub k}, {sigma}{sub k}, k=1,...,m, enables us to make this problem have any prescribed number of exponentially stable time-quasiperiodic solutions bifurcating from zero.
Recent topics in non-linear partial differential equations 4
Mimura, M
1989-01-01
This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
Directory of Open Access Journals (Sweden)
Carlos A Bustamante Chaverra
2013-03-01
Full Text Available Un método sin malla es desarrollado para solucionar una versión genérica de la ecuación no lineal de convección-difusión-reacción en dominios bidimensionales. El método de Interpolación Local Hermítica (LHI es empleado para la discretización espacial, y diferentes estrategias son implementadas para solucionar el sistema de ecuaciones no lineales resultante, entre estas iteración de Picard, método de Newton-Raphson y el Método de Homotopía truncado (HAM. En el método LHI las Funciones de Base Radial (RBFs son empleadas para construir una función de interpolación. A diferencia del Método de Kansa, el LHI es aplicado localmente y los operadores diferenciales de las condiciones de frontera y la ecuación gobernante son utilizados para construir la función de interpolación, obteniéndose una matriz de colocación simétrica. El método de Newton-Rapshon se implementa con matriz Jacobiana analítica y numérica, y las derivadas de la ecuación gobernante con respecto al paramétro de homotopía son obtenidas analíticamente. El esquema numérico es veriﬁcado mediante la comparación de resultados con las soluciones analíticas de las ecuaciones de Burgers en una dimensión y Richards en dos dimensiones. Similares resultados son obtenidos para todos los solucionadores que se probaron, pero mejores ratas de convergencia son logradas con el método de Newton-Raphson en doble iteración.A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diﬀusion-reaction equation in two-dim-ensional domains. The Local Hermitian Interpolation (LHI method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM. The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Directory of Open Access Journals (Sweden)
Kishan N.
2014-05-01
Full Text Available A fluid flow and heat transfer analysis of an electrically conducting non-Newtonian power law fluid flowing over a non-linear stretching surface in the presence of a transverse magnetic field taking into consideration viscous dissipation effects is investigated. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. By using quasi-linearization techniques first linearize the non linear momentum equation is linearized and then the coupled ordinary differential equations are solved numerically by an implicit finite difference scheme. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, Eckert number, velocity exponent parameter, temperature exponent parameter, modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed.
Hoelzl, M.; Huijsmans, G. T. A.; Merkel, P.; Atanasiu, C.; Lackner, K.; Nardon, E.; Aleynikova, K.; Liu, F.; Strumberger, E.; McAdams, R.; Chapman, I.; Fil, A.
2014-11-01
The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.
The Linear-Non-Linear Frontier for the Goldstone Higgs
Energy Technology Data Exchange (ETDEWEB)
Gavela, M. B. [Madrid, IFT; Kanshin, K. [Padua U.; Machado, P. A.N. [Madrid, IFT; Saa, S. [Madrid, IFT
2016-10-25
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.
Left-Right Non-Linear Dynamical Higgs
Shu, Jing; Yepes, Juan
2016-12-01
All the possible CP-conserving non-linear operators up to the p4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)L × SU(2)R × U(1)B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators. J. Y. also acknowledges KITPC financial support during the completion of this work
Reconstructing the dark energy equation of state with varying couplings
Pina-Avelino, P; Nunes, N J; Olive, Keith A
2006-01-01
We revisit the idea of using varying couplings to probe the nature of dark energy, in particular by reconstructing its equation of state. We show that this method can be far superior to the standard methods (using type Ia supernovae or weak lensing). We also show that the simultaneous use of measurements of the fine-structure constant $\\alpha$ and the electron-to-proton mass ratio $\\mu$ allows a direct probe of grand unification scenarios. We present forecasts for the sensitivity of this method, both for the near future and for the next generation of spectrographs -- for the latter we focus on the planned CODEX instrument for ESO's Extremely Large Telescope (formerly known as OWL). A high-accuracy reconstruction of the equation of state may be possible all the way up to redshift $z\\sim4$.
Non-linear time series analysis: methods and applications to atrial fibrillation.
Hoekstra, B P; Diks, C G; Allessie, M A; Degoede, J
2001-01-01
We apply methods from non-linear statistical time series analysis to characterize electrograms of atrial fibrillation. These are based on concepts originating from the theory of non-linear dynamical systems and use the empirical reconstruction density in reconstructed phase space. Application of these methods is not restricted to deterministic chaos but is valid in a general time series context. We illustrate this by applying three recently proposed non-linear time series methods to fibrillation electrograms: 1) a test for time reversibility in atrial electrograms during paroxysmal atrial fibrillation in patients; 2) a test to detect differences in the dynamical behaviour during the pharmacological conversion of sustained atrial fibrillation in instrumented conscious goats; 3) a test for general Granger causality to identify couplings and information transport in the atria during fibrillation. We conclude that a characterization of the dynamics via the reconstruction density offers a useful framework for the non-linear analysis of electrograms of atrial fibrillation.
Estimations of non-linearities in structural vibrations of string musical instruments
Ege, Kerem; Boutillon, Xavier
2012-01-01
Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies, we characterise weak non-linearities by a signal-model approach based on cascade of Hammerstein models. In this approach, in a chain of two non-linear systems, two measurements are sufficient to estimate the non-linear contribution of the second (sub-)system which cannot be directly linearly driven, as a function of the exciting frequency. The experiment consists in exciting the instrument acoustically. The linear and non-linear contributions to the response of (a) the loudspeaker coupled to the room, (b) the instrument can be separated. Some methodological issues will be discussed. Findings pertaining to several instruments - one piano, two guitars, one violin - will be presented.
Two-component coupled KdV equations and its connection with the generalized Harry Dym equations
Energy Technology Data Exchange (ETDEWEB)
Popowicz, Ziemowit, E-mail: ziemek@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wrocław, Wrocław pl. M. Borna 9, 50-205 Wrocław (Poland)
2014-01-15
It is shown that three different Lax operators in the Dym hierarchy produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component Korteweg de Vries (KdV) system. The first equation gives us known integrable two-component KdV system, while the second reduces to the known symmetrical two-component KdV equation. The last one reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax representation for these equations.
Two-component coupled KdV equations and its connection with the generalized Harry Dym equations
Popowicz, Ziemowit
2014-01-01
It is shown that three different Lax operators in the Dym hierarchy produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component Korteweg de Vries (KdV) system. The first equation gives us known integrable two-component KdV system, while the second reduces to the known symmetrical two-component KdV equation. The last one reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax representation for these equations.
Analytical solutions of coupled-mode equations for microring resonators
Indian Academy of Sciences (India)
ZHAO C Y
2016-06-01
We present a study on analytical solutions of coupled-mode equations for microring resonators with an emphasis on occurrence of all-optical EIT phenomenon, obtained by using a cofactor. As concrete examples, analytical solutions for a $3 \\times 3$ linearly distributed coupler and a circularly distributed coupler are obtained. The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a $4 \\times 4$ linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics communities.
General Electromagnetic Nonminimal Couplings in the Dirac Equation
Araujo, J B; Ferreira, M M
2016-01-01
We examine a new class of CPT-even and dimension-five nonminimal interactions between fermions and photons, deprived of higher-order derivatives, yielding electric dipole moment and magnetic dipole moment in the context of the Dirac equation. These couplings are Lorentz-violating nonminimal structures, composed of a rank-2 tensor, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial hermitian versions. We use the electron's anomalous magnetic and electric dipole moment measurements to reach upper bounds of $1$ part in $10^{11}$ and $10^{16}$ GeV$^{-1}$.
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Automatic derivation and evaluation of vibrational coupled cluster theory equations
Seidler, Peter; Christiansen, Ove
2009-12-01
A scheme for automatic derivation and evaluation of the expressions occurring in vibrational coupled cluster theory is introduced. The method is based on a Baker-Campbell-Hausdorff expansion of the similarity transformed Hamiltonian and is general both with respect to the excitation level in the parameter space and the mode coupling level in the Hamiltonian. In addition to deriving general expressions, intermediates that lower the computational scaling are automatically detected. The final equations are then evaluated. Due to the commutator based nature of the algorithm, it is also applicable to the evaluation of quantities needed for response theory. Different aspects of the theory and implementation are illustrated by calculations on model systems. Furthermore, all fundamental excitation energies of ethylene oxide are calculated.
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Nicolae–Doru Stănescu
2010-01-01
In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of...
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Directory of Open Access Journals (Sweden)
Nicolae–Doru Stănescu
2010-01-01
Full Text Available In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of the motion. Finally a numerical application is presented.
New holographic dark energy model with non-linear interaction
Oliveros, A
2014-01-01
In this paper the cosmological evolution of a holographic dark energy model with a non-linear interaction between the dark energy and dark matter components in a FRW type flat universe is analysed. In this context, the deceleration parameter $q$ and the equation state $w_{\\Lambda}$ are obtained. We found that, as the square of the speed of sound remains positive, the model is stable under perturbations since early times; it also shows that the evolution of the matter and dark energy densities are of the same order for a long period of time, avoiding the so--called coincidence problem. We have also made the correspondence of the model with the dark energy densities and pressures for the quintessence and tachyon fields. From this correspondence we have reconstructed the potential of scalar fields and their dynamics.
Non-linear Kalman filters for calibration in radio interferometry
Tasse, Cyril
2014-01-01
We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly cheap algorithm that we believe to be robust, especially in low signal-to-noise regime. Potentially the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visib...
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We consider a $d$-dimensional random field $u = \\{u(t,x)\\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \\in \\{1,2,3\\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
Black Hole Hair Removal: Non-linear Analysis
Jatkar, Dileep P; Srivastava, Yogesh K
2009-01-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, -- degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Black hole hair removal: non-linear analysis
Jatkar, Dileep P.; Sen, Ashoke; Srivastava, Yogesh K.
2010-02-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, — degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Non-Linear Electrohydrodynamics in Microfluidic Devices
Directory of Open Access Journals (Sweden)
Jun Zeng
2011-03-01
Full Text Available Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications.
Hayes, E. F.; Kouri, D. J.
1971-01-01
Coupled integral equations are derived for the full scattering amplitudes for both reactive and nonreactive channels. The equations do not involve any partial wave expansion and are obtained using channel operators for reactive and nonreactive collisions. These coupled integral equations are similar in nature to equations derived for purely nonreactive collisions of structureless particles. Using numerical quadrature techniques, these equations may be reduced to simultaneous algebraic equations which may then be solved.
Computational models of signalling networks for non-linear control.
Fuente, Luis A; Lones, Michael A; Turner, Alexander P; Stepney, Susan; Caves, Leo S; Tyrrell, Andy M
2013-05-01
Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.
A Collocation Method for Numerical Solutions of Coupled Burgers' Equations
Mittal, R. C.; Tripathi, A.
2014-09-01
In this paper, we propose a collocation-based numerical scheme to obtain approximate solutions of coupled Burgers' equations. The scheme employs collocation of modified cubic B-spline functions. We have used modified cubic B-spline functions for unknown dependent variables u, v, and their derivatives w.r.t. space variable x. Collocation forms of the partial differential equations result in systems of first-order ordinary differential equations (ODEs). In this scheme, we did not use any transformation or linearization method to handle nonlinearity. The obtained system of ODEs has been solved by strong stability preserving the Runge-Kutta method. The proposed scheme needs less storage space and execution time. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed scheme. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. The scheme is simple as well as easy to implement. The scheme provides approximate solutions not only at the grid points, but also at any point in the solution range.
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations
Directory of Open Access Journals (Sweden)
A. R. Seadawy
2014-01-01
Full Text Available An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.
Water wave solutions of the coupled system Zakharov-Kuznetsov and generalized coupled KdV equations.
Seadawy, A R; El-Rashidy, K
2014-01-01
An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.
Energy Technology Data Exchange (ETDEWEB)
Russell, Steven J. [Los Alamos National Laboratory; Carlsten, Bruce E. [Los Alamos National Laboratory
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
Non-linear model for compression tests on articular cartilage.
Grillo, Alfio; Guaily, Amr; Giverso, Chiara; Federico, Salvatore
2015-07-01
Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.
Coupled Nonlinear Schr(o)dinger Equations and the Miura Transformation
Institute of Scientific and Technical Information of China (English)
LOU Yan; ZHU Jun-Yi
2011-01-01
@@ A wide class of coupled nonlinear Schr?dinger(NLS)equations are derived by virtue of the dressing method,and the associated parametric solutions are discussed.As an illustration,the explicit solution of the coupled NLS-type equation associated with σ1 is given.The Miura transformation for a AKNS-type hierarchy is established,from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.%A wide class of coupled nonlinear Schrodinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with O\\ is given. The Miura transformation for a AKNS-type hierarchy is established, from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
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.
Solution of QCD⊗QED coupled DGLAP equations at NLO
Zarrin, S.; Boroun, G. R.
2017-09-01
In this work, we present an analytical solution for QCD⊗QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in perturbative QCD using double Laplace transform. This technique is applied to obtain the singlet, gluon and photon distribution functions and also the proton structure function. We also obtain contribution of photon in proton at LO and NLO at high energy and successfully compare the proton structure function with HERA data [1] and APFEL results [2]. Some comparisons also have been done for the singlet and gluon distribution functions with the MSTW results [3]. In addition, the contribution of photon distribution function inside the proton has been compared with results of MRST [4] and with the contribution of sea quark distribution functions which obtained by MSTW [3] and CTEQ6M [5].
Solution of QCD$\\otimes$QED coupled DGLAP equations
Zarrin, S
2016-01-01
In this work, we present an analytical solution for QCD$\\otimes$QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order accuracy using double Laplace transform. This technique is applied to obtain the singlet, gluon and photon distribution functions and also the proton structure function. We successfully compare the proton structure function with HERA data \\cite{12} and APFEL results \\cite{7}. Some comparisons also have been done for the singlet and gluon distribution functions with the MSTW results\\cite{9}. In addition, the contribution of photon distribution function inside the proton has been compared with results of MRST \\cite{11} and with the contribution of sea quark distribution functions which obtained by MSTW \\cite{9} and CTEQ6M \\cite{14}.
Landau-Lifhsitz-Bloch equation for exchange coupled grains
Vogler, Christoph; Bruckner, Florian; Suess, Dieter
2014-01-01
Heat assisted recording is a promising technique to further increase the storage density in hard disks. Multilayer recording grains with graded Curie temperature is discussed to further assist the write process. Describing the correct magnetization dynamics of these grains, from room temperature to far above the Curie point, during a write process is required for the calculation of bit error rates. We present a coarse grained approach based on the Landau-Lifshitz-Bloch (LLB) equation to model exchange coupled grains with low computational effort. The required temperature dependent material properties such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities are obtained by atomistic Landau-Lifshitz-Gilbert (LLB) simulations. Each grain is described with one magnetization vector. In order to mimic the atomistic exchange interaction between the grains a special treatment of the exchange field in the coarse grained approach is presented.
Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito
2017-08-01
A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representaton. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation...
A variational model for fully non-linear water waves of Boussinesq type
Klopman, Gert; Dingemans, Maarten W.; Groesen, van Brenny; Grue, J.
2005-01-01
Using a variational principle and a parabolic approximation to the vertical structure of the velocity potential, the equations of motion for surface gravity waves over mildly sloping bathymetry are derived. No approximations are made concerning the non-linearity of the waves. The resulting model equ
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Response of Non-Linear Systems to Renewal Impulses by Path Integration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Iwankiewicz, R.
The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... additional discrete-valued state variables for which the stochastic equations are also formulated....
Non-Linear Unit Root Properties of Crude Oil Production
Svetlana Maslyuk; Russell Smyth
2007-01-01
While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as permanent stochastic disturbances. The objective of this paper is to test for non-linearities and un...
Papas, Brian N; Schuurman, Michael S; Yarkony, David R
2008-09-28
A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.
Experiments with Geometric Non-Linear Coupling for Analytical Validation
2010-03-01
presented by Hartog . [11] The critical load before buckling in a simple cantilevered beam is calculated using: Pcr = 4.01 Eℎt3 6l2 √ 1 2 (1 + ) (3.1) where...Loads. Master’s thesis, Air Force Institute of Technologies, Jun 2009. 11. Hartog , J.P. Advanced Strength of Materials. McGraw-Hill Book Company, Inc
Non-linear Constitutive Model for the Oligocarbonate Polyurethane Material
Institute of Scientific and Technical Information of China (English)
Marek Pawlikowski
2014-01-01
The polyurethane,which was the subject of the constitutive research presented in the paper,was based on oligocarbonate diols Desmophen C2100 produced by Bayer@.The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses.The polyurethane was assumed to be non-linearly viscohyperelastic,isotropic and incompressible.The constitutive equation was derived from the postulated strain energy function.The elastic and rheological constants were identified on the basis of experimental tests,i.e.relaxation tests and monotonic uniaxial tests at two different strain rates,i.e.λ =0.1 min-1 and λ =1.0 min-1.The stiffness tensor was derived and introduced to Abaqus@finite element (FE) software in order to numerically validate the constitutive model.The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material.
Energy Technology Data Exchange (ETDEWEB)
Mvogo, Alain, E-mail: mvogal_2009@yahoo.fr [Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Ben-Bolie, G.H., E-mail: gbenbolie@yahoo.fr [Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); Kofané, T.C., E-mail: tckofane@yahoo.com [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); The Abdus Salam International Center for Theoretical Physics, P.O. Box 586, Strada Costiera 11, I-34014 Trieste (Italy)
2014-07-04
An improved quantum model for exciton–phonon dynamics in an α-helix is investigated taking into account the interspine coupling and the influence of power-law long-range exciton–exciton interactions. Having constructed the model Hamiltonian, we derive the lattice equations and employ the Fourier transforms to go in continuum space showing that the long-range interactions (LRI) lead to a nonlocal integral term in the equations of motion. Indeed, the non-locality originating from the LRI results in the dynamic equations with space derivatives of fractional order. New theoretical frameworks are derived, such that: fractional generalization of coupled Zakharov equations, coupled nonlinear fractional Schrödinger equations, coupled fractional Ginzburg–Landau equations, coupled Hilbert–Zakharov equations, coupled nonlinear Hilbert–Ginzburg–Landau equations, coupled nonlinear Schrödinger equations and coupled nonlinear Hilbert–Schrödinger equations. Through the F-expansion method, we derive a set of exact Jacobian solutions of coupled nonlinear Schrödinger equations. These solutions include Jacobian periodic solutions as well as bright and dark soliton which are important in the process of energy transport in the molecule. We also discuss of the impact of LRI on the energy transport in the molecule.
Savović, Svetislav; Djordjevich, Alexandar
2002-05-20
The power-flow equation is approximated by the Fokker-Planck equation that is further transformed into a stochastic differential (Langevin) equation, resulting in an efficient method for the estimation of the state of mode coupling along step-index optical fibers caused by their intrinsic perturbation effects. The inherently stochastic nature of these effects is thus fully recognized mathematically. The numerical integration is based on the computer-simulated Langevin force. The solution matches the solution of the power-flow equation reported previously. Conceptually important steps of this work include (i) the expression of the power-flow equation in a form of the diffusion equation that is known to represent the solution of the stochastic differential equation describing processes with random perturbations and (ii) the recognition that mode coupling in multimode optical fibers is caused by random perturbations.
A Non-linear Stochastic Model for an Office Building with Air Infiltration
DEFF Research Database (Denmark)
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...... parameters are estimated using a maximum likelihood technique. Based on the maximum likelihood value, the different models are statistically compared to each other using Wilk's likelihood ratio test. The model showing the best performance is finally verified in both the time domain and the frequency domain...
General treatment of the non-linear Rsub(Xi) gauge condition
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Malleville, C.; Sorba, P. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1982-11-04
It is shown that the non-linear Rsub(xi) gauge condition already introduced for the standard SU(2)xU(1) model can be generalized for any gauge model with the same type of simplification, namely the suppression of any coupling of the form: (massless gauge boson)x(massive gauge boson)x(unphysical Higgs).
Non-linear dynamics in photochemistry
Pimienta, V.; Lévy, G.; Lavabre, D.; Laplante, J. P.; Micheau, J. C.
1992-09-01
The rate law of an elementary photochemical reaction: A → B ( hv), contains 4 independent factors: the quantum yield, the photon flux, the concentration of the photosensitive substrate and the photokinetic factor. This type of reaction will always slow down. However, by increasing one of these 4 factors artificially, the reaction can be made to speed up. Using kinetic models comprising one or more photochemical reactions, we show that appropriate coupling between two or more elementary processes gives rise to a cooperative effect. This effect increases one or more of these 4 factors, and makes the coupled photochemical model bistable in a CSTR. The values of the parameters for which one observes bistability are experimentally realistic. One of these models provides a simplified simulation of the stages underlying the bistable photochemical behavior of the TPID/CHCl 3, system.
Singular solitons and other solutions to a couple of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
Directory of Open Access Journals (Sweden)
Jincun Liu
2013-01-01
Full Text Available By introducing the fractional derivative in the sense of Caputo and combining the pretreatment technique to deal with long nonlinear items, the generalized two-dimensional differential transform method is proposed for solving the time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equation. The presented method is a numerical method based on the generalized Taylor series expansion which constructs an analytical solution in the form of a polynomial. The numerical results show that the generalized two-dimensional differential transform method is very effective for the fractional coupled equations.
Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
Directory of Open Access Journals (Sweden)
Andrea Quadri
2014-04-01
Full Text Available We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE encoding the invariance of the SU(2 Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI amplitudes (both on-shell and off-shell can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed.
Graphical and Analytical Analysis of the Non-Linear PLL
de Boer, Bjorn; Radovanovic, S.; Annema, Anne J.; Nauta, Bram
The fixed width control pulses from the Bang-Bang Phase Detector in non-linear PLLs allow for operation at higher data rates than the linear PLL. The high non-linearity of the Bang- Bang Phase Detector gives rise to unwanted effects, such as limit-cycles, not yet fully described. This paper
Non-linear stochastic response of a shallow cable
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2004-01-01
The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two-degrees-of-freedom...
Non-linear Frequency Scaling Algorithm for FMCW SAR Data
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran
Non Linear Gauge Fixing for FeynArts
Gajdosik, Thomas
2007-01-01
We review the non-linear gauge-fixing for the Standard Model, proposed by F. Boudjema and E. Chopin, and present our implementation of this non-linear gauge-fixing to the Standard Model and to the minimal supersymmetric Standard Model in FeynArts.
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Non-Linearly Interacting Ghost Dark Energy in Brans-Dicke Cosmology
Ebrahimi, E
2016-01-01
In this paper we extend the form of interaction term into the non-linear regime in the ghost dark energy model. A general form of non-linear interaction term is presented and cosmic dynamic equations are obtained. Next, the model is detailed for two special choice of the non-linear interaction term. According to this the universe transits at suitable time ($z\\sim 0.8$) from deceleration to acceleration phase which alleviate the coincidence problem. Squared sound speed analysis revealed that for one class of non-linear interaction term $v_s^2$ can gets positive. This point is an impact of the non-linear interaction term and we never find such behavior in non interacting and linearly interacting ghost dark energy models. Also statefinder parameters are introduced for this model and we found that for one class the model meets the $\\Lambda CDM$ while in the second choice although the model approaches the $\\Lambda CDM$ but never touch that.
New Complexiton Solutions of the KdV and Coupled KdV Equations
Pekcan, Aslı
2016-01-01
A new approach to double-sub equation method is introduced to construct novel solutions for the nonlinear partial differential equations. It is applied to the Korteweg-de Vries (KdV) equation and yields new complexiton solutions of both the KdV and coupled KdV equations. The graphs of the solutions are also illustrated.
Formulating Weak Lensing from the Boltzmann Equation and Application to Lens-lens Couplings
Su, S -C
2014-01-01
The Planck mission has conclusively detected lensing of the Cosmic Microwave Background (CMB) radiation from foreground sources to an overall significance of greater than $25\\sigma$. The high precision of this measurement motivates the development of a more complete formulation of the calculation of this effect. While most effects on the CMB anisotropies are widely studied through direct solutions of the Boltzmann equation, the non-linear effect of CMB lensing is formulated through the solutions of the geodesic equation. In this paper, we present a new formalism to the calculation of the lensing effect by \\emph{directly solving the Boltzmann equation}, as we did in the calculation of the CMB anisotropies at recombination. In particular, we developed a diagrammatic approach to efficiently keep track of all the interaction terms and calculate all possible non-trivial correlations to arbitrary high orders. Using this formalism, we explicitly articulate the approximations required to recover the usual remapping a...
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Non-linear dielectric monitoring of biological suspensions
Energy Technology Data Exchange (ETDEWEB)
Treo, E F; Felice, C J [Departamento de BioingenierIa, Universidad Nacional de Tucuman and Consejo Nacional de Investigaciones Cientificas y Tecnicas. CC327, CP4000, San Miguel de Tucuman (Argentina)
2007-11-15
Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response.
Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation.
Geng, Xianguo; Ren, Hongfeng; He, Guoliang
2009-05-01
A Darboux transformation for the generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation is derived with the aid of the gauge transformation between the corresponding 4x4 matrix spectral problems with three potentials, by which some explicit solutions of the generalized Hirota-Satsuma coupled KdV equation are constructed. As a reduction, a Darboux transformation of the complex coupled KdV equation and its explicit solutions are obtained.
Raslan, K. R.; EL-Danaf, Talaat S.; Ali, Khalid K.
2017-07-01
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.
Non-linear controls on the persistence of La Nina
Di Nezio, P. N.; Deser, C.
2013-12-01
Non-linear controls on the persistence of La Nina Pedro DiNezio and Clara Deser Up to half of the observed La Nina events last for two years or more. Most El Nino events, in contrast, last no longer than one year. The physical processes causing this asymmetry in the duration of warm and cold ENSO events is unknown. The persistence of La Nina, not only exacerbates the climate impacts, especially in regions prone to drought, but also is highly unpredictable. In this talk we will explore the nonlinear processes that generate the persistence of La Nina in observations and in CCSM4 - a coupled climate model that simulates this feature realistically. First, we develop a non-linear delayed-oscillator model (nonlinDO) based on CCSM4's heat budget. All positive and negative feedbacks of nonlinDO capture the nonlinear and seasonal dependence exhibited by CCSM4. The nonlinear behavior is due to: 1) weaker atmospheric damping of cold events with respect to warm events, 2) stronger wind response for large warm events, and 3) weaker coupling between thermocline and sea-surface temperature anomalies when the thermocline deepens. We force the simple model with white Gaussian noise resulting in seasonal modulation of variance and skewness, and a spectral peak, that are in agreement with CCSM4. Sensitivity experiments with nonlinDO show that the thermocline nonlinearity (3) is the sole process controlling the duration of La Nina events. Linear ENSO theory indicates that La Nina events drive a delayed thermocline deepening that leads to their demise. However, the thermocline nonlinearity (3) renders this response ineffective as La Nina events become stronger. This diminishing of the delayed-thermocline feedback prevents the equatorial Pacific from returning to neutral or warm conditions and cold conditions persist for a second year. Observations show evidence for this thermocline nonlinearity suggesting that this process could be at work in the real world. Last, we show evidence that
Non-linear simulations of ELMs in ASDEX Upgrade including diamagnetic drift effects
Energy Technology Data Exchange (ETDEWEB)
Lessig, Alexander; Hoelzl, Matthias; Krebs, Isabel; Franck, Emmanuel; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstrasse 2, 85748 Garching (Germany); Orain, Francois; Morales, Jorge; Becoulet, Marina [CEA-IRFM, Cadarache, 13108 Saint-Paul-Lez-Durance (France); Huysmans, Guido [ITER Organization, 13067 Saint-Paul-Lez-Durance (France)
2015-05-01
Large edge localized modes (ELMs) are a severe concern for ITER due to high transient heat loads on divertor targets and wall structures. Using the non-linear MHD code JOREK, we have performed ELM simulations for ASDEX Upgrade (AUG) including diamagnetic drift effects. The influence of diamagnetic terms onto the evolution of the toroidal mode spectrum for different AUG equilibria and the non-linear interaction of the toroidal harmonics are investigated. In particular, we confirm the diamagnetic stabilization of high mode numbers and present new features of a previously introduced quadratic mode coupling model for the early non-linear evolution of the mode structure. Preliminary comparisons of full ELM crashes with experimental observations are shown aiming at code validation and the understanding of different ELM types. Work is ongoing to include toroidal and neoclassical poloidal rotation in our simulations.
A Comparison Theorem for Solution of the Fully Coupled Backward Stochastic Differential Equations
Institute of Scientific and Technical Information of China (English)
郭子君; 吴让泉
2004-01-01
The comparison theorems of solutions for BSDEs in fully coupled forward-backward stochastic differential equations (FBSDEs) are studied in this paper, here in the fully coupled FBSDEs the forward SDEs are the same structure.
Directory of Open Access Journals (Sweden)
A. D. Pataraya
Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.
Fem Formulation of Coupled Partial Differential Equations for Heat Transfer
Ameer Ahamad, N.; Soudagar, Manzoor Elahi M.; Kamangar, Sarfaraz; Anjum Badruddin, Irfan
2017-08-01
Heat Transfer in any field plays an important role for transfer of energy from one region to another region. The heat transfer in porous medium can be simulated with the help of two partial differential equations. These equations need an alternate and relatively easy method due to complexity of the phenomenon involved. This article is dedicated to discuss the finite element formulation of heat transfer in porous medium in Cartesian coordinates. A triangular element is considered to discretize the governing partial differential equations and matrix equations are developed for 3 nodes of element. Iterative approach is used for the two sets of matrix equations involved representing two partial differential equations.
A conformal approach for the analysis of the non-linear stability of radiation cosmologies
Energy Technology Data Exchange (ETDEWEB)
Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Department of Mathematics, University of Leicester, University Road, LE1 8RH (United Kingdom); Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)
2013-01-15
The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.
Non-linear vorticity upsurge in Burgers flow
Lam, F
2016-01-01
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers, are chosen for our computations. Most of the solutions are carried out well into the fully turbulent regime over finely-resolved scales in space and in time. It is found that an abrupt spatio-temporal concentration in shear constitutes an essential part during the flow evolution. The vorticity surge has been instigated by the non-linearity complying with instantaneous enstrophy production while ad hoc disturbances play no role in the process. In particular, the present method predicts the precipitous vorticity re-distribution and accumulation, predominantly over localised regions of minute dimension. The growth rate depends on viscosity and is a strong function of initial data. Nevertheless, the long-time energy decay is history-independent and is inversely proportional to ti...
Supersymmetry and the Dirac Equation with Vector and Scalar Coupling Potentials
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper shows that one type of first-order Dirac equation with vector coupling and scalar coupling potentials can be brought into the framework of non-relativistic supersymmetric quantum mechanics. The conclusion is independent of the concrete forms of the vector and scalar coupling potentials because of the nilpotent matrix realization of supersymmetric quantum mechanical algebra. The supersymmetry of this kind of Dirac equation requires that a spin-orbit coupling term be introduced into the associated supersymmetric Hamiltonian.
Non linear behaviour of cell tensegrity models
Alippi, A.; Bettucci, A.; Biagioni, A.; Conclusio, D.; D'Orazio, A.; Germano, M.; Passeri, D.
2012-05-01
Tensegrity models for the cytoskeleton structure of living cells is largely used nowadays for interpreting the biochemical response of living tissues to mechanical stresses. Microtubules, microfilaments and filaments are the microscopic cell counterparts of struts (microtubules) and cables (microfilaments and filaments) in the macroscopic world: the formers oppose to compression, the latters to tension, thus yielding an overall structure, light and highly deformable. Specific cell surface receptors, such as integrins, act as the coupling elements that transmit the outside mechanical stress state into the cell body. Reversible finite deformations of tensegrity structures have been widely demonstrated experimentally and in a number of living cell simulations. In the present paper, the bistability behaviour of two general models, the linear bar oscillator and the icosahedron, is studied, as they are both obtained from mathematical simulation, the former, and from larger scale experiments, the latter. The discontinuity in the frequency response of the oscillation amplitude and the lateral bending of the resonance curves are put in evidence, as it grows larger as the driving amplitude increases, respectively.
Cosmic neutrinos: dispersive and non-linear
Inman, Derek
2016-01-01
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By comparing with neutrino N-body simulations, we measure the small scale sound speed and find it to be lower than linear theory predictions. This allows for an explanation of the discrepency between N-body and linear response predictions for the neutrino power spectrum: neutrinos are still driven predominantly by the cold dark matter, but the sound speed on small scales is not stable to perturbations and decreases. Finally, w...
The late Universe with non-linear interaction in the dark sector: the coincidence problem
Bouhmadi-López, Mariam; Zhuk, Alexander
2016-01-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction $Q = 3\\mathcal{H}\\gamma \\overline\\varepsilon_{\\mathrm{DE}} \\overline\\varepsilon_{\\mathrm{DM}} / (\\overline\\varepsilon_{\\mathrm{DE}} + \\overline\\varepsilon_{\\mathrm{DM}})$, where $\\gamma$ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter $w$. In the considered model, the energy densities of the dark sector components present a scaling behaviour with $\\overline\\varepsilon_{\\mathrm{DM}} / \\overline\\varepsilon_{\\mathrm{DE}} \\sim \\left({a_0} / {a} \\right)^{-3(w+\\gamma)}$. We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the ...
Non-linear modulation of short wavelength compressional Alfven eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Bortolon, A. [University of California, Irvine, California 92697 (United States); Crocker, N. A. [University of California, Los Angeles, California 90095 (United States); Levinton, F. M.; Yuh, H. [Nova Photonics, Princeton, New Jersey 08543 (United States)
2013-04-15
Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Galiev, Sh. U.
2003-08-01
A non-linear theory of transresonant wave phenomena based on consideration of perturbed wave equations is presented. In particular, the waves in a surface layer of a porous compressible viscoelastoplastic material are considered. For such layers the 3-D equations of deformable media are reduced to 1-D or 2-D perturbed wave equations. A set of approximate, closed-form, general solutions of these equations are presented, which take into account non-linear, dissipative, dispersive, topographic and boundary effects. Then resonant, site and liquefaction effects are analysed. Resonance is considered as a global parameter. Transresonant evolution of the equations is studied. Within the resonant band, utt~a20∇2u and the perturbed wave equations transform into non-linear diffusion equations, either to a basic highly non-linear ordinary differential equation or to the basic algebraic equation for travelling waves. Resonances can destroy predictability and wave reversibility. Surface topography (valleys, islands, etc.) is considered as a series of earthquake-induced resonators. A non-linear transresonant evolution of smooth seismic waves into shock-, jet- and mushroom-like waves and vortices is studied. The amplitude of the resonant waves may be of the order of the square or cube root of the exciting amplitude. Therefore, seismic waves with a moderate amplitude can be amplified very strongly in natural resonators, whereas strong seismic waves can be attenuated. Reports of the 1835 February 20 Chilean earthquake given by Charles Darwin are qualitatively examined using the non-linear theory. The theory qualitatively describes the `shivering' of islands and ridges, volcano spouts and generation of tsunami-like waves and supports Darwin's opinion that these events were part of a single phenomenon. Same-day earthquake/eruption events and catastrophic amplification of seismic waves near the edge of sediment layers are discussed. At the same time the theory can account for recent
Bifurcation and Resonance of a Mathematical Model for Non-Linear Motion of a Flooded Ship in Waves
Murashige, S.; Aihara, K.; Komuro, M.
1999-02-01
A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-linear phenomenon, the non-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonant points and the bifurcation curves suggests that non-linear resonance of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonate state of the linearized system.
New Doubly Periodic Solutions for the Coupled Nonlinear Klein-Gordon Equations
Institute of Scientific and Technical Information of China (English)
LIU Chun-Ping
2005-01-01
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
Uniform stability of displacement coupled second-order equations
Directory of Open Access Journals (Sweden)
Abdelaziz Soufyane
2001-04-01
Full Text Available We prove that the uniform stability of semigroups associated to displacement coupled dissipator systems is equivalent to the uniform stability of velocity coupled dissipator systems. Using this equivalence, we give sufficient conditions for obtaining uniform stability and exact controllability of displacement coupled dissipator systems.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
Byrd, Jason N.; Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.
2015-10-01
A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
Uniqueness of non-linear ground states for fractional Laplacians in R
DEFF Research Database (Denmark)
Frank, Rupert L.; Lenzmann, Enno
2013-01-01
We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 ... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... Benjamin–Ono (BO) and Benjamin–Bona–Mahony (BBM) water wave equations....
New iterative method for fractional gas dynamics and coupled Burger's equations.
Al-Luhaibi, Mohamed S
2015-01-01
This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger's equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
A Difference Scheme for the Coupled KdV Equation 14
Institute of Scientific and Technical Information of China (English)
ShaohongZHU
1999-01-01
In this paper,a difference scheme for the periodic initial-boundary problem of the coupled KdV equation is given.The scheme keeps the first two conserved quantities which the differential equation possesses.The catch-ran iterative method is used to solve the difference equations.The numerical simulation exhibits the existence of two-soliton solutions.
Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.
Wigren, Torbjörn
2015-01-01
The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.
Periodic solutions for a coupled pair of delay difference equations
Directory of Open Access Journals (Sweden)
Kang Shugui
2005-01-01
Full Text Available Based on the fixed-point index theory for a Banach space, positive periodic solutions are found for a system of delay difference equations. By using such results, the existence of nontrivial periodic solutions for delay difference equations with positive and negative terms is also considered.
Frequency and Phase Noise in Non-Linear Microwave Oscillator Circuits
Tannous, C.
2003-01-01
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of stochastic differential equations representing the circuit. Our theoretical evaluations can be used in order to make detailed comparisons with the experimental measurements of phase noise spectra in selected oscillating circuits.
Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems
Energy Technology Data Exchange (ETDEWEB)
Yanchuk, S.; Wolfrum, M. [Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin (Germany); Perlikowski, P. [Division of Dynamics, Technical University of Lodz, 90-924 Lodz (Poland); Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore, Singapore 117576 (Singapore); Stefański, A.; Kapitaniak, T. [Division of Dynamics, Technical University of Lodz, 90-924 Lodz (Poland)
2015-03-15
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.
Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems.
Yanchuk, S; Perlikowski, P; Wolfrum, M; Stefański, A; Kapitaniak, T
2015-03-01
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above.
Lyubimova, T; Zubova, N; Shevtsova, V
2017-03-01
The paper deals with the investigation of the onset and non-linear regimes of convection of liquid binary mixtures with negative Soret effect heated from above. The linear stability of a convectionless state in a horizontal layer is studied by the numerical solution of the linearized problem on the temporal evolution of small perturbations of the unsteady base state. Non-linear regimes of convection are investigated by the numerical solution of the non-linear unsteady equations for a horizontally elongated rectangular cavity. The calculations are performed for water-ethanol and water-isopropanol liquid mixtures and for colloidal suspensions. The dependences of the instability onset time and wave number of the most dangerous perturbations on the solutal Rayleigh number (gravity level) obtained by a linear stability analysis and non-linear calculations are found to be in a very good agreement. A favorable comparison with the existing experimental and numerical data is presented.
Towards a non-linear theory for induced seismicity in shales
Salusti, Ettore; Droghei, Riccardo
2014-05-01
We here analyze the pore transmission of fluid pressure pand solute density ρ in porous rocks, within the framework of the Biot theory of poroelasticity extended to include physico-chemical interactions. In more details we here analyze the effect of a strong external stress on the non-linear evolution of p and ρ in a porous rock. We here focus on the consequent deformation of the rock pores, relative to a non-linear Hooke equation among strain, linear/quadratic pressure and osmosis in 1-D. We in particular analyze cases with a large pressure, but minor than the 'rupture point'. All this gives relations similar to those discussed by Shapiro et al. (2013), which assume a pressure dependent permeability. Thus we analyze the external stress necessary to originate quick non-linear transients of combined fluid pressure and solute density in a porous matrix, which perturb in a mild (i.e. a linear diffusive phenomenon) or a more dramatic non-linear way (Burgers solitons) the rock structure. All this gives a novel, more realistic insight about the rock evolution, fracturing and micro-earthquakes under a large external stress.
Non-linear structural dynamics characterization using a scanning laser vibrometer
Pai, P. F.; Lee, S.-Y.
2003-07-01
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal velocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second, third, and fourth natural frequencies are examined in detail. Influences of the fixture mass, gravity, mass centers of mode shapes, and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances, energy transfer from high-frequency modes to the first mode, and amplitude- and phase-modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics
Institute of Scientific and Technical Information of China (English)
NI Guangjian; ZHANG Junhong; CHENG Xiaoming
2009-01-01
Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.
The late Universe with non-linear interaction in the dark sector: The coincidence problem
Bouhmadi-López, Mariam; Morais, João; Zhuk, Alexander
2016-12-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction Q = 3 HγεbarDEεbarDM /(εbarDE +εbarDM) , where γ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter w. In the considered model, the energy densities of the dark sector components present a scaling behaviour with εbarDM /εbarDE ∼(a0 / a) - 3(w + γ). We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the former being concentrated around them. To carry our analysis, we consider the theory of scalar perturbations (within the mechanical approach), and obtain the sets of parameters (w , γ) which do not contradict it. We conclude that two sets: (w = - 2 / 3 , γ = 1 / 3) and (w = - 1 , γ = 1 / 3) are of special interest. First, the energy densities of DM and DE on these cases are concentrated around galaxies confirming that they are coupled fluids. Second, we show that for both of them, the coincidence problem is less severe than in the standard ΛCDM. Third, the set (w = - 1 , γ = 1 / 3) is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.
Solution behaviors in coupled Schrödinger equations with full-modulated nonlinearities
Pınar, Zehra; Deliktaş, Ekin
2017-02-01
The nonlinear partial differential equations have an important role in real life problems. To obtain the exact solutions of the nonlinear partial differential equations, a number of approximate methods are known in the literature. In this work, a time- space modulated nonlinearities of coupled Schrödinger equations are considered. We provide a large class of Jacobi-elliptic solutions via the auxiliary equation method with sixth order nonlinearity and the Chebyshev approximation.
Non-linear QCD dynamics and exclusive production
Machado, M V T; Meneses, A R
2010-01-01
In this contribution we analyse the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky-Kovchegov equation including running coupling corrections. Comparisons to DESY-HERA data on exclusive processes and predictions to the Large Hadron Electron Collider, LHeC, are presented.
Non-linear pattern formation in bone growth and architecture.
Salmon, Phil
2014-01-01
The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here - chaotic non-linear pattern formation (NPF) - which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of "group intelligence" exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called "particle swarm optimization" (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating "socially" in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or "feedback" between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the emergent
Creation of Entanglement Entropy by a Non-linear Inflaton Potential
Mazur, Dan
2008-01-01
The density fluctuations that we observe in the universe today are thought to originate from quantum fluctuations produced during a phase of the early universe called inflation. By evolving a wavefunction describing two coupled Fourier modes of a scalar field forward in time, we demonstrate that non-linearities in the inflaton potential can result in a generation of entanglement entropy during the inflationary period when just one of the modes is observed. Through this mechanism, the field would experience decoherence and appear more like a classical distribution today. We find that the amount of entanglement entropy generated scales roughly as a power law $S \\propto \\lambda^{1.75}$, where $\\lambda$ is the coupling coeficient of the non-linear potential term. We also investigate how the entanglement entropy scales with the duration of inflation. This demonstration explicitly follows particle creation and interactions between modes; consequently, the mechanism contributing to the generation of the von Neumann ...
Key components for nano-assembled plasmon-excited single molecule non-linear devices
Kewes, Günter; Mazzamuto, Giacomo; Neitzke, Oliver; Schönfeld, Rolf-Simon; Schell, Andreas W; Probst, Jürgen; Wolters, Janik; Löchel, Bernd; Toninelli, Costanza; Benson, Oliver
2015-01-01
Tremendous enhancement of light-matter interaction in plasmon-excited molecular hybrid devices allows for non-linearities on the level of single emitters and few photons. This promises a plethora of novel applications like single photon transistors. Nevertheless, building the components of such devices is technologically extremely challenging. We tackle this task by lithographically fabricating on-chip plasmonic waveguides, efficiently connected to far-field in- and out-coupling ports via low-loss dielectric waveguides. Furthermore, a nano-assembling technology is developed, enabling the controlled coupling of single organic emitters to the plasmonic waveguides. Dibenzoterrylene fluorescent molecules hosted in anthracene crystals are investigated for this purpose. Here we present all key-components and technologies for a plasmon-excited single molecule non-linear device.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
Burau, Viola; Vrangbaek, Karsten
2008-01-01
The paper aims to account for the substance of non-linear governance change by analysing the importance of sector-specific institutions and the pathways of governing they create. The analysis uses recent reforms of the governance of medical performance in four European countries as a case, adopting an inductively oriented approach to comparison. The governance of medical performance is a good case as it is both, closely related to redistributive policies, where the influence of institutions tends to be pertinent, and is subject to considerable policy pressures. The overall thrust of reforms is similar across countries, while there are important differences in relation to how individual forms of governance and the balance between different forms of governance are changing. More specifically, sector-specific institutions can account for the specific ways in which reforms redefine hierarchy and professional self-regulation and for the extent to which reforms strengthen hierarchy and affect the balance with other forms of governance. The recent literature on governance mainly focuses on mapping out the substance of non-linear change, whereas the development of explanations of the substance of governance change is less systematic. In the present paper, therefore, it is suggested coupling the notion of non-linear change with an analysis of sector specific institutions inspired by the historical institutionalist tradition to better account for the substance of non-linear governance change. Further, the analysis offers interesting insights into the complexity of redrawing boundaries between the public and the private in health care.
Adaptive discontinuous Galerkin methods for non-linear reactive flows
Uzunca, Murat
2016-01-01
The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.
Energy Technology Data Exchange (ETDEWEB)
Bal, G.
1995-07-01
To achieve whole core calculations of the neutron transport equation, we have to follow this 2 step method: space and energy homogenization of the assemblies; resolution of the homogenized equation on the whole core. However, this is no more valid when accidents occur (for instance depressurization causing locally strong heterogeneous media). One solution consists then in coupling two kinds of resolutions: a fine computation on the damaged cell (fine mesh, high number of energy groups) coupled with a coarse one everywhere else. We only deal here with steady state solutions (which already live in 6D spaces). We present here two such methods: The coupling by transmission of homogenized sections and the coupling by transmission of boundary conditions. To understand what this coupling is, we first restrict ourselves to 1D with respect to space in one energy group. The first two chapters deal with a recall of basic properties of the neutron transport equation. We give at chapter 3 some indications of the behaviour of the flux with respect to the cross sections. We present at chapter 4 some couplings and give some properties. Chapter 5 is devoted to a presentation of some numerical applications. (author). 9 refs., 7 figs.
Traveling wave solutions of degenerate coupled multi-KdV equations
Gürses, Metin; Pekcan, Aslı
2016-10-01
Traveling wave solutions of degenerate coupled ℓ-KdV equations are studied. Due to symmetry reduction these equations reduce to one ordinary differential equation (ODE), i.e., (f')2 = Pn(f) where Pn(f) is a polynomial function of f of degree n = ℓ + 2, where ℓ ≥ 3 in this work. Here ℓ is the number of coupled fields. There is no known method to solve such ordinary differential equations when ℓ ≥ 3. For this purpose, we introduce two different types of methods to solve the reduced equation and apply these methods to degenerate three-coupled KdV equation. One of the methods uses the Chebyshev's theorem. In this case, we find several solutions, some of which may correspond to solitary waves. The second method is a kind of factorizing the polynomial Pn(f) as a product of lower degree polynomials. Each part of this product is assumed to satisfy different ODEs.
Massive Neutrinos and the Non-linear Matter Power Spectrum
Bird, Simeon; Haehnelt, Martin G
2011-01-01
We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation (Smith et al. 2003) to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k \\sim 1hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced n...
Darboux transformation of generalized coupled KdV soliton equation and its odd-soliton solutions
Institute of Scientific and Technical Information of China (English)
LIU Ping
2008-01-01
Based on the resulting Lax pairs of the generalized coupled KdV soliton equation,a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem.By using Darboux transformation,the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form.As an application,the first two cases are given.
Nonlinear Dynamics of Globally Coupled Sine-Gordon Equations
2011-05-01
studied too, including a triangular configuration of linearly coupled parallel fiber Bragg gratings [15], coupled triplets of Gross-Pitaevskii...B. Dueholm, O. A. Levring, J. Mygind, N. F. Pedersen , O. H. Soerensen, and M. Cirillo, Phys. Rev. Lett. 46, 1299 (1981); E. Joergensen, V. P...Malomed, Phys. Rev. B 37, 9325 (1988); A. V. Ustinov, H. Kohlstedt, M. Cirillo, N. F. Pedersen , G. Hallmanns, and C. Heiden, ibid. B 48, 10614
Kumar, K Vasanth; Sivanesan, S
2005-08-31
Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.
Continuous limits for an integrable coupling system of Toda equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Li Li [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China); Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-09-21
In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.
Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material.
Qin, Qin; Tian, Ming-Liang; Zhang, Peng
2017-04-13
High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10(-4)-10(-2) s(-1)) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations.
A study of non-linearity in rainfall-runoff response using 120 UK catchments
Mathias, Simon A.; McIntyre, Neil; Oughton, Rachel H.
2016-09-01
This study presents a catchment characteristic sensitivity analysis concerning the non-linearity of rainfall-runoff response in 120 UK catchments. Two approaches were adopted. The first approach involved, for each catchment, regression of a power-law to flow rate gradient data for recession events only. This approach was referred to as the recession analysis (RA). The second approach involved calibrating a rainfall-runoff model to the full data set (both recession and non-recession events). The rainfall-runoff model was developed by combining a power-law streamflow routing function with a one parameter probability distributed model (PDM) for soil moisture accounting. This approach was referred to as the rainfall-runoff model (RM). Step-wise linear regression was used to derive regionalization equations for the three parameters. An advantage of the RM approach is that it utilizes much more of the observed data. Results from the RM approach suggest that catchments with high base-flow and low annual precipitation tend to exhibit greater non-linearity in rainfall-runoff response. In contrast, the results from the RA approach suggest that non-linearity is linked to low evaporative demand. The difference in results is attributed to the aggregation of storm-flow and base-flow into a single system giving rise to a seemingly more non-linear response when applying the RM approach to catchments that exhibit a strongly dual storm-flow base-flow response. The study also highlights the value and limitations in a regionlization context of aggregating storm-flow and base-flow pathways into a single non-linear routing function.
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
Controlling ultrafast currents by the non-linear photogalvanic effect
Wachter, Georg; Lemell, Christoph; Tong, Xiao-Min; Yabana, Kazuhiro; Burgdörfer, Joachim
2015-01-01
We theoretically investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femto-second optical laser pulses. Ab-initio simulations based on time-dependent density functional theory predict ultrafast DC currents that can be viewed as a non-linear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the transition from non-linear polarization currents to the tunneling excitation regime. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. We find the ultrafast current control by the non-linear photogalvanic effect to be remarkably robust and insensitive to laser-pulse shape and carrier-envelope phase.
An algorithm for earthwork allocation considering non-linear factors
Institute of Scientific and Technical Information of China (English)
WANG Ren-chao; LIU Jin-fei
2008-01-01
For solving the optimization model of earthwork allocation considering non-linear factors, a hybrid al-gorithm combined with the ant algorithm (AA) and particle swarm optimization (PSO) is proposed in this pa-per. Then the proposed method and the LP method are used respectively in solving a linear allocation model of a high rockfill dam project. Results obtained by these two methods are compared each other. It can be conclu-ded that the solution got by the proposed method is extremely approximate to the analytic solution of LP method. The superiority of the proposed method over the LP method in solving a non-linear allocation model is illustrated by a non-linear case. Moreover, further researches on improvement of the algorithm and the allocation model are addressed.
Non-linear behaviour of large-area avalanche photodiodes
Fernandes, L M P; Monteiro, C M B; Santos, J M; Morgado, R E
2002-01-01
The characterisation of photodiodes used as photosensors requires a determination of the number of electron-hole pairs produced by scintillation light. One method involves comparing signals produced by X-ray absorptions occurring directly in the avalanche photodiode with the light signals. When the light is derived from light-emitting diodes in the 400-600 nm range, significant non-linear behaviour is reported. In the present work, we extend the study of the linear behaviour to large-area avalanche photodiodes, of Advanced Photonix, used as photosensors of the vacuum ultraviolet (VUV) scintillation light produced by argon (128 nm) and xenon (173 nm). We observed greater non-linearities in the avalanche photodiodes for the VUV scintillation light than reported previously for visible light, but considerably less than the non-linearities observed in other commercially available avalanche photodiodes.
Non-linear Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Rudin, Sergey; Rupper, Greg
2012-02-01
The non-linear electron plasma response to electromagnetic signal applied to a gated graphene conduction channel can be used to make a graphene based Dyakonov-Shur terahertz detector. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. With less damping and higher mobility, the graphene conduction channels may provide higher quality plasma response than possible with semiconductor channels. Our analysis of plasma oscillations in a graphene channel is based on the hydrodynamic equations which we derive from the Boltzmann equation accounting for both electrons and holes, and including the effects of viscosity and finite mobility.
On the theory of ternary melt crystallization with a non-linear phase diagram
Toropova, L. V.; Dubovoi, G. Yu; Alexandrov, D. V.
2017-04-01
The present study is concerned with a theoretical analysis of unidirectional solidification process of ternary melts in the presence of a phase transition (mushy) layer. A new analytical solution of heat and mass transfer equations describing the steady-state crystallization scenario is found with allowance for a non-linear liquidus equation. The model under consideration takes into account the presence of two phase transition layers, namely, the primary and cotectic mushy regions. We demonstrate that the phase diagram nonlinearity leads to substantial changes of analytical solutions.
Classical and quantum modes of coupled Mathieu equations
DEFF Research Database (Denmark)
Landa, H.; Reznik, B.; Drewsen, M.
2012-01-01
is that of decoupled linear oscillators. We use this transformation to solve the Heisenberg equations of the corresponding quantum-mechanical problem, and find the quantum wavefunctions for stable oscillations, expressed in configuration space. The obtained transformation and quantum solutions can be applied to more...
Non-linear growth and condensation in multiplex networks
Nicosia, Vincenzo; Latora, Vito; Barthelemy, Marc
2013-01-01
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which a single node connects to nearly all other nodes of a layer.
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...
Non-linear effects in bunch compressor of TARLA
Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin
2016-03-01
Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
The role of dendritic non-linearities in single neuron computation
Directory of Open Access Journals (Sweden)
Boris Gutkin
2014-05-01
Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.
Integrable quartic potentials and coupled KdV equations
Baker, S; Fordy, A P; Enolskii, V Z; Fordy, A P
1995-01-01
We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1:6:1 integrable case quartic potential. A generalisation of the 1:6:8 case is similarly related to a different (but gauge related) fourth order Lax operator. We exploit this connection to derive a Lax representation for each of these integrable systems. In this context a canonical transformation is derived through a gauge transformation.
New Exact Solutions for a Class of Nonlinear Coupled Differential Equations
Institute of Scientific and Technical Information of China (English)
ZHAO Hong; GUO Jun; BAI Cheng-Lin; HAN Ji-Guang
2005-01-01
More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.
Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Linares, Jesus [Area de Optica, Departamento de Fisica Aplicada, Facultade de Fisica, Escola Universitaria de Optica e Optometria, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain)], E-mail: suso.linares.beiras@usc.es; Nistal, Maria C. [Area de Optica, Departamento de Fisica Aplicada, Facultade de Fisica, Escola Universitaria de Optica e Optometria, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain)
2009-05-04
A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Xu Shu-Shan; Weng Yu-Quan
2008-01-01
A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.
Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition
Institute of Scientific and Technical Information of China (English)
王明新
2001-01-01
This paper deals with the blow-up rate estimates of solutions for semilinear parabolic systems coupled in an equation and a boundary condition. The upper and lower bounds of blow-up rates have been obtained.
Equilibrium dynamics of the Dean-Kawasaki equation: Mode-coupling theory and its extension
Kim, Bongsoo; Kawasaki, Kyozi; Jacquin, Hugo; van Wijland, Frédéric
2014-01-01
We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004, 10.1088/1742-5468/2008/02/P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-coupling approach.
Coupled Nonlinear Schr(o)dinger Equation: Symmetries and Exact Solutions
Institute of Scientific and Technical Information of China (English)
LIU Ping; LOU Sen-Yue
2009-01-01
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schr(o)dinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory
Markovich, Tomer; Podgornik, Rudi
2016-01-01
We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.
GPU linear and non-linear Poisson–Boltzmann solver module for DelPhi
Colmenares, José; Ortiz, Jesús; Rocchia, Walter
2014-01-01
Summary: In this work, we present a CUDA-based GPU implementation of a Poisson–Boltzmann equation solver, in both the linear and non-linear versions, using double precision. A finite difference scheme is adopted and made suitable for the GPU architecture. The resulting code was interfaced with the electrostatics software for biomolecules DelPhi, which is widely used in the computational biology community. The algorithm has been implemented using CUDA and tested over a few representative cases of biological interest. Details of the implementation and performance test results are illustrated. A speedup of ∼10 times was achieved both in the linear and non-linear cases. Availability and implementation: The module is open-source and available at http://www.electrostaticszone.eu/index.php/downloads. Contact: walter.rocchia@iit.it Supplementary information: Supplementary data are available at Bioinformatics online PMID:24292939
Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data
Kukreja, Sunil L.
2008-01-01
Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
An efficient implementation of massive neutrinos in non-linear structure formation simulations
Ali-Haïmoud, Yacine
2012-01-01
Massive neutrinos make up a fraction of the dark matter, but due to their large thermal velocities, cluster significantly less than cold dark matter (CDM) on small scales. An accurate theoretical modelling of their effect during the non-linear regime of structure formation is required in order to properly analyse current and upcoming high-precision large-scale structure data, and constrain the neutrino mass. Taking advantage of the fact that massive neutrinos remain linearly clustered up to late times, this paper treats the linear growth of neutrino overdensities in a non-linear CDM background. The evolution of the CDM component is obtained via N-body computations. The smooth neutrino component is evaluated from that background by solving the Boltzmann equation linearised with respect to the neutrino overdensity. CDM and neutrinos are simultaneously evolved in time, consistently accounting for their mutual gravitational influence. This method avoids the issue of shot-noise inherent to particle-based neutrino ...
The SPH approach to the process of container filling based on non-linear constitutive models
Institute of Scientific and Technical Information of China (English)
Tao Jiang; Jie Ouyang; Lin Zhang; Jin-Lian Ren
2012-01-01
In this work,the transient free surface of container filling with non-linear constitutive equation's fluids is numerically investigated by the smoothed particle hydrodynamics (SPH) method.Specifically,the filling process of a square container is considered for non-linear polymer fluids based on the Cross model.The validity of the presented SPH is first verified by solving the Newtonian fluid and OldroydB fluid jet.Various phenomena in the filling process are shown,including the jet buckling,jet thinning,splashing or spluttering,steady filling.Moreover,a new phenomenon of vortex whirling is more evidently observed for the Cross model fluid compared with the Newtonian fluid case.
Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
Lee, Seungjin; Schlotterer, Oliver
2015-01-01
Recent progress on scattering amplitudes in super Yang--Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang--Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. In this work we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern--Carrasco--Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL MARTINGALE
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations (BSDEs) with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale.It is proved that their solutions exist and are unique under the monotonicity conditions.
Institute of Scientific and Technical Information of China (English)
郭柏灵; 苗长兴
1995-01-01
The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
GENERAL SOLUTION FOR THE COUPLED EQUATIONS OF TRANSVERSELY ISOTROPIC MAGNETOELECTROELASTIC SOLIDS
Institute of Scientific and Technical Information of China (English)
刘金喜; 王祥琴; 王彪
2003-01-01
The coupling feature of transversely isotropic magnetoelectroelastic solids aregoverned by a system of five partial differential equations with respect to the elasticdisplacerments, the electric potential and the magnetic potential. Based on the potentialtheory, the coupled equations are reduced to the five uncoupled generalized Laplaceequations with respect to five potential functions. Further, the elastic fields andelectromagnetic fields are expressed in terms of the potential functions. These expressionsconstruct the general solution of transversely isotropic magnetoelectroelastic media.
Stability analysis of a system coupled to a transport equation using integral inequalities
Baudouin, Lucie; Seuret, Alexandre; Safi, Mohammed
2016-01-01
International audience; We address the stability of a system of ordinary differential equations coupled with a transport partial differential equation, using a Lyapunov functional approach. This system can also be interpreted as a finite dimensional system subject to a state delay. Inspired from recent developments on time-delay systems, a novel method to assess stability of such a class of coupled systems is developed here. We will specifically take advantage of a polynomial approximation of...
Johansen, A; Johansen, Anders; Youdin, Andrew
2007-01-01
We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random wal...
On Vector Helmholtz Equation with a Coupling Boundary Condition
Institute of Scientific and Technical Information of China (English)
Gang Li; Jiangsong Zhang; Jiang Zhu; Danping Yang
2007-01-01
The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown. In this paper,we study the vector Helmholtz problem in domains of both C1,1 and Lipschitz. We establish a rigorous variational analysis such as equivalence, existence and uniqueness.And we propose finite element approximations based on the uncoupled solutions. Finally we present a convergence analysis and error estimates.
Energy Technology Data Exchange (ETDEWEB)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.
Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations
J. Bajars (Janis); J.E. Frank (Jason); B.J. Leimkuhler (Ben)
2013-01-01
textabstractThermal bath coupling mechanisms as utilized in molecular dynamics are applied to partial differential equation models. Working from a semi-discrete (Fourier mode) formulation for the Burgers–Hopf or Korteweg–de Vries equation, we introduce auxiliary variables and stochastic
Coupled equations for Kähler metrics and Yang-Mills connections
DEFF Research Database (Denmark)
Garcia Fernandez, Mario; Alvarez-Consul, Luis; Garcia-Prada, Oscar
2012-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K¨ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K¨ahler metric and Hermite– Yang–Mills for a connection. We provide a moment...
The fractional coupled KdV equations: Exact solutions and white noise functional approach
Institute of Scientific and Technical Information of China (English)
Hossam A.Ghany; A.S.Okb El Bab; A.M.Zabel; Abd-Allah Hyder
2013-01-01
Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated.By using the modified fractional sub-equation method,Hermite transform,and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained,including the generalized exponential,hyperbolic,and trigonometric types.
Non-linear properties of R-R distributions as a measure of heart rate variability
Energy Technology Data Exchange (ETDEWEB)
Irurzun, I.M.; Bergero, P.; Cordero, M.C.; Defeo, M.M.; Vicente, J.L.; Mola, E.E
2003-06-01
We analyze the dynamic quality of the R-R interbeat intervals of electrocardiographic signals from healthy people and from patients with premature ventricular contractions (PVCs) by applying different measure algorithms to standardised public domain data sets of heart rate variability. Our aim is to assess the utility of these algorithms for the above mentioned purposes. Long and short time series, 24 and 0.50 h respectively, of interbeat intervals of healthy and PVC subjects were compared with the aim of developing a fast method to investigate their temporal organization. Two different methods were used: power spectral analysis and the integral correlation method. Power spectral analysis has proven to be a powerful tool for detecting long-range correlations. If it is applied in a short time series, power spectra of healthy and PVC subjects show a similar behavior, which disqualifies power spectral analysis as a fast method to distinguish healthy from PVC subjects. The integral correlation method allows us to study the fractal properties of interbeat intervals of electrocardiographic signals. The cardiac activity of healthy and PVC people stems from dynamics of chaotic nature characterized by correlation dimensions d{sub f} equal to 3.40{+-}0.50 and 5.00{+-}0.80 for healthy and PVC subjects respectively. The methodology presented in this article bridges the gap between theoretical and experimental studies of non-linear phenomena. From our results we conclude that the minimum number of coupled differential equations to describe cardiac activity must be six and seven for healthy and PVC individuals respectively. From the present analysis we conclude that the correlation integral method is particularly suitable, in comparison with the power spectral analysis, for the early detection of arrhythmias on short time (0.5 h) series.
Non-linear diffusion of cosmic rays escaping from supernova remnants - I. The effect of neutrals
Nava, L.; Gabici, S.; Marcowith, A.; Morlino, G.; Ptuskin, V. S.
2016-10-01
Supernova remnants are believed to be the main sources of galactic cosmic rays (CR). Within this framework, particles are accelerated at supernova remnant shocks and then released in the interstellar medium. The mechanism through which CRs are released and the way in which they propagate still remain open issues. The main difficulty is the high non-linearity of the problem: CRs themselves excite the magnetic turbulence that confines them close to their sources. We solve numerically the coupled differential equations describing the evolution in space and time of the escaping particles and of the waves generated through the CR streaming instability. The warm ionized and warm neutral phases of the interstellar medium are considered. These phases occupy the largest fraction of the disc volume, where most supernovae explode, and are characterized by the significant presence of neutral particles. The friction between those neutrals and ions results in a very effective wave damping mechanism. It is found that streaming instability affects the propagation of CRs even in the presence of ion-neutral friction. The diffusion coefficient can be suppressed by more than a factor of ˜2 over a region of few tens of pc around the remnant. The suppression increases for smaller distances. The propagation of ≈10 GeV particles is affected for several tens of kiloyears after escape, while ≈1 TeV particles are affected for few kiloyears. This might have a great impact on the interpretation of gamma-ray observations of molecular clouds located in the vicinity of supernova remnants.
Krak, Michael D.; Dreyer, Jason T.; Singh, Rajendra
2016-03-01
A vehicle clutch damper is intentionally designed to contain multiple discontinuous non-linearities, such as multi-staged springs, clearances, pre-loads, and multi-staged friction elements. The main purpose of this practical torsional device is to transmit a wide range of torque while isolating torsional vibration between an engine and transmission. Improved understanding of the dynamic behavior of the device could be facilitated by laboratory measurement, and thus a refined vibratory experiment is proposed. The experiment is conceptually described as a single degree of freedom non-linear torsional system that is excited by an external step torque. The single torsional inertia (consisting of a shaft and torsion arm) is coupled to ground through parallel production clutch dampers, which are characterized by quasi-static measurements provided by the manufacturer. Other experimental objectives address physical dimensions, system actuation, flexural modes, instrumentation, and signal processing issues. Typical measurements show that the step response of the device is characterized by three distinct non-linear regimes (double-sided impact, single-sided impact, and no-impact). Each regime is directly related to the non-linear features of the device and can be described by peak angular acceleration values. Predictions of a simplified single degree of freedom non-linear model verify that the experiment performs well and as designed. Accordingly, the benchmark measurements could be utilized to validate non-linear models and simulation codes, as well as characterize dynamic parameters of the device including its dissipative properties.
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method...
Range non-linearities correction in FMCW SAR
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
The limiting factor to the use of Frequency Modulated Continuous Wave (FMCW) technology with Synthetic Aperture Radar (SAR) techniques to produce lightweight, cost effective, low power consuming imaging sensors with high resolution, is the well known presence of non-linearities in the transmitted si
Non-Linear Interactive Stories in Computer Games
DEFF Research Database (Denmark)
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter is gra...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
Development and Control of a Non Linear Magnetic Levitation System
Directory of Open Access Journals (Sweden)
A Sanjeevi Gandhi
2013-06-01
Full Text Available Nowadays, studies to develop and control non linear systems is of great significance. Magnetic Levitation System has gained considerable interests due to its great practical importance in different engineering fields In this paper an electromagnetic levitation system was developed and mathematical model for the system was derived. The developed system was controlled manually.
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations
Directory of Open Access Journals (Sweden)
Mohamed S. Al-luhaibi
2015-01-01
Full Text Available This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.
Exact Shock Solution of a Coupled System of Delay Differential Equations: A Car-Following Model
Tutiya, Yohei; Kanai, Masahiro
2007-08-01
In this letter, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called car-following model. We use the Hirota method, originally developed in order to solve soliton equations. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundaries, representing the stationary propagation of a traffic jam.
Coupled equations for K\\"ahler metrics and Yang-Mills connections
Alvarez-Consul, Luis; Garcia-Prada, Oscar
2011-01-01
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\\"ahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, Mabuchi functional and geodesic stability. We finish by giving some examples of solutions.
From coupled map lattices to the stochastic Kardar Parisi Zhang equation
Katzav, Eytan; Cugliandolo, Leticia F.
2006-11-01
We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar-Parisi-Zhang growth equation and of the Fisher-Kolmogorov-Petrovskii-Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space-time behaviour is of KPZ type.
Eikonal solutions to optical model coupled-channel equations
Cucinotta, Francis A.; Khandelwal, Govind S.; Maung, Khin M.; Townsend, Lawrence W.; Wilson, John W.
1988-01-01
Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.
Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation
Energy Technology Data Exchange (ETDEWEB)
Cotter, Colin J [Department of Aeronautics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D; Ivanov, Rossen I; Percival, James R, E-mail: colin.cotter@ic.ac.uk, E-mail: d.holm@ic.ac.uk, E-mail: r.ivanov@imperial.ac.uk, E-mail: rivanov@dit.ie, E-mail: j.percival@ic.ac.uk [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom)
2011-07-01
We consider singular solutions of a system of two cross-coupled Camassa-Holm (CCCH) equations. This CCCH system admits peakon solutions, but it is not in the two-component CH integrable hierarchy. The system is a pair of coupled Hamiltonian partial differential equations for two types of solutions on the real line, each of which separately possesses exp ( - |x|) peakon solutions with a discontinuity in the first derivative at the peak. However, there are no self-interactions, so each of the two types of peakon solutions moves only under the induced velocity of the other type. We analyse the 'waltzing' solution behaviour of the cases with a single bound peakon pair (a peakon couple), as well as the over-taking collisions of peakon couples and the antisymmetric case of the head-on collision of a peakon couple and a peakon anti-couple. We then present numerical solutions of these collisions, which are inelastic because the waltzing peakon couples each possess an internal degree of freedom corresponding to their 'tempo'-that is, the period at which the two peakons of opposite type in the couple cycle around each other in phase space. Finally, we discuss compacton couple solutions of the cross-coupled Euler-Poincare (CCEP) equations and illustrate the same types of collisions as for peakon couples, with triangular and parabolic compacton couples. We finish with a number of outstanding questions and challenges remaining for understanding couple dynamics of the CCCH and CCEP equations.
Energy Technology Data Exchange (ETDEWEB)
Meister, Selina; Kubala, Bjoern; Gramich, Vera; Mecklenburg, Michael; Stockburger, Juergen T.; Ankerhold, Joachim [Institute for Complex Quantum Systems, Ulm University, Albert-Einstein-Allee 11, 89069 Ulm (Germany)
2015-07-01
Motivated by recent experiments a superconducting hybrid circuit consisting of a voltage biased Josephson junction in series with a resonator is studied. For strong driving the dynamics of the system can be very complex, even in the classical regime. Studying the dissipative dynamics within a Langevin-type description, we obtain well-defined dynamical steady states. In contrast to the well-known case of anharmonic potentials, like the Duffing or parametric oscillator, in our case the non-linearity stems from the peculiar way the external drive couples to the system [2]. We investigate the resonance behaviour of this non-linear hybrid system, in particular when driving at higher- or subharmonics. The resulting down- and up-conversions can be observed both, as resonances in the I-V curve, and in the emitted microwave radiation, which yields additional spectral information.
Non-Linear Beam Dynamics Studies of the Diamond Storage Ring
Bartolini, Riccardo; Belgroune, Mahdia; Henry Rowland, James; Jones, James; Martin, Ian; Singh, Beni
2005-01-01
The non-linear beam dynamics have been investigated for the non-zero dispersion lattice of the Diamond storage ring. Effects in realistic lattice configurations such as the introduction of coupling errors, beta beating, closed orbit correction, quadrupole fringe field and in-vacuum and helical insertion devices have been studied in the presence of realistic physical aperture limitations. Frequency map analysis together with 6D tracking allows identification of the limiting resonances as well as the loss locations and calculation of the influence of non-linear longitudinal motion on the Touschek lifetime. The sensitivity of the lattice to some of these effects leads to the identification of a better working point for the machine.
Modeling the Non-Linear Behavior of Library Cells for an Accurate Static Noise Analysis
Forzan, Cristiano
2011-01-01
In signal integrity analysis, the joint effect of propagated noise through library cells, and of the noise injected on a quiet net by neighboring switching nets through coupling capacitances, must be considered in order to accurately estimate the overall noise impact on design functionality and performances. In this work the impact of the cell non-linearity on the noise glitch waveform is analyzed in detail, and a new macromodel that allows to accurately and efficiently modeling the non-linear effects of the victim driver in noise analysis is presented. Experimental results demonstrate the effectiveness of our method, and confirm that existing noise analysis approaches based on linear superposition of the propagated and crosstalk-injected noise can be highly inaccurate, thus impairing the sign-off functional verification phase.
Orain, François; Bécoulet, M.; Morales, J.; Huijsmans, G. T. A.; Dif-Pradalier, G.; Hoelzl, M.; Garbet, X.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Fil, A.; Cahyna, P.
2015-01-01
The dynamics of a multi-edge localized mode (ELM) cycle as well as the ELM mitigation by resonant magnetic perturbations (RMPs) are modeled in realistic tokamak X-point geometry with the non-linear reduced MHD code JOREK. The diamagnetic rotation is found to be a key parameter enabling us to reproduce the cyclical dynamics of the plasma relaxations and to model the near-symmetric ELM power deposition on the inner and outer divertor target plates consistently with experimental measurements. Moreover, the non-linear coupling of the RMPs with unstable modes are found to modify the edge magnetic topology and induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. At larger diamagnetic rotation, a bifurcation from unmitigated ELMs—at low RMP current—towards fully suppressed ELMs—at large RMP current—is obtained.
Non-linear dynamics of Kelvin-Helmholtz unstable magnetized jets three-dimensional effects
Keppens, R
1999-01-01
A numerical study of the Kelvin-Helmholtz instability in compressible magnetohydrodynamics is presented. The three-dimensional simulations consider shear flow in a cylindrical jet configuration, embedded in a uniform magnetic field directed along the jet axis. The growth of linear perturbations at specified poloidal and axial mode numbers demonstrate intricate non-linear coupling effects. The physical mechanims leading to induced secondary Kelvin-Helmholtz instabilities at higher mode numbers are identified. The initially weak magnetic field becomes locally dominant in the non-linear dynamics before and during saturation. Thereby, it controls the jet deformation and eventual breakup. The results are obtained using the Versatile Advection Code [G. Toth, Astrophys. Lett. Comm. 34, 245 (1996)], a software package designed to solve general systems of conservation laws. An independent calculation of the same Kelvin-Helmholtz unstable jet configuration using a three-dimensional pseudo-spectral code gives important ...
Directory of Open Access Journals (Sweden)
G. C. Shit
2014-01-01
Full Text Available An analysis has been made to investigate the effects of thermal radiation on the magnetohydrodynamic (MHD flow and heat transfer over an inclined non-linear stretching sheet. The surface velocity of the stretching sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The effect of internal heat generation/absorption is taken into account. The fluid viscosity is assumed to vary as an inverse linear function of temperature. A generalized similarity transformation is used to reduce the governing partial differential equations to a system of non-linear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concerned with the velocity, temperature and concentration distributions as well as the skin-friction coefficient and the Nusselt number for various values of the dimensionless parameters of interest are obtained. Some important findings reported in this paper reveal that the effect of thermal radiation and heat generation/absorption have significant role in controlling the rate of heat transfer in the boundary layer region.
Hölder continuity of Keller-Segel equations of porous medium type coupled to fluid equations
Chung, Yun-Sung; Hwang, Sukjung; Kang, Kyungkeun; Kim, Jaewoo
2017-08-01
We consider a coupled system consisting of a degenerate porous medium type of Keller-Segel system and Stokes system modeling the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global existence of weak solutions and Hölder continuous solutions in dimension three, under the assumption that the power of degeneracy is above a certain number depending on given parameter values. To show Hölder continuity of weak solutions, we consider a single degenerate porous medium equation with lower order terms, and via a unified method of proof expanded to generalized porous medium equations, we obtain Hölder regularity, which is of independent interest.
Hamiltonian Structures and Integrability for a Discrete Coupled KdV-Type Equation Hierarchy
Institute of Scientific and Technical Information of China (English)
ZHAO Hai-Qiong; ZHU Zuo-Nong; ZHANG Jing-Li
2011-01-01
@@ Coupled Korteweg-de Vries(KdV) systems have many important physical applications.By considering a 4 × 4spectral problem,we derive a discrete coupled KdV-type equation hierarchy.Our hierarchy includes the coupled Volterra system proposed by Lou et al.(e-print arXiv:0711.0420) as the first member which is a discrete version of the coupled KdV equation.We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.%Coupled Korteweg-de Vries (KdV) systems have many important physical applications.By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy.Our hierarchy includes the coupled Volterra system proposed by Lou et al.(e-print arXiv: 0711.0420) as the first member which is a discrete version of the coupled KdV equation.We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.
Energy Technology Data Exchange (ETDEWEB)
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
SPATIO-TEMPORAL CHAOTIC SYNCHRONIZATION FOR MODES COUPLED TWO GINZBURG-LANDAU EQUATIONS
Institute of Scientific and Technical Information of China (English)
HU Man-feng; XU Zhen-yuan
2006-01-01
On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE.MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
Coupled Nosé-Hoover equations of motion to implement a fluctuating heat-bath temperature
Fukuda, Ikuo; Moritsugu, Kei
2016-03-01
The Nosé-Hoover (NH) equation provides a universal and powerful computer simulation protocol to realize an equilibrium canonical temperature for a target physical system. Here we demonstrate a general formalism to couple such NH equations. We provide a coupled NH equation that is constructed by coupling the NH equation of a target physical system and the NH equation of a temperature system. Thus, in contrast to the conventional single NH equation, the heat-bath temperature is a dynamical variable. The temperature fluctuations are not ad hoc, but instead are generated by the newly defined temperature system, and the statistical distribution of the temperature is completely described with an arbitrarily given probability function. The current equations of motion thus describe the physical system that develops with a predistributed fluctuating temperature, which allows enhanced sampling of the physical system. Since the total system is governed by a prescribed distribution, the equilibrium of the physical system is also reconstructed by reweighting. We have formulated a scheme for specifically setting the distribution of the dynamical inverse temperature and demonstrate the statistical relationship between the dynamical and physical temperatures. The statistical features, dynamical properties, and sampling abilities of the current method are demonstrated via the distributions, trajectories, dynamical correlations, and free energy landscapes for both a model system and a biomolecular system. These results indicated that the current coupled NH scheme works well.
Burg, van der Eeke; Leeuw, de Jan
1988-01-01
In this paper we discuss the estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS). Starting points are the delta method equations, but the jack-knife and bootstrap are used to provide finite differen
A NOTE ON "THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS"
Institute of Scientific and Technical Information of China (English)
Hongxia GUO; Guowang CHEN
2013-01-01
In this article,we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations utt-a△utt =△f(u,v),x ∈ RN,t ＞ 0,vtt-a△vtt =△g(u,v),x ∈ RN,t ＞ 0 admits a unique global generalized solution in C3([0,∞); Wm,p(RN) ∩ L∞(RN) f∩ L2(RN))(m ≥ 0 is an integer,1 ≤ p ≤ ∞) and a unique global classical solution in C3([0,∞); Wm,p ∩ L∞ ∩ L2) (m ＞ 2 + N/p),the sufficient conditions of the blow up of the solution in finite time are given,and also two examples are given.
Coupled equations for transient water flow, heat flow, and deformation in hydrogeological systems
Indian Academy of Sciences (India)
T N Narasimhan
2006-04-01
Hydrogeological systems are earth systems inﬂuenced by water.Their behaviors are governed by interacting processes,including ﬂow of ﬂuids,deformation of porous materials,chemical reactions, and transport of matter and energy.Here,coupling among three of these processes is considered: ﬂow of water,heat,and deformation,each of which is represented by a diffusion-type of partial differential equation.One side of the diffusion-type equation relates to motion of matter or energy, while the other relates to temporal changes of state variables at a given location.The coupling arises from processes that govern motion as well as those that relate to change of state.In this work, attention is devoted to coupling arising from changes in state.Partial derivatives of equations of state constitute the capacitance terms of diffusion-type equations.Of the many partial derivatives that are mathematically possible in physical systems characterized by several variables,only a few are physically signi ﬁcant.Because the state variables are related to each other through an equation of state,the partial derivatives must collectively satisfy a closure criterion.This framework offers a systematic way of developing the coupled set of equations that govern hydrogeological systems involving the ﬂow of water,heat,and deformation.Such systems are described in terms of four variables,and the associated partial derivatives.The physical import of these derivatives are discussed,followed by a description of partial derivatives that are of practical interest.These partial derivatives are then used as the basis to develop a set of coupled equations.A brief discussion is presented on coupled equations from a perspective of energy optimization.
Generalized Lorentz-Dirac equation for a strongly coupled gauge theory.
Chernicoff, Mariano; García, J Antonio; Güijosa, Alberto
2009-06-19
We derive a semiclassical equation of motion for a "composite" quark in strongly coupled large-N_{c} N = 4 super Yang-Mills theory, making use of the anti-de Sitter space/conformal field theory correspondence. The resulting nonlinear equation incorporates radiation damping, and reduces to the standard Lorentz-Dirac equation for external forces that are small on the scale of the quark Compton wavelength, but has no self-accelerating or preaccelerating solutions. From this equation one can read off a nonstandard dispersion relation for the quark, as well as a Lorentz-covariant formula for its radiation rate.
Non-linear effects on solute transfer between flowing water and a sediment bed.
Higashino, Makoto; Stefan, Heinz G
2011-11-15
A previously developed model of periodic pore water flow in space and time, and associated solute transport in a stream bed of fine sand is extended to coarse sand and fine gravel. The pore water flow immediately below the sediment/water interface becomes intermittently a non-Darcy flow. The periodic pressure and velocity fluctuations considered are induced by near-bed coherent turbulent motions in the stream flow; they penetrate from the sediment/water interface into the sediment pore system and are described by a wave number (χ) and a period (T) that are given as functions of the shear velocity (U(∗)) between the flowing water and the sediment bed. The stream bed has a flat surface without bed forms. The flow field in the sediment pore system is described by the continuity equation and a resistance law that includes both viscous (Darcy) and non-linear (inertial) effects. Simulation results show that non-linear (inertial) effects near the sediment/water interface increase flow resistance and reduce mean flow velocities. Compared to pure Darcy flow, non-linear (inertial) effects reduce solute exchange rates between overlying water and the sediment bed but only by a moderate amount (less than 50%). Turbulent coherent flow structures in the stream flow enhance solute transfer in the pore system of a stream bed compared to pure molecular diffusion, but by much less than standing surface waves or bed forms.
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
Chmielewski, P; Murawski, K; Musielak, Z E
2014-01-01
We present simulation results of the impulsively generated linear and non-linear Alfven waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic equations to find the temporal signatures of the small and large-amplitude Alfven waves in the model atmosphere of open and expanding magnetic field configuration with a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfven waves at different heights of the model atmosphere, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfven waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfven waves show that they can contribute only to the plasma dynamics and heating of t...
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
Chmielewski, P.; Srivastava, A. K.; Murawski, K.; Musielak, Z. E.
2014-01-01
We present simulation results of the impulsively generated linear and non-linear Alfvén waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic equations to find the temporal signatures of the small and large-amplitude Alfvén waves in the model atmosphere of open and expanding magnetic field configuration with a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfvén waves at different heights of the model atmosphere, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfvén waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfvén waves shows that they can contribute only to the plasma dynamics and heating of the funnel-like magnetic flux-tubes associated with the polar coronal holes.
Nonlinear Klein-Gordon equations coupled with Born-Infeld type equations
Directory of Open Access Journals (Sweden)
Pietro D'Avenia
2002-03-01
Full Text Available In this paper we prove the existence of infinitely many radially symmetric standing waves in equilibrium with their own electro-magnetic field. The interaction is described by means of the minimal coupling rule; on the other hand the Lagrangian density for the electro-magnetic field is the second order approximation of the Born-Infeld Lagrangian density.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-01
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Non-linear Behavior of Curved Sandwich Panels
DEFF Research Database (Denmark)
Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.;
2003-01-01
In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure load...... and results are compared to test data. A novel test arrangement utilizing a water filled cushion to create the uniform pressure load on curved panel specimen is used to obtain the experimental data. The panel is modeled with three different commercial finite element codes. Two implicit and one explicit code...... are used with various element types, modeling approaches and material models. The results show that the theoretical and experimental methods generally show fair agreement in panel non-linear behavior before collapse. It is also shown that special attention to detail has to be taken, because the predicted...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Measuring the Non-Linear Effects of Monetary Policy
Christian Matthes; Regis Barnichon
2015-01-01
This paper proposes a method to identify the non-linear effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to monetary policy and find that the effect of a monetary intervention depends strongly on (i) the sign of the intervention, (ii) the size of the intervention, and (iii) the state of the business cycle at the time of the intervention. A contractionary policy has a strong adverse effect on output, much stronger t...
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Adaptive spectral identification techniques in presence of undetected non linearities
Cella, G; Guidi, G M
2002-01-01
The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and stationary noise. We study the possibility of improving the detection efficiency with a class of adaptive spectral identification techniques, analyzing their effect in presence of non stationarities and undetected non linearities in the noise
Non-linear dark matter collapse under diffusion
Velten, Hermano E S
2014-01-01
Diffusion is one of the physical processes allowed for describing the large scale dark matter dynamics. At the same time, it can be seen as a possible mechanism behind the interacting cosmologies. We study the non-linear spherical "top-hat" collapse of dark matter which undergoes velocity diffusion into a solvent dark energy field. We show constraints on the maximum magnitude allowed for the dark matter diffusion. Our results reinforce previous analysis concerning the linear perturbation theory.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Non-linear Higgs portal to Dark Matter
Bajo, Rocío del Rey
2016-01-01
The Higgs portal to scalar Dark Matter is considered in the context of non-linearly realised electroweak symmetry breaking. We determine the interactions of gauge bosons and the physical Higgs particle $h$ to a scalar singlet Dark Matter candidate $S$ in an effective description. The main phenomenological differences with respect to the standard scenario can be seen in the Dark Matter relic abundance, in direct/indirect searches and in signals at colliders.
BFKL equation with running QCD coupling and HERA data
Levin, Eugene
2013-01-01
In this paper we developed approach based on the BFKL evolution in $\\ln\\Lb Q^2\\Rb$. We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good $\\chi^2/d.o.f. \\approx 1.3$. From our description of the experimental data we learned several lessons; (i) the non-perturbative physics at long distances started to show up at $Q^2 = 0.25\\,GeV^2$; (ii) the scattering amplitude at $Q^2 = 0.25\\,GeV^2$ cannot be written as sum of soft Pomeron and the secondary Reggeon but the Pomeron interactions should be taken into account; (iii) the Pomeron interactions can be reduced to the enhanced diagrams and, therefore, we do not see any needs for the shadowing corrections at HERA energies; and (iv) we demonstrated that the shadowing correction could be sizable at higher than HERA energies without any contradiction with our initial conditions.
BFKL equation with running QCD coupling and HERA data
Levin, Eugene; Potashnikova, Irina
2014-02-01
In this paper we developed approach based on the BFKL evolution in ln( Q 2). We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good χ2 /d .o .f . ≈ 1 .3. From our description of the experimental data we learned several lessons; (i) the non-perturbative physics at long distances started to show up at Q 2 = 0 .25 GeV2; (ii) the scattering amplitude at Q 2 = 0 .25 GeV2 cannot be written as sum of soft Pomeron and the secondary Reggeon but the Pomeron interactions should be taken into account; (iii) the Pomeron interactions can be reduced to the enhanced diagrams and, therefore, we do not see any needs for the shadowing corrections at HERA energies; and (iv) we demonstrated that the shadowing correction could be sizable at higher than HERA energies without any contradiction with our initial conditions.
A review on non-linear aeroelasticity of high aspect-ratio wings
Afonso, Frederico; Vale, José; Oliveira, Éder; Lau, Fernando; Suleman, Afzal
2017-02-01
Current economic constraints and environmental regulations call for design of more efficient aircraft configurations. An observed trend in aircraft design to reduce the lift induced drag and improve fuel consumption and emissions is to increase the wing aspect-ratio. However, a slender wing is more flexible and subject to higher deflections under the same operating conditions. This effect may lead to changes in dynamic behaviour and in aeroelastic response, potentially resulting in instabilities. Therefore, it is important to take into account geometric non-linearities in the design of high aspect-ratio wings, as well as having accurate computational codes that couple the aerodynamic and structural models in the presence of non-linearities. Here, a review on the state-of-the-art on non-linear aeroelasticity of high aspect-ratio wings is presented. The methodologies employed to analyse high aspect-ratio wings are presented and their applications discussed. Important observations from the state-of-the-art studies are drawn and the current challenges in the field are identified.
Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case
Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem
2015-01-01
In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance. PMID:25964756
Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity
Apolo, Luis
2016-01-01
We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders. This theory is based on the SO(1,5) group, in analogy with the SO(2,4) formulation of conformal gravity, but has a quadratic spectrum free of ghost instabilities. The action contains a vector field associated to a local SO(2) symmetry which is manifest in the vielbein formulation of the theory. We show that, in a perturbative expansion, the SO(2) symmetry transmutes into the PM transformations of a massive spin-2 field. In this context, the vector field is crucial to circumvent earlier obstructions to an order-by-order construction of PM symmetry. Although the non-linear theory lacks enough first class constraints to remove all helicity-0 modes from the spectrum, the PM transformations survive to all orders. The absence of ghosts and strong coupling effects at the non-linear level are not addressed here.
A non-linear homogeneous model for bone-like materials under compressive load.
Mengoni, M; Voide, R; de Bien, C; Freichels, H; Jérôme, C; Léonard, A; Toye, D; Müller, R; van Lenthe, G H; Ponthot, J P
2012-02-01
Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strain framework. This material model was implemented into metafor (LTAS-MNNL, University of Liège, Belgium), a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested: aluminum foams of variable density (ERG, Oakland, CA, USA), polylactic acid foam (CERM, University of Liège, Liège, Belgium), and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège, Liège, Belgium).
Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan
2017-01-01
This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Non-linear polaronic conduction in magnetite nanowires
Energy Technology Data Exchange (ETDEWEB)
Singh, Pooja, E-mail: pooja7503@gmail.com [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rout, P.K., E-mail: pkrout.phy@gmail.com [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Husale, Sudhir; Gupta, Anurag [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Singh, Manju [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rakshit, R.K. [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Dogra, Anjana, E-mail: anjanad@nplindia.org [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India)
2016-12-01
We report the temperature dependent current (I) – voltage (V) characteristics of Fe{sub 3}O{sub 4} nanowires with varying width (w) of 132, 358, and 709 nm. While the widest nanowire (w=709 nm) shows ohmic I (V) curves for all temperatures, those for w=132 and 358 nm show nonlinearity, which can be expressed by a combination of linear (V) and cubic (V{sup 3}) terms. The behaviour of conductance (linear bias component of current) and non-linearity in these nanowires is related to small polaron hopping related conduction. Moreover, we observed an anomalously large hopping lengths, which may be related to the size of percolation cluster and/or antiphase domain. Our study presents first experimental evidence for such non-linear polaronic conduction in magnetite nanowires. - Highlights: • Temperature dependent I–V measurements of FIB fabricated magnetite nanowires. • Small polaron based conduction in non-linear I–V curves. • Anomalously large hopping lengths due to percolation effect and/or antiphase domains.
Non-linear Q-clouds around Kerr black holes
Directory of Open Access Journals (Sweden)
Carlos Herdeiro
2014-12-01
Full Text Available Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.
Testing non-linear vacuum electrodynamics with Michelson interferometry
Schellstede, Gerold O; Lämmerzahl, Claus
2015-01-01
We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Pleba\\'nski class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental set-ups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and...
Painleve analysis and symmetry group for the coupled Zakharov-Kuznetsov equation
Energy Technology Data Exchange (ETDEWEB)
Hu, Heng-Chun, E-mail: hhengchun@163.com [College of Science, University of Shanghai for Science and Technology, Shanghai 200093 (China); Jia, Xiao-Qing; Sang, Ben-Wen [College of Science, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2011-09-12
The Painleve property for the coupled Zakharov-Kuznetsov equation is verified with the WTC approach and new exact solutions of bell-type are constructed from standard truncated expansion. A symmetry transformation group theorem is also given out from a simple direct method. -- Highlights: → Painleve property for coupled Zakharov-Kuznetsov system is verified by WTC method. → Symmetry group for coupled ZK system is given out by a simple direct method. → Bell-type solution for coupled ZK system is constructed from standard truncation.
On the theory of a non-linear neutral scalar field with spontaneously broken symmetry
Poluektov, Yu M
2015-01-01
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main approximation of the relativistic self-consistent field model, in which the influence of vacuum fluctuations is taken into account in constructing the one-particle states. The solutions of the self-consistent equations determine possible states, which also include the states with broken symmetries. Different states of the field are matched to particles, whose masses are determined by both parameters of the Lagrangian and vacuum fluctuations.
Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics
Lam, F
2013-01-01
A vorticity theory for incompressible fluid flows in the absence of solid boundaries is proposed. Some apriori bounds are established. They are used in an interpolation theory to show the well-posedness of the vorticity Cauchy problem. A non-linear integral equation for vorticity is derived and its solution is expressed in an expansion. Interpretations of flow evolutions starting from given initial data are given and elaborated. The kinetic theory for Maxwellian molecules with cut-off is revisited in order to link microscopic properties to flow characters on the continuum.
Beta-functions of non-linear $\\sigma$-models for disordered and interacting electron systems
Dell'Anna, Luca
2016-01-01
We provide and study complete sets of one-loop renormalization group equations, calculated at all orders in the interaction parameters, of several Finkel'stein non-linear $\\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors.
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representation. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation. ...... and are systematically compared with the experimental results given by Watanabe et al. (1989, J. Soc. Naval Architects Japan, 166) and O’Dea et al. (1992, Proc. 19th Symp. on Naval Hydrodynamics). The agreement between the present predictions and the experiments is very encouraging....
The global non-linear stability of the Kerr-de Sitter family of black holes
Hintz, Peter
2016-01-01
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extending the linear and non-linear analysis on black hole spacetimes described in a sequence of earlier papers by the authors: We develop a general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations. In particular, the iteration scheme used to solve Einstein's equations automatically finds the parameters of the Kerr-de Sitter black hole that the solution is asymptotic to, the exponentially decaying tail of the solution, and the gauge in which we are able to find the solution; the gauge here is a wave map/DeTurck type gauge, modified by source terms which are treated as unknowns, lying in a suitable finite-dimensional space.
A finite element perspective on non-linear FFT-based micromechanical simulations
Zeman, Jan; Vondřejc, Jaroslav; Peerlings, Ron H J; Geers, Marc G D
2016-01-01
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the Fast Fourier Transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to non-linear problems conceptually difficult. This paper aims to establish a link between FE- and FFT-based methods, in order to develop a solver applicable to general history- and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of non-linear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus nee...
Energy Technology Data Exchange (ETDEWEB)
Meili, G.; Dubroca, G.; Pasquier, M.; Thepenier, J.
1982-06-01
The paper discusses a method for the mechanical testing of casebonded composite modified double base charges (CMDB) subjected to thermal cycling. The method proposed to determine stresses and safety margins takes into account the non-linear viscoelastic behaviour and the compressibility of the propellant. The non-linear behaviour is derived from tensile testing. The equations of equilibrium are solved numerically by deviding the grain web into many layers. The nonlinearities mainly concern the modulus; a multiaxial criterion and the time-temperature shift factors are used. At each time-step and for each layer the temperature, the reduced time, the non-linear factor, the Poisson's ratio and the damage according to the concept of Farris are calculated. Different charges (star, wagon wheel, finocyl) were subjected to various types of thermal cycles. The comparison between prediction and experimentation is acceptable even for complex histories in strain and temperature.