Energy Technology Data Exchange (ETDEWEB)
Wang Dengshan [CEMA and CIAS, Central Univ. of Finance and Economics, BJ (China); BNLCMP, Inst. of Physics, Chinese Academy of Sciences, BJ (China); Liu Yifang [School of Economics, Central Univ. of Finance and Economics, BJ (China)
2010-01-15
In this paper, with the aid of symbolic computation the bright soliton solutions of two variable-coefficient coupled nonlinear Schroedinger equations are obtained by Hirota's method. Some figures are plotted to illustrate the properties of the obtained solutions. The properties are meaningful for the investigation on the stability of soliton propagation in the optical soliton communications. (orig.)
Liu, De-Yin; Tian, Bo; Xie, Xi-Yang
2017-03-01
Bound-state vector soliton solutions for the coupled variable-coefficient higher-order nonlinear Schrödinger equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fiber, are investigated. Introducing auxiliary functions, we derive the bilinear forms and corresponding constraints on the variable coefficients. Through symbolic computation, we construct the one- and two-soliton solutions. We see that the variable coefficients in the equations affect the soliton structures. With different choices of the variable coefficients, we obtain the cubic, periodic, and parabolic solitons. Bound-state solitons and interactions are analyzed graphically.
Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K
2017-02-01
We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.
Coupling coefficients for coupled-cavity lasers
Energy Technology Data Exchange (ETDEWEB)
Lang, R.J.; Yariv, A.
1987-03-01
The authors derive simple, analytic formulas for the field coupling coefficients in a two-section coupled-cavity laser using a local field rate equation treatment. They show that there is a correction to the heuristic formulas based on power flow calculated by Marcuse; the correction is in agreement with numerical calculations from a coupled-mode approach.
Describing spatiotemporal couplings in ultrashort pulses using coupling coefficients
Institute of Scientific and Technical Information of China (English)
Zeng Shu-Guang; Dan You-Quan; Zhang Bin; Sun Nian-Chun; Sui Zhan
2011-01-01
Three coupling coefficients are defined to describe spatiotemporal coupling in ultrashort pulses.With these coupling coefficients,the first-order spatiotemporal couplings of Gaussian pulse and beam are described analytically.Also,the first-order and the second-order spatiotemporal couplings caused by angular dispersion elements are studied using these coupling coefficients.It can be shown that these coupling coefficients are dimensionless and normalized,and readily indicate the severity of spatiotemporal coupling.
Institute of Scientific and Technical Information of China (English)
刘建平; 郑崇勋; 张崇
2009-01-01
Computing the Nonlinear regressive (NLR) coefficients of electroencephalogram (EEG) rhythms at different brain cortical areas for the mental fatigue caused by long term cognitive task, the variations of NLR coefficients of EEG rhythms under different mental fatigue level are sought out.The experimental results show that the NLR coefficients of EEG rhythms can effectively characterize the changes of amplitude coupling at different brain cortical areas under different mental fatigue level.The NLR coefficient provides a powerful tool for the EEG functional coupling analysis of mental fatigue.%本文通过对连续长时间脑力劳动前后状态下的脑电节律进行幅度耦合分析,提取了非线性回归系数,研究它们在不同中枢疲劳状态下的变化规律.实验结果表明,非线性回归系数能有效地反映出导联间幅度耦合同步程度随中枢疲劳程度的变化情况.为中枢疲劳脑电幅度耦合分析提供了有力工具.
General Symmetry Approach to Solve Variable-Coefficient Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
RUAN HangYu; CHEN YiXin; LOU SenYue
2001-01-01
After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schrodinger equation as a concrete example, the method is recommended in detail.``
Inverse Coefficient Problems for Nonlinear Elliptic Variational Inequalities
Institute of Scientific and Technical Information of China (English)
Run-sheng Yang; Yun-hua Ou
2011-01-01
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
Some new solutions of nonlinear evolution equations with variable coefficients
Virdi, Jasvinder Singh
2016-05-01
We construct the traveling wave solutions of nonlinear evolution equations (NLEEs) with variable coefficients arising in physics. Some interesting nonlinear evolution equations are investigated by traveling wave solutions which are expressed by the hyperbolic functions, the trigonometric functions and rational functions. The applied method will be used in further works to establish more entirely new solutions for other kinds of such nonlinear evolution equations with variable coefficients arising in physics.
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations
Institute of Scientific and Technical Information of China (English)
Yun Hua OU; Alemdar HASANOV; Zhen Hai LIU
2008-01-01
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
Multistability in nonlinearly coupled ring of Duffing systems
Jaros, P.; Kapitaniak, T.; Perlikowski, P.
2016-11-01
In this paper we consider dynamics of three unidirectionally coupled Duffing oscillators with nonlinear coupling function in the form of third degree polynomial. We focus on the influence of the coupling on the occurrence of different bifurcation's scenarios. The stability of equilibria, using Routh-Hurwitz criterion, is investigated. Moreover, we check how coefficients of the nonlinear coupling influence an appearance of different types of periodic solutions. The stable periodic solutions are computed using path-following. Finally, we show the two parameters' bifurcation diagrams with marked areas where one can observe the coexistence of solutions.
Exact solutions to a nonlinear dispersive model with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Yin Jun [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China); Lai Shaoyong [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)], E-mail: laishaoy@swufe.edu.cn; Qing Yin [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)
2009-05-15
A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Overall mass-transfer coefficients in non-linear chromatography
DEFF Research Database (Denmark)
Mollerup, Jørgen; Hansen, Ernst
1998-01-01
In case of mass transfer where concentration differences in both phases must be taken into account, one may define an over-all mass-transfer coefficient basd on the apparent over-all concentration difference. If the equilibrium relationship is linear, i.e. in cases where a Henry´s law relationship...... can be applied, the over-all mass-transfer coefficient will be concentration independent. However, in mass-transfer operations, a linear equilibrium relationship is in most cases not a valid approximation wherefore the over-all mass-transfer coefficient becomes strongly concentration dependent...... as shown in this paper. In this case one has to discard the use of over-all mass-transfer coefficients and calculate the rate of mass transfer from the two film theory using the appropriate non-linear relationship to calculate the equilibrium ratio at the interface between the two films....
Primordial fluctuations from nonlinear couplings
Calzetta, E A; Calzetta, Esteban A.; Gonorazky, Sonia
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tiltilng it towards the blue. We discuss in some detail wether these fluctuations are quantum or classical in nature.
Stable estimation of two coefficients in a nonlinear Fisher-KPP equation
Cristofol, Michel; Roques, Lionel
2013-09-01
We consider the inverse problem of determining two non-constant coefficients in a nonlinear parabolic equation of the Fisher-Kolmogorov-Petrovsky-Piskunov type. For the equation ut = DΔu + μ(x) u - γ(x)u2 in (0, T) × Ω, which corresponds to a classical model of population dynamics in a bounded heterogeneous environment, our results give a stability inequality between the couple of coefficients (μ, γ) and some observations of the solution u. These observations consist in measurements of u: in the whole domain Ω at two fixed times, in a subset ω⊂⊂Ω during a finite time interval and on the boundary of Ω at all times t ∈ (0, T). The proof relies on parabolic estimates together with the parabolic maximum principle and Hopf’s lemma which enable us to use a Carleman inequality. This work extends previous studies on the stable determination of non-constant coefficients in parabolic equations, as it deals with two coefficients and with a nonlinear term. A consequence of our results is the uniqueness of the couple of coefficients (μ, γ), given the observation of u. This uniqueness result was obtained in a previous paper but in the one-dimensional case only.
Directory of Open Access Journals (Sweden)
A. H. Bhrawy
2014-01-01
Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.
Changes in Electrokinetic Coupling Coefficients of Granite under Triaxial Deformation
Directory of Open Access Journals (Sweden)
Osamu Kuwano
2012-01-01
Full Text Available Electrokinetic phenomena are believed to be the most likely origin of electromagnetic signals preceding or accompanying earthquakes. The intensity of the source current due to the electrokinetic phenomena is determined by the fluid flux and the electrokinetic coupling coefficient called streaming current coefficient; therefore, how the coefficient changes before rupture is essential. Here, we show how the electrokinetic coefficients change during the rock deformation experiment up to failure. The streaming current coefficient did not increase before failure, but continued to decrease up to failure, which is explained in terms of the elastic closure of capillary. On the other hand, the streaming potential coefficient, which is the product of the streaming current coefficient and bulk resistivity of the rock, increased at the onset of dilatancy. It may be due to change in bulk resistivity. Our result indicates that the zeta potential of the newly created surface does not change so much from that of the preexisting fluid rock interface.
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
Directory of Open Access Journals (Sweden)
Catalina Hurtado Castano
2016-01-01
Full Text Available A detailed procedure is presented to compute analytically the acoustooptic coupling coefficient between copropagating core and lowest-order cladding modes in tapered fiber optics. Based on the effect of the local bending, the linear and nonlinear variations in the refractive index are modeled. A set of equations and parameters are presented in order to calculate the influence of acoustooptic effect in nonlinear pulse propagation. We will show that as the tapered fiber diameter decreases more energy can be transferred to the cladding and the nonlinear phenomena can compensate the coupling coefficients effects.
Multiwave nonlinear couplings in elastic structures
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.
Nonlinearly Coupled Superconducting Lumped Element Resonators
Collodo, Michele C.; Potočnik, Anton; Rubio Abadal, Antonio; Mondal, Mintu; Oppliger, Markus; Wallraff, Andreas
We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust et al., Phys Rev. B 91 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light
Examination of a Theoretical Model of Streaming Potential Coupling Coefficient
Luong, D.T.; Sprik, R.
2014-01-01
Seismoelectric effects and streaming potentials play an important role in geophysical applications. The key parameter for those phenomena is the streaming potential coupling coefficient, which is, for example, dependent on the zeta potential of the interface of the porous rocks. Comparison of an
Analysis of the Coupling Coefficient in Inductive Energy Transfer Systems
Directory of Open Access Journals (Sweden)
Rafael Mendes Duarte
2014-01-01
Full Text Available In wireless energy transfer systems, the energy is transferred from a power source to an electrical load without the need of physical connections. In this scope, inductive links have been widely studied as a way of implementing these systems. Although high efficiency can be achieved when the system is operating in a static state, it can drastically decrease if changes in the relative position and in the coupling coefficient between the coils occur. In this paper, we analyze the coupling coefficient as a function of the distance between two planar and coaxial coils in wireless energy transfer systems. A simple equation is derived from Neumann’s equation for mutual inductance, which is then used to calculate the coupling coefficient. The coupling coefficient is computed using CST Microwave Studio and compared to calculation and experimental results for two coils with an excitation signal of up to 10 MHz. The results showed that the equation presents good accuracy for geometric parameters that do not lead the solution of the elliptic integral of the first kind to infinity.
Scaling properties of weakly nonlinear coefficients in the Faraday problem.
Skeldon, A C; Porter, J
2011-07-01
Interesting and exotic surface wave patterns have regularly been observed in the Faraday experiment. Although symmetry arguments provide a qualitative explanation for the selection of some of these patterns (e.g., superlattices), quantitative analysis is hindered by mathematical difficulties inherent in a time-dependent, free-boundary Navier-Stokes problem. More tractable low viscosity approximations are available, but these do not necessarily capture the moderate viscosity regime of the most interesting experiments. Here we focus on weakly nonlinear behavior and compare the scaling results derived from symmetry arguments in the low viscosity limit with the computed coefficients of appropriate amplitude equations using both the full Navier-Stokes equations and a reduced set of partial differential equations due to Zhang and Vinãls. We find the range of viscosities over which one can expect "low viscosity" theories to hold. We also find that there is an optimal viscosity range for locating superlattice patterns experimentally-large enough that the region of parameters giving stable patterns is not impracticably small, yet not so large that crucial resonance effects are washed out. These results help explain some of the discrepancies between theory and experiment.
Anomaly induced transport coefficients, from weak to strong coupling
Pena-Benitez, Francisco
2013-01-01
The existence of new transport phenomena associated to the presence of quantum anomalies has atracted very recently the attention of theorist. These transport coefficient have very interesting properties, for example, they do not renormalize. The most famous case of anomaly induced transport phenomena is the Chiral Magnetic Effect, in which an electric current is produced by a magnetic field if the system has a different number of right handed fermions respect the left handed one. In this thesis we have studied those transport coefficients from Kubo formulas at weak and strong coupling. To finish a fluid/gravity approach is used to compute all the second order anomalous coefficients in an anomalous conformal fluid.
R. Vlokh; M. Kostyrko
2006-01-01
Nonlinear effect of the gravitation field of spherically symmetric mass on the gravitational coefficient G has been analysed. In frame of the approaches of parametric optics and gravitation nonlinearity we have shown that the gravitation field of spherically symmetric mass can lead to changes in the gravitational coefficient G.
Directory of Open Access Journals (Sweden)
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Labyrinth seal can cause steamexciting,the structural and operating parameters of labyrinth seal have effect on stability of rotorsystem.For investigating the coupling influences of the structure and operating parameters of labyrinth seals on dynamic coefficients,a model of calculating dynamic coefficients of labyrinth seals is presented using a two control volume model.The coupling influences of parameters on crosscoupled stiffness and direct damping of labyrinth seal are discussed.In the conclusion,a reference of pre venting steamexciting vibration and optimum determination of design parameters of labyrinth seals are provided.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FUZun-Tao; LIUShi-Da; LIUShi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Novel Localized Excitations of Nonlinear Coupled Scalar Fields
Institute of Scientific and Technical Information of China (English)
ZHU Ren-Gui; LI Jin-Hua; WANG An-Min; WU Huang-Jiao
2008-01-01
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ4 model are presented. Simultaneously, inspired by the new solutions of the famous φ4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scalar field (NCSF) system are obtained.
Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy
Directory of Open Access Journals (Sweden)
Xiuzhi Xing
2014-01-01
Full Text Available Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.
Nonlinear interaction of meta-atoms through optical coupling
Energy Technology Data Exchange (ETDEWEB)
Slobozhanyuk, A. P.; Kapitanova, P. V.; Filonov, D. S.; Belov, P. A. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Powell, D. A. [Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Shadrivov, I. V.; Kivshar, Yu. S. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Lapine, M., E-mail: mlapine@physics.usyd.edu.au [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia); McPhedran, R. C. [Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia)
2014-01-06
We propose and experimentally demonstrate a multi-frequency nonlinear coupling mechanism between split-ring resonators. We engineer the coupling between two microwave resonators through optical interaction, whilst suppressing the direct electromagnetic coupling. This allows for a power-dependent interaction between the otherwise independent resonators, opening interesting opportunities to address applications in signal processing, filtering, directional coupling, and electromagnetic compatibility.
Examination of a Theoretical Model of Streaming Potential Coupling Coefficient
Directory of Open Access Journals (Sweden)
D. T. Luong
2014-01-01
Full Text Available Seismoelectric effects and streaming potentials play an important role in geophysical applications. The key parameter for those phenomena is the streaming potential coupling coefficient, which is, for example, dependent on the zeta potential of the interface of the porous rocks. Comparison of an existing theoretical model to experimental data sets from available published data for streaming potentials has been performed. However, the existing experimental data sets are based on samples with dissimilar fluid conductivity, pH of pore fluid, temperature, and sample compositions. All those dissimilarities may cause the observed deviations. To critically assess the models, we have carried out streaming potential measurement as a function of electrolyte concentration and temperature for a set of well-defined consolidated samples. The results show that the existing theoretical model is not in good agreement with the experimental observations when varying the electrolyte concentration, especially at low electrolyte concentration. However, if we use a modified model in which the zeta potential is considered to be constant over the electrolyte concentration, the model fits the experimental data well in a whole range of concentration. Also, for temperature dependence, the comparison shows that the theoretical model is not fully adequate to describe the experimental data but does describe correctly the increasing trend of the coupling coefficient as function of temperature.
Variational Problem with Complex Coefficient of a Nonlinear Schrödinger Equation
Indian Academy of Sciences (India)
Nigar Yildirim Aksoy; Bunyamin Yildiz; Hakan Yetiskin
2012-08-01
An optimal control problem governed by a nonlinear Schrödinger equation with complex coefficient is investigated. The paper studies existence, uniqueness and optimality conditions for the control problem.
Institute of Scientific and Technical Information of China (English)
Wei-zhong Dai; Raja Nassar
2000-01-01
A finite difference scheme for the generalized nonlinear Schrodinger equation with variable coefficients is developed. The scheme is shown to satisfy two conser vation laws. Numerical results show that the scheme is accurate and efficient.
Influence of nonlinear chemical reactions on the transport coefficients in oscillatory Couette flow
Barik, Swarup; Dalal, D. C.
2016-10-01
A multiple-scale method of averaging is applied to the study of transport of a chemical species in oscillatory Couette flow where the species may undergoes a reversible phase exchange with the boundary wall and nonlinear chemical reactions both within the fluid and at the boundary wall. Analytical expressions are obtained for transport coefficients. The results shows how the transport coefficients are influenced by the reversible phase exchange reaction kinetics and the rate and degree of the nonlinear decay chemical reaction.
Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable
du Toit, Stephen H. C.; Cudeck, Robert
2009-01-01
A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
Directory of Open Access Journals (Sweden)
Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate ap...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
A modified WTC algorithm for the Painlevé test of nonlinear variable-coefficient PDEs
Zhao, Yin-Long; Liu, Yin-Ping; Li, Zhi-Bin
2009-11-01
A modified WTC algorithm for the Painlevé test of nonlinear PDEs with variable coefficients is proposed. Compared to the Kruskal's simplification algorithm, the modified algorithm further simplifies the computation in the third step of the Painlevé test for variable-coefficient PDEs to some extent. Two examples illustrate the proposed modified algorithm.
Ocean wave nonlinearity and phase couplings
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
Bispectrum of a swell dominated sea state is computed using Fourier coefficients from an original record and from simulated Fourier coefficients using pseudorandom (uniform) phase spectrum. The differences in the bispectra clearly bring out...
Exploring non-linear cosmological matter diffusion coefficients
Velten, Hermano
2014-01-01
Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the nature of the diffusion coefficient $\\sigma$ which measures the magnitude of such transport phenomena. We test dynamics where $\\sigma$ has a phenomenological dependence on the scale factor, the matter density, the dark energy and the expansion rate.
Dynamic nonlinear thermal optical effects in coupled ring resonators
Directory of Open Access Journals (Sweden)
Chenguang Huang
2012-09-01
Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
Directory of Open Access Journals (Sweden)
Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
Evolution of optimal Hill coefficients in nonlinear public goods games.
Archetti, Marco; Scheuring, István
2016-10-07
In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.
Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model
Directory of Open Access Journals (Sweden)
Yue-bao Deng
2016-01-01
Full Text Available A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.
Inertial Force Coupling to Nonlinear Aeroelasticity of Flexible Wing Aircraft
Nguyen, Nhan T.; Ting, Eric
2016-01-01
This paper investigates the inertial force effect on nonlinear aeroelasticity of flexible wing aircraft. The geometric are nonlinearity due to rotational and tension stiffening. The effect of large bending deflection will also be investigated. Flutter analysis will be conducted for a truss-braced wing aircraft concept with tension stiffening and inertial force coupling.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Thermally induced nonlinear mode coupling in high power fiber amplifiers
DEFF Research Database (Denmark)
Johansen, Mette Marie; Hansen, Kristian Rymann; Alkeskjold, Thomas T.;
2013-01-01
Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W.......Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W....
Entanglement Dynamics of Quantum Oscillators Nonlinearly Coupled to Thermal Environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2014-01-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We fin...
Caprio, M A; McCoy, A E; 10.1063/1.3445529
2010-01-01
It is shown that the method of infinitesimal generators ("Racah's method") can be broadly and systematically formulated as a method applicable to the calculation of reduced coupling coefficients for a generic subalgebra chain G>H, provided the reduced matrix elements of the generators of G and the recoupling coefficients of H are known. The calculation of SO(5)>SO(4) reduced coupling coefficients is considered as an example, and a procedure for transformation of reduced coupling coefficients between canonical and physical subalegebra chains is presented. The problem of calculating coupling coefficients for generic irreps of SO(5), reduced with respect to any of its subalgebra chains, is completely resolved by this approach.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Du Wei-Shih
2010-01-01
Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.
Nonlinear feedback control of spatiotemporal chaos in coupled map lattices
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
1998-01-01
Full Text Available We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Measurement of the Third-Order Nonlinear Optical Coefficient of ZnO Crystals by Using ICCD-Z-Scan
Institute of Scientific and Technical Information of China (English)
JIA Guang-Ming; ZHANG Gui-Zhong; XIANG Wang-Hua; J.B.Ketterson
2004-01-01
We present an image-intensified charge-coupled-device (ICCD) version of Z-scan by employing an ICCD detector and fixing the sample at the beam waist, and a measurement of the third-order nonlinear optical coefficient of single crystal zinc oxide (ZnO). The X(3) value of -9.1 × 10-15 cm2/W measured is in agreement with the published result. Our Z-scan configuration of placing sample at beam waist and collecting the whole wavefront by an ICCD detector is simple and can be deployed in cryogenic research where the sample cannot be Z-scanned.
Çakır, Bekir; Yakar, Yusuf; Özmen, Ayhan
2015-02-01
Linear and nonlinear absorption coefficients of two-electron spherical quantum dot (QD) with parabolic potential are investigated in this paper. Wave functions and energy eigenvalues of the 1s2, 1s1p, 1s1d and 1s1f electronic states have been computed by using an optimization approach, which is a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method. It is found that the strength of S→P transition is stronger than P→D and D→F transitions. Also the peak positions and amplitudes of the absorption coefficients are sensitive to the electron spin. It should be noted that the peak positions and amplitudes of absorption coefficients are strongly dependent on the parabolic potential. Additionally, dot radius, impurity charge, incident optical intensity and relaxation time have a great influence on the linear and nonlinear absorption coefficients.
Energy Technology Data Exchange (ETDEWEB)
Çakır, Bekir, E-mail: bcakir@selcuk.edu.tr [Physics Department, Faculty of Science, Selcuk University, Campus 42075, Konya (Turkey); Yakar, Yusuf, E-mail: yuyakar@yahoo.com [Physics Department, Faculty of Arts and Science, Aksaray University, Campus 68100, Aksaray (Turkey); Özmen, Ayhan [Physics Department, Faculty of Science, Selcuk University, Campus 42075, Konya (Turkey)
2015-02-01
Linear and nonlinear absorption coefficients of two-electron spherical quantum dot (QD) with parabolic potential are investigated in this paper. Wave functions and energy eigenvalues of the 1s{sup 2}, 1s1p, 1s1d and 1s1f electronic states have been computed by using an optimization approach, which is a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothaan (HFR) method. It is found that the strength of S→P transition is stronger than P→D and D→F transitions. Also the peak positions and amplitudes of the absorption coefficients are sensitive to the electron spin. It should be noted that the peak positions and amplitudes of absorption coefficients are strongly dependent on the parabolic potential. Additionally, dot radius, impurity charge, incident optical intensity and relaxation time have a great influence on the linear and nonlinear absorption coefficients.
Nonlinear absorption coefficient of pulsed laser deposited MgZnO thin film
Energy Technology Data Exchange (ETDEWEB)
Agrawal, Arpana, E-mail: agrawal.arpana01@gmail.com; Dar, Tanveer A.; Solanki, Ravi; Sen, Pratima [Laser Bhawan, School of Physics, Devi Ahilya University, Khandwa Road, Indore-452001 (India); Phase, D. M. [UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore 452001 (India)
2015-06-24
We report the imaginary part of 3{sup rd} order nonlinear susceptibility and the nonlinear absorption coefficient of Mg doped ZnO thin film using standard Z-scan technique. The origin of nonlinear absorption is attributed to the two photon absorption followed by the free carrier absorption because of the presence of oxygen vacancy defects. We have also confirmed the experimental results with the theoretical results obtained by considering the steady state response of a two level atom with the monochromatic field models.
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Indian Academy of Sciences (India)
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Coupling coefficient for TEA CO2 laser propulsion with variable pulse repetition rate
Institute of Scientific and Technical Information of China (English)
Yijun Zheng; Rongqing Tan; Donglei Wang; Guang Zheng; Changjun Ke; Kuohai Zhang; Chongyi Wan; Jin Wu
2006-01-01
@@ Because pulse repetition rate affected directly the momentum coupling coefficient of transversely excited atmospheric (TEA) CO2 laser propulsion, a double pulse trigger, controlling high voltage switch of laser excitation circuit, was designed. The pulse interval ranged between 5 and 100 ms. The momentum coupling coefficient for air-breathing mode laser propulsion was studied experimentally. It was found that the momentum coupling coefficient decreased with the pulse repetition rate increasing.
Energy Technology Data Exchange (ETDEWEB)
Elnaggar, Sameh Y. [School of Engineering and Information Technology, University of New South Wales, Canberra (Australia); Tervo, Richard J. [Department of Electrical and Computer Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3 Canada (Canada); Mattar, Saba M., E-mail: mattar@unb.ca [Chemistry Department, University of New Brunswick, Fredericton, NB, E3B 5A3 Canada (Canada)
2015-11-21
The theory and operation of various devices and systems, such as wireless power transfer via magnetic resonant coupling, magneto-inductive wave devices, magnetic resonance spectroscopy probes, and metamaterials can rely on coupled tuned resonators. The coupling strength is usually expressed in terms of the coupling coefficient κ, which can have electrical κ{sub E} and/or magnetic κ{sub M} components. In the current article, general expressions of κ are derived. The relation between the complex Poynting equation in its microscopic form and κ is made and discussed in detail. It is shown that κ can be expressed in terms of the interaction energy between the resonators' modes. It thus provides a general form that combines the magnetic and electric components of κ. The expressions make it possible to estimate the frequencies and fields of the coupled modes for arbitrarily oriented and spaced resonators. Thus, enabling the calculation of system specific parameters such as the transfer efficiency of wireless power transfer systems, resonator efficiency for electron spin resonance probes, and dispersion relations of magneto-inductive and stereo-metamaterials structures.
Nonlinear perturbations of systems of partial differential equations with constant coefficients
Directory of Open Access Journals (Sweden)
Carmen J. Vanegas
2000-01-01
Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.
Demetrashvili, Nino; Van den Heuvel, Edwin R.
This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the
Directory of Open Access Journals (Sweden)
Juan Carlos Ceballos V.
2005-10-01
Full Text Available The exact boundary controllability of the higher order nonlinear Schrodinger equation with constant coefficients on a bounded domain with various boundary conditions is studied. We derive the exact boundary controllability for this equation for sufficiently small initial and final states.
Demetrashvili, Nino; Van den Heuvel, Edwin R.
2015-01-01
This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the hetero
ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD
Institute of Scientific and Technical Information of China (English)
1998-01-01
The estimate model for a nonlinear system of squeeze-film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed.
Coupled parametric processes in binary nonlinear photonic structures
Saygin, M Yu
2016-01-01
We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially-broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: 1) single parametric down-conversion, and 2) coupled parametric down-conversion and up-conversion processes. The efficacy of the fields' generation in these examples is analyzed through comparison with the cases of traditional single periodically poled crystal and aperiodic photonic structure, respectively. It has been shown that the relative s...
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
A Coupled Analysis of Nonlinear Sloshing and Ship Motion
Institute of Scientific and Technical Information of China (English)
Shuo Huang; Wenyang Duan; Hao Zhang
2012-01-01
Nonlinear interactions among incident wave,tank-sloshing and floating body coupling motion are investigated.The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory.A robust and stable improved iterative procedure (Yan and Ma,2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion.An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model.A two-dimensional tank model test was performed to identify its validity.The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)'s experimental results,showing fair agreement.Thus,the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.
Asymptotic analysis of a coupled nonlinear parabolic system
Institute of Scientific and Technical Information of China (English)
Lan QIAO; Sining ZHENG
2008-01-01
This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes. Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions in all the previous literature, where the blow-up rates were known as absorption-independent. The results of the paper rely on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present paper shows that the newly observed phenomena of absorption-related blow-up rates should be due to the coupling mechanism, rather than the mixed type nonlinearities.
UV Nano Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
AFRL-AFOSR-JP-TR-2016-0072 UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling Eric Waclawik QUEENSLAND UNIVERSITY OF TECHNOLOGY Final Report 06...Final 3. DATES COVERED (From - To) 03 Feb 2014 to 02 Feb 2016 4. TITLE AND SUBTITLE UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling 5a...CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4056 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S) Eric Waclawik 5d. PROJECT NUMBER 5e. TASK NUMBER 5f
Institute of Scientific and Technical Information of China (English)
GE Jian-Ya; WANG Rui-Min; DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schr(o)dinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.
Nonlinear magnetoplasmons in strongly coupled Yukawa plasmas
Bonitz, M; Ott, T; Kaehlert, H; Hartmann, P
2010-01-01
The existence of plasma oscillations at multiples of the magnetoplasmon frequency in a strongly coupled two-dimensional magnetized Yukawa plasma is reported, based on extensive molecular dynamics simulations. These modes are the analogues of Bernstein modes which are renormalized by strong interparticle correlations. Their properties are theoretically explained by a dielectric function incorporating the combined effect of a magnetic field, strong correlations and finite temperature.
Wang, Y. B.; Xu, Y.; Zhang, Y.; Song, G. F.; Chen, L. H.
2012-12-01
We calculated the coupling coefficient of different types of laterally coupled distributed feedback (LC-DFB) structures with coupled-wave theory and the two-dimensional semivectorial finite difference method. Effects neglected in previous studies such as other partial waves, the ohmic contact and metal contact layers are taken into account in this calculation. The LC-DFB structure with metal gratings is especially studied due to its advantage over index-coupled structures. The dependence of coupling coefficient on structure parameters is theoretically calculated such as grating order, ridge width, thickness of the residual cladding layer, grating depth and lateral proximity of gratings to the ridge waveguide. A complex-coupled GaSb-based 2 µm LC-DFB structure is optimized to achieve a high coupling coefficient of 14.5 cm-1.
On separation of exchange term from the coefficient of the magnetoelectromechanical coupling
Indian Academy of Sciences (India)
ZAKHARENKO A A
2016-06-01
The purpose of this analysis is to introduce the separated exchange coefficient and to graphically investigate it. This coefficient, depending on the electromagnetic constant plus two coefficients of the electromechanical and magnetomechanical couplings, form the coefficient of magnetoelectromechanical coupling (CMEMC), a very important characteristic used for analysingmagnetoelectroelastic smart (composite) materials. It was analytically and graphically demonstrated that the CMEMC can have a minimum due to the minimum of the exchange coefficient at a certain value of the electromagnetic constant. For graphical investigation, the frequently used transverselyisotropic (6$mm$) composite materials such as BaTiO$_3$–CoFe$_2$O$_4$ and PZT–5H–Terfenol–D are exploited.
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Directory of Open Access Journals (Sweden)
Zhengduo Shan
2014-01-01
Full Text Available With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Zhengduo Shan; Hongwei Yang; Baoshu Yin
2014-01-01
With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
Institute of Scientific and Technical Information of China (English)
CAO Zheng-rui; HONG Yan-ji; WEN Ming
2009-01-01
A dimensionless factor was introduced to deduce the analytic expression of impulse coupling coefficient for conical nozzles in the case of spherical symmetry, and a high precision impact pendulum system was used to measure impulse coupling coefficients of 15 conical nozzles with different cone angles and lengths. The expression was corrected according to experi-mental values. The results indicate that: 1) impulse coupling coefficient increases firstly and then decreases with augment of dimensionless length when cone angle is fixed;2) impulse coupling coefficient decreases monotonously with augment of cone angle when dimensionless length is fixed;3) it is of great importance for improving impulse coupling coefficient to increase the rate of laser energy deposition.
Dilaton black holes coupled to nonlinear electrodynamic field
Sheykhi, A
2015-01-01
The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In ...
Redox Couples with Unequal Diffusion Coefficients: Effect on Redox Cycling
Mampallil Augustine, Dileep; Mathwig, Klaus; Kang, Shuo; Lemay, Serge G.
2013-01-01
Redox cycling between two electrodes separated by a narrow gap allows dramatic amplification of the faradaic current. Unlike conventional electrochemistry at a single electrode, however, the mass-transport-limited current is controlled by the diffusion coefficient of both the reduced and oxidized fo
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
Energy Technology Data Exchange (ETDEWEB)
Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Exact periodic solution in coupled nonlinear Schrodinger equations
Institute of Scientific and Technical Information of China (English)
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
On the recovering of a coupled nonlinear Schroedinger potential
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx
2000-04-28
We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)
Nonlinear Observers for Gyro Calibration Coupled with a Nonlinear Control Algorithm
Thienel, Julie; Sanner, Robert M.
2003-01-01
Nonlinear observers for gyro calibration are presented. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The observers are then combined. The convergence properties of all three observers, and the combined observers, are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. Simulated test results are presented for each system.
Indian Academy of Sciences (India)
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
Directory of Open Access Journals (Sweden)
Jialin Wang
2013-01-01
Full Text Available This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group ℍn. Based on a generalization of the technique of -harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.
Boundary control of nonlinear coupled heat systems using backstepping
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
Nonlinear simulations of the convection-pulsation coupling
Gastine, T
2011-01-01
In cold Cepheids close to the red edge of the classical instability strip, a strong coupling between the stellar pulsations and the surface convective motions occurs. This coupling is by now poorly described by 1-D models of convection, the so-called "time-dependent convection models" (TDC). The intrinsic weakness of such models comes from the large number of unconstrained free parameters entering in the description of turbulent convection. A way to overcome these limits is to compute two-dimensional direct simulations (DNS), in which all the nonlinearities are correctly solved. Two-dimensional DNS of the convection-pulsation coupling are presented here. In an appropriate parameter regime, convective motions can actually quench the radial pulsations of the star, as suspected in Cepheids close to the red edge of the instability strip. These nonlinear simulations can also be used to determine the limits and the relevance of the TDC models.
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
Application of Exp-function method for nonlinear evolution equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A.; Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Faculty of Education for Girls, Physics Department, King Kahlid University, Bisha, Kingdom Saudi Arabia (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com
2007-09-10
In this Letter, the Exp-function method with the aid of symbolic computational system Maple is used to obtain generalized solitary solutions and periodic solutions of a generalized Zakharov-Kuznetsov equation with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.
Rogue wave solutions of the nonlinear Schrödinger eqution with variable coefficients
Indian Academy of Sciences (India)
Changfu Liu; Yan Yan Li; Meiping Gao; Zeping Wang; Zhengde Dai; Chuanjian Wang
2015-12-01
In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time and several arbitrary parameters are involved to generate a large number of wave structures.
A New Variable-Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations
Directory of Open Access Journals (Sweden)
Fanwei Meng
2013-01-01
Full Text Available We propose a new variable-coefficient Riccati subequation method to establish new exact solutions for nonlinear differential-difference equations. For illustrating the validity of this method, we apply it to the discrete (2 + 1-dimensional Toda lattice equation. As a result, some new and generalized traveling wave solutions including hyperbolic function solutions, trigonometric function solutions, and rational function solutions are obtained.
Measurement of nonlinear coefficient of optical fiber based on small chirped soliton transmission
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
We measure the waveform and phase curves of short optical pulses before and after transmission over different lengths of fibers by use of the pulse analyzer with the frequency-resolved optical gating (FROG),and numerically simulate pulse evolution under the experimental conditions.The nonlinear coefficient of the fiber is given by comparing the experimental results with the numerical ones.Difference between the experiment and numerical simulation is analyzed.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs. The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.
Directory of Open Access Journals (Sweden)
Ćosić Mladen
2015-01-01
Full Text Available The paper deals with methodology developed and presented for analyzing the damage on structures exposed to accidental and seismic actions. The procedure is based on non-linear numerical analysis, taking into account the principles of Performance-Based Seismic Design (PBSD. The stiffness matrix of the effects of vertical action is used as the initial stiffness matrix in non-linear analysis which simulates the collapse of individual ground-floor columns, forming thereby a number of possible scenarios. By the end of the analysis that simulates the collapse of individual columns, the stiffness matrix is used as the initial stiffness matrix for Non-linear Static Pushover Analysis (NSPA of bi-directional seismic action (X and Y directions. Target displacement analyses were conducted using the Capacity Spectrum Method (CSM. The structure's conditions/state was assessed based on the calculated global and inter-storey drifts and the damage coefficient developed. The damage level to the building was established using an integrated approach based on global and inter-storey drifts, so that, depending on the level of displacements for which the drifts are identified, a more reliable answer can be obtained. Applying the damage coefficient, a prompt, reliable and accurate indication can be obtained on the damage level to the entire structure in the capacitive domain, from elastic and non-linear to collapse state.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Nonlinear coupled dynamics analysis of a truss spar platform
Li, Cheng-xi; Zhang, Jun
2016-12-01
Accurate prediction of the offshore structure motion response and associate mooring line tension is important in both technical applications and scientific research. In our study, a truss spar platform, operated in Gulf of Mexico, is numerically simulated and analyzed by an in-house numerical code `COUPLE'. Both the platform motion responses and associated mooring line tension are calculated and investigated through a time domain nonlinear coupled dynamic analysis. Satisfactory agreement between the simulation and corresponding field measurements is in general reached, indicating that the numerical code can be used to conduct the time-domain analysis of a truss spar interacting with its mooring and riser system. Based on the comparison between linear and nonlinear results, the relative importance of nonlinearity in predicting the platform motion response and mooring line tensions is assessed and presented. Through the coupled and quasi-static analysis, the importance of the dynamic coupling effect between the platform hull and the mooring/riser system in predicting the mooring line tension and platform motions is quantified. These results may provide essential information pertaining to facilitate the numerical simulation and design of the large scale offshore structures.
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Institute of Scientific and Technical Information of China (English)
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
Directory of Open Access Journals (Sweden)
R. Naz
2011-01-01
Full Text Available We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
Heat and mass transfer across phase boundaries: Estimates of coupling coefficients
Directory of Open Access Journals (Sweden)
Bedeaux, Dick
2008-02-01
Full Text Available Heat and mass transport across phase boundaries are central in many engineering problems. The systematic description offered by classical non-equilibrium thermodynamics theory, when extended to surfaces, gives the interaction between the two fluxes in terms of coupling coefficients. It is shown in this paper that these coupling coefficients are large. The few experimental and computational results that are available confirm this. Neglect of coupling coefficients, which is common in most models for surface transport, may lead to errors in the heat flux. We present values for the coupling coefficient in a one-component system in terms of the heat of transfer, as obtained from non-equilibrium molecular dynamics simulations, kinetic theory and the integrated non-equilibrium van der Waals' square gradient model.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-03-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion.
Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks
Directory of Open Access Journals (Sweden)
Chengrong Xie
2013-01-01
Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.
Global solution for coupled nonlinear Klein-Gordon system
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2007-01-01
The global solution for a coupled nonlinear Klein-Gordon system in twodimensional space was studied.First,a sharp threshold of blowup and global existenoe for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.
Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.;
2011-01-01
The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when...... nonlinear model....
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
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...
Study on electromechanical coupling nonlinear vibration of flywheel energy storage system
Institute of Scientific and Technical Information of China (English)
JIANG; Shuyun
2006-01-01
The electromechanical coupling dynamics of the flywheel energy storage system (FESS) with a hybrid permanent magnetic-dynamic spiral groove bearing has been studied. The functions of the kinetic energy, the potential energys, the magnetic field energy in air gap of the flywheel motor and the energy dissipation of the whole system were obtained, and the differential equations set with electromagnetic parameters of FESS was established by applying the extended Lagrange-Maxwell equation. The four-order implicit Runge-Kutta formula to the equations was derived, and the nonlinear algebraic equations were solved by using the Gauss-Newton method. The analytical solution of an example shows that the upper damping coefficient, the lower damping coefficient and the residual magnetic induction of the rare earth permanent magnet play an important role in electromechanical resonance of the flywheel rotor system. There is a small change for the electromechanical coupling resonance frequency with the upper damping coefficient increasing, but the resonance amplitude decreases with the upper damping coefficient increasing. With the lower damping coefficient increasing, the resonance frequency increases, and the resonance amplitude decreases. With the residual magnetic induction of the permanent magnet increasing, the resonance frequency decreases, and the resonance amplitude increases.
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
Measurement of nonlinear coefficient and phase matching characteristics of AgGaS sub 2
Energy Technology Data Exchange (ETDEWEB)
Canarelli, P.; Benko, Z.; Hielscher, A.H.; Curl, R.F.; Tittle, F.K. (Dept. of Electrical and Computer Engineering, Rice Quantum Inst., Rice Univ., Houston, TX (US))
1992-01-01
This paper reports on a nonlinear optical characteristics of AgGaS{sub 2} that were investigated by measuring visible parametric fluorescence with a pump wavelength of 600 nm. A value of d{sub 36}(AgGaS{sub 2}) = 31 {plus minus} 5 10{sup {minus}12} m/V for the nonlinear coefficient was determined. The temperature dependence of phase matching up to 100{degrees}C was studied. A significant temperature effect, although much smaller than the LiNbO{sub 3}, was found and results in a change in the infrared difference frequency generated of {approximately}0.6 cm{sup {minus}1} {center dot} {degrees}C{sup {minus}1}.
A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search
Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd
2017-08-01
A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.
Dynamic coefficients of axial spline couplings in high-speed rotating machinery
Energy Technology Data Exchange (ETDEWEB)
Ku, C.P.R.; Walton, J.F. Jr. (Mechanical Technology Inc., Latham, NY (United States)); Lund, J.W. (Technical Univ. of Denmark, Lyngby (Denmark). Dept. of Machine Elements)
1994-07-01
This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating shaft was excited by an external shaker. A rotordynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. The effects of external force and frequency were also investigated. The angular stiffness and damping coefficients were used to perform a linear steady-state rotordynamics stability analysis, and the unstable natural frequency was calculated and compared to the experimental measurements.
Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients.
Ge, Shuzhi Sam; Hong, Fan; Lee, Tong Heng
2004-02-01
In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.
Experiments on oscillator ensemble with global nonlinear coupling
Rosenblum, Michael; Temirbayev, Amirkhan; Zhanabaev, Zeinulla; Tarasov, Stanislav; Ponomarenko, Vladimir
2012-02-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a linear or nonlinear phase-shifting unit in the global feedback loop. With linear unit we observe, with increase of the coupling strength, a standard Kuramoto-like transition to a fully synchronous state; the threshold of the transition depends on the phase shift. In case of nonlinear global coupling we first observe a transition to a state when approximately half of the population forms a synchronous cluster. With further increase of the coupling strength we observe destruction of this cluster and formation of a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. The transition is characterized by a non-monotonic dependence of the order parameter on the coupling strength. We demonstrate a good correspondence between theory and experiment.
Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling
Zheng, Song; Wang, Shuguo; Dong, Gaogao; Bi, Qinsheng
2012-01-01
This paper investigates the adaptive synchronization between two nonlinearly delay-coupled complex networks with the bidirectional actions and nonidentical topological structures. Based on LaSalle's invariance principle, some criteria for the synchronization between two coupled complex networks are achieved via adaptive control. To validate the proposed methods, the unified chaotic system as the nodes of the networks are analyzed in detail, and numerical simulations are given to illustrate the theoretical results.
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco
2015-11-01
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Light-enhanced electron-phonon coupling from nonlinear electron-phonon coupling
Sentef, M. A.
2017-05-01
We investigate an exact nonequilibrium solution of a two-site electron-phonon model, where an infrared-active phonon that is nonlinearly coupled to the electrons is driven by a laser field. The time-resolved electronic spectrum shows coherence-incoherence spectral weight transfer, a clear signature of light-enhanced electron-phonon coupling. The present study is motivated by recent evidence for enhanced electron-phonon coupling in pump-probe terahertz and angle-resolved photoemission spectroscopy in bilayer graphene when driven near resonance with an infrared-active phonon mode [E. Pomarico et al., Phys. Rev. B 95, 024304 (2017), 10.1103/PhysRevB.95.024304], and by a theoretical study suggesting that transient electronic attraction arises from nonlinear electron-phonon coupling [D. M. Kennes et al., Nat. Phys. 13, 479 (2017), 10.1038/nphys4024]. We show that a linear scaling of light-enhanced electron-phonon coupling with the pump field intensity emerges, in accordance with a time-nonlocal self-energy based on a mean-field decoupling using quasiclassical phonon coherent states. Finally, we demonstrate that this leads to enhanced double occupancies in accordance with an effective electron-electron attraction. Our results suggest that materials with strong phonon nonlinearities provide an ideal playground to achieve light-enhanced electron-phonon coupling and possibly light-induced superconductivity.
Higher-order spectra for identification of nonlinear modal coupling
Hickey, Daryl; Worden, Keith; Platten, Michael F.; Wright, Jan R.; Cooper, Jonathan E.
2009-05-01
Over the past four decades considerable work has been done in the area of power spectrum estimation. The information contained within the power spectrum relates to a signal's autocorrelation or 'second-order statistics'. The power spectrum provides a complete statistical description of a Gaussian process; however, a problem with this information is that it is phase blind. This problem is addressed if one turns to a system's frequency response function (FRF). The FRF graphs the magnitude and phase of the frequency response of a system; in order to do this it requires information regarding the frequency content of the input and output signals. Situations arise in science and engineering whereby signal analysts are required to look beyond second-order statistics and analyse a signal's higher-order statistics (HOS). HOS or spectra give information on a signal's deviation from Gaussianity and consequently are a good indicator function for the presence of nonlinearity within a system. One of the main problems in nonlinear system identification is that of high modal density. Many modelling schemes involve making some expansion of the nonlinear restoring force in terms of polynomial or other basis terms. If more than one degree-of-freedom is involved this becomes a multivariate problem and the number of candidate terms in the expansion grows explosively with the order of nonlinearity and the number of degrees-of-freedom. This paper attempts to use HOS to detect and qualify nonlinear behaviour for a number of symmetrical and asymmetrical systems over a range of degrees-of-freedom. In doing so the paper also attempts to show that HOS are a more sensitive tool than the FRF in detecting nonlinearity. Furthermore, the object of this paper is to try and identify which modes couple in a nonlinear manner in order to reduce the number of candidate coupling terms, for a model, as much as possible. The bispectrum method has previously been applied to simple low-DOF systems with high
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.
2011-11-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It has been proved that there exists a cross coupling between vertical heat turbulent transport and vertical velocity by using linear thermodynamics. This result asserts that the vertical component of heat turbulent transport flux is composed of both the transport of the vertical potential temperature gralient and the coupling transport of the vertical velocity. In this paper, the coupling effect of vertical velocity on vertical heat turbulent transportation is validated by using observed data from the atmospheric boundary layer to determine cross coupling coefficients, and a series of significant properties of turbulent transportation are opened out. These properties indicate that the cross coupling coefficient is a logarithm function of the dimensionless vertical velocity and dimensionless height, and is not only related to the friction velocity u*,but also to the coupling roughness height zwo and the coupling temperature Two of the vertical velocity.In addition, the function relations suggest that only when the vertical velocity magnitude conforms to the limitation |W/u* | ≠ 1, and is above the level zwo, then the vertical velocity leads to the cross coupling effect on the vertical heat turbulent transport flux. The cross coupling theory and experimental results provide a challenge to the traditional turbulent K closure theory and the Monin-Obukhov similarity theory.
Nonlinear electrodynamics coupled to teleparallel theory of gravity
Institute of Scientific and Technical Information of China (English)
Gamal G. L. Nashed
2011-01-01
Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy-momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy-momentum we obtain the value of energy.
Nonlinear localized flatband modes with spin-orbit coupling
Gligorić, G; Hadžievski, Lj; Flach, S; Malomed, B
2016-01-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's bandgap structure, and preserves the existence of CLSs at the flatband frequency, simultaneously lowering their symmetry. Adding onsite cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies which are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Rotating Dilaton Black Strings Coupled to Exponential Nonlinear Electrodynamics
Directory of Open Access Journals (Sweden)
Ahmad Sheykhi
2014-01-01
Full Text Available We construct a new class of charged rotating black string solutions coupled to dilaton and exponential nonlinear electrodynamic fields with cylindrical or toroidal horizons in the presence of a Liouville-type potential for the dilaton field. Due to the presence of the dilaton field, the asymptotic behaviors of these solutions are neither flat nor (AdS. We analyze the physical properties of the solutions in detail. We compute the conserved and thermodynamic quantities of the solutions and verify the first law of thermodynamics on the black string horizon. When the nonlinear parameter β2 goes to infinity, our results reduce to those of black string solutions in Einstein-Maxwell-dilaton gravity.
Unconventional Hamilton-type variational principles for nonlinear coupled thermoelastodynamics
Institute of Scientific and Technical Information of China (English)
罗恩; 邝君尚; 黄伟江; 罗志国
2002-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometrically nonlinear coupled thermoelastodynamics can be established system atically. The new unconventional Hamilton-type variational principle can fully characterize the initia boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlin ear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of vir tual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton type variational principles by the generalized Legendre transformations given in this paper. Further more, with this approach, the intrinsic relationship among various principles can be explained clearly.
Instability of coupled geostrophic density fronts and its nonlinear evolution
Scherer, Emilie; Zeitlin, Vladimir
Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.
Institute of Scientific and Technical Information of China (English)
JIANG Zhi-ping
2012-01-01
With the help of the variable-coefficient generalized projected Ricatti equation expansion method,we present exact solutions for the generalized (2+1)-dimensional nonlinear Schr(o)dinger equation with variable coefficients.These solutions include solitary wave solutions,soliton-like solutions and trigonometric function solutions.Among these solutions,some are found for the first time.
Indian Academy of Sciences (India)
Hussain A Badran; Alaa Y Al-Ahmad; Qusay M Ali Hassan; Chassib A Emshary
2016-01-01
The optical properties of Violet 1-doped polyvinyl alcohol (PVA) have been investigated using Wemble and Didomenico (WD) method. The optical constants such as refractive index , the dispersion energy , the oscillation energy 0, the lattice dielectric constant ∞, light frequency dielectric constant 0 and the ratio of carrier concentration to the effective mass /* have been determined using reflection spectra in the wavelength range 300–900 nm. The singlebeam Z-scan technique was used to determine the nonlinear optical properties of Violet 1:polyvinylalcohol (PVA) thin film. The experiments were performed using continuous wave (cw) laser with a wavelength of 635 nm. The calculated nonlinear refractive index of the film, $n_{2} = -2.79 \\times 10^{-7}$ cm2/Wand nonlinear absorption coefficient, $\\beta = 6.31\\times10^{−3}$ cm/W. Optical limiting characteristics of the dye-doped polymer film was studied. The result reveals that Violet 1 can be a promising material for optical limiting applications.
Demetrashvili, Nino; Van den Heuvel, Edwin R
2015-06-01
This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the heterogeneity across studies. To interpret the size of heterogeneity, an accurate estimate of ICC and its confidence interval is required. The goal is to apply a recently proposed generic beta-approach for construction the confidence intervals on ICCs for linear mixed effects models to nonlinear mixed effects models using four estimation methods. These estimation methods are the maximum likelihood, second-order generalized estimating equations and two two-step procedures. The beta-approach is compared with a large sample normal approximation (delta method) and bootstrapping. The confidence intervals based on the delta method and the nonparametric percentile bootstrap with various resampling strategies failed in our settings. The beta-approach demonstrates good coverages with both two-step estimation methods and consequently, it is recommended for the computation of confidence interval for ICCs in nonlinear mixed effects models for small studies.
A Finite Mixture of Nonlinear Random Coefficient Models for Continuous Repeated Measures Data.
Kohli, Nidhi; Harring, Jeffrey R; Zopluoglu, Cengiz
2016-09-01
Nonlinear random coefficient models (NRCMs) for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development (or growth) over time in measured variables. As an extension of this model, this study considers the finite mixture of NRCMs that combine features of NRCMs with the idea of finite mixture (or latent class) models. The efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations, thus allowing the simultaneous investigation of intra-individual (within-person) variability, inter-individual (between-person) variability, and subpopulation heterogeneity. Effectiveness of this model to work under real data analytic conditions was examined by executing a Monte Carlo simulation study. The simulation study was carried out using an R routine specifically developed for the purpose of this study. The R routine used maximum likelihood with the expectation-maximization algorithm. The design of the study mimicked the output obtained from running a two-class mixture model on task completion data.
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.
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.
Nonlinear thermoelectric properties of molecular junctions with vibrational coupling
DEFF Research Database (Denmark)
Leijnse, Martin Christian; Wegewijs, M. R.; Flensberg, Karsten
2010-01-01
We present a detailed study of the nonlinear thermoelectric properties of a molecular junction, represented by a dissipative Anderson-Holstein model. A single-orbital level with strong Coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon...... exchange with both electrodes, investigating how these contribute to the heat and charge transports. We calculate the efficiency and power output of the device operated as a heat to electric power converter in the regime of weak tunnel coupling and phonon exchange rate and identify the optimal operating...... conditions, which are found to be qualitatively changed by the presence of the vibrational mode. Based on this study of a generic model system, we discuss the desirable properties of molecular junctions for thermoelectric applications....
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
Nonlinear coupling analysis of coal seam floor during mining based on FLAC3D
Institute of Scientific and Technical Information of China (English)
YAO Duo-xi; XU Ji-ying; LU Hai-feng
2011-01-01
Based on the hydro-geological conditions of 1028 mining face in Suntuan Coal Mine, mining seepage strain mechanism of seam floor was simulated by a nonlinear coupling method, which applied fluid-solid coupling analysis module of FLAC3D. The results indicate that the permeability coefficient of adjoining rock changes a lot due to mining. The maximum value reaches 1 379.9 times to the original value, where it is at immediate roof of the mined-out area. According to the analysis on the seepage field, mining does not destroy water resistance of the floor aquiclude. The mining fissure does not conduct lime-stone aquifer, and it is less likely to form damage. The plastic zone does not exactly correspond to the seepage area, and the scope of the altered seepage area is much larger than the plastic zone.
On the average uncertainty for systems with nonlinear coupling
Nelson, Kenric P.; Umarov, Sabir R.; Kon, Mark A.
2017-02-01
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions. The Shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities. For the exponential and Gaussian distributions, we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale (i.e. at the width of the distribution). The average uncertainty is generalized via the weighted generalized mean, in which the moment is a function of the nonlinear source. Both the Rényi and Tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain. For the generalized Pareto and Student's t-distributions, which are the maximum entropy distributions for these generalized entropies, the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale. A coupled entropy function is proposed, which is equal to the normalized Tsallis entropy divided by one plus the coupling.
Experiments on oscillator ensembles with global nonlinear coupling
Temirbayev, Amirkhan A.; Zhanabaev, Zeinulla Zh.; Tarasov, Stanislav B.; Ponomarenko, Vladimir I.; Rosenblum, Michael
2012-01-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.064101 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient
Directory of Open Access Journals (Sweden)
John D. Towers
2002-10-01
Full Text Available We study the Cauchy problem for the nonlinear (possibly strongly degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(xf(u=partial_x^2 A(u, quad A'(cdotge 0, $$ where the coefficient $gamma(x$ is possibly discontinuous and $f(u$ is genuinely nonlinear, but not necessarily convex or concave. Existence of a weak solution is proved by passing to the limit as $varepsilondownarrow 0$ in a suitable sequence ${u_{varepsilon}}_{varepsilon>0}$ of smooth approximations solving the problem above with the transport flux $gamma(xf(cdot$ replaced by $gamma_{varepsilon}(xf(cdot$ and the diffusion function $A(cdot$ replaced by $A_{varepsilon}(cdot$, where $gamma_{varepsilon}(cdot$ is smooth and $A_{varepsilon}'(cdot>0$. The main technical challenge is to deal with the fact that the total variation $|u_{varepsilon}|_{BV}$ cannot be bounded uniformly in $varepsilon$, and hence one cannot derive directly strong convergence of ${u_{varepsilon}}_{varepsilon>0}$. In the purely hyperbolic case ($A'equiv 0$, where existence has already been established by a number of authors, all existence results to date have used a singular maolinebreak{}pping to overcome the lack of a variation bound. Here we derive instead strong convergence via a series of a priori (energy estimates that allow us to deduce convergence of the diffusion function and use the compensated compactness method to deal with the transport term. Submitted April 29, 2002. Published October 27, 2002. Math Subject Classifications: 35K65, 35D05, 35R05, 35L80 Key Words: Degenerate parabolic equation; nonconvex flux; weak solution; discontinuous coefficient; viscosity method; a priori estimates; compensated compactness
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.
Yan, Zhenya
2013-01-01
The higher-order dispersive and nonlinear effects (alias {\\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse propagation. We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schr\\"odinger (NLS) equation with space- and time-modulated parameters. A proper transformation is presented to reduce the generalized higher-order NLS equation to the integrable Hirota equation with constant coefficients. This transformation allows us to relate certain class of exact solutions of the generalized higher-order NLS equation to the variety of solutions of the integrable Hirota equation. In particular, we illustrate the approach in terms of two lowest-order rational solutions of the Hirota equation as seeding functions to generate rogue wave solutions localized in time that have complicated evolution in space with or without the differential gain or lo...
Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft
Su, Weihua
This dissertation introduces an approach to effectively model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircraft. A reduced-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in preliminary vehicle design and control synthesis. The cross-sectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the one-dimensional nonlinear beam formulation. Finite-state unsteady subsonic aerodynamics is used to compute airloads along lifting surfaces. Flight dynamic equations are then introduced to complete the aeroelastic/flight dynamic system equations of motion. Instead of merely considering the flexibility of the wings, the current work allows all members of the vehicle to be flexible. Due to their characteristics of being slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. New kinematic relationships are developed to handle the split beam systems, such that fully flexible vehicles can be effectively modeled within the existing framework. Different aircraft configurations are modeled and studied, including Single-Wing, Joined-Wing, Blended-Wing-Body, and Flying-Wing configurations. The Lagrange Multiplier Method is applied to model the nodal displacement constraints at the joint locations. Based on the proposed models, roll response and stability studies are conducted on fully flexible and rigidized models. The impacts of the flexibility of different vehicle members on flutter with rigid body motion constraints, flutter in free flight condition, and roll maneuver performance are presented. Also, the static stability of the compressive member of the Joined-Wing configuration is studied. A spatially-distributed discrete gust model is incorporated into the time simulation
A method to fast determine the coupling coefficients in CI calculation
Institute of Scientific and Technical Information of China (English)
甘正汀; 苏克和; 王育邠; 文振翼
1999-01-01
A new algorithm for evaluating the coupling coefficients and the addresses of molecular integrals in configuration interaction (CI) calculations is presented, which leads to an improved CI calculation program CGUGA. The validity and efficiency of the new code are compared with other programs, such as MELD and GAUSSIAN-94.
EXPLICIT SOLUTIONS TO THE COUPLED KdV EQUATIONS WITH VARIABLE COEFFICIENTS
Institute of Scientific and Technical Information of China (English)
徐桂琼; 李志斌
2005-01-01
By means of sn-function expansion method and cn-function expansion method,several kinds of explicit solutions to the coupled KdV equations with variable coefficients are obtained, which include three sets of periodic wave-like solutions. These solutions degenerate to solitary wave-like solutions at a certain limit. Some new solutions are presented.
ELECTRICAL AND DYNAMIC BRAKING OF THE HYBRID VEHICLE ON THE ROADS WITH LOW COUPLING COEFFICIENT
Directory of Open Access Journals (Sweden)
Sitovskyi, O.
2013-06-01
Full Text Available There were carried out theoretical researches of the processes of the electrical and dynamic braking of the vehicle with hybrid power-plant on the roads with low coupling coefficient, it was proved the probability of the wheels blocking appearing, during electrical and dynamic braking.
Indian Academy of Sciences (India)
EMRULLAH YA¸SAR; YAKUP YILDIRIM; ILKER BURAK GIRESUNLU
2016-08-01
Fin materials can be observed in a variety of engineering applications. They are used to ease the dissipation of heat from a heated wall to the surrounding environment. In this work, we consider a nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The equation(s) under study are highly nonlinear. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. Firstly, we consider the Lie group analysis for different cases of thermal conductivity and the heat transfer coefficients. These classifications are obtained from the Lie group analysis. Then, the first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether’s classical method, partial Noether approach and Ibragimov’s nonlocal conservation method. Some exact analytical solutions are also constructed. The obtained result is also compared with the result obtained by other methods.
Iacocca, Ezio
2012-01-01
Modulation of Spin Torque Oscillators (STOs) is investigated by analytically solving the time-dependent coupled equations of an auto-oscillator. A Fourier series solution is proposed, leading to the coefficients being determined with a linear set of equations, from which a Nonlinear Amplitude and Frequency Modulation (NFAM) scheme is obtained. In this framework, the NFAM features are related to the intrinsic STO parameters, revealing a frequency-dependence of the harmonic-dependent modulation index that allows a modulation bandwidth to be defined for these devices. The presented results expose a rich parameter space, where the modulation and the STO's operation conditions define the observed modulation features. The Fourier-series representation of the time signal is suitable for studying periodic perturbations on the auto-oscillator equation.
Institute of Scientific and Technical Information of China (English)
Liu Xiao-Bei; Li Biao
2011-01-01
We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters.Different shapes of bright solitons,a train of bright solitons and dark solitons are observed.The obtained results may raise the possibilities of relevant experiments and potential applications.
Yang, T C
2014-02-01
This paper applies the mode coupling equation to calculate the mode-coupling matrix for nonlinear internal waves appearing as a train of solitons. The calculation is applied to an individual soliton up to second order expansion in sound speed perturbation in the Dyson series. The expansion is valid so long as the fractional sound speed change due to a single soliton, integrated over range and depth, times the wavenumber is smaller than unity. Scattering between the solitons are included by coupling the mode coupling matrices between the solitons. Acoustic fields calculated using this mode-coupling matrix formulation are compared with that obtained using a parabolic equation (PE) code. The results agree very well in terms of the depth integrated acoustic energy at the receivers for moving solitary internal waves. The advantages of using the proposed approach are: (1) The effects of mode coupling can be studied as a function of range and time as the solitons travel along the propagation path, and (2) it allows speedy calculations of sound propagation through a packet or packets of solitons saving orders of magnitude computations compared with the PE code. The mode coupling theory is applied to at-sea data to illustrate the underlying physics.
Elementary Superconductivity in Nonlinear Electrodynamics Coupled to Gravity
Dymnikova, Irina
2015-01-01
Source-free equations of nonlinear electrodynamics minimally coupled to gravity admit regular axially symmetric asymptotically Kerr-Newman solutions which describe charged rotating black holes and electromagnetic spinning solitons (lumps). Asymptotic analysis of solutions shows, for both black holes and solitons, the existence of de Sitter vacuum interior which has the properties of a perfect conductor and ideal diamagnetic and displays superconducting behaviour which can be responsible for practically unlimited life time of an object. Superconducting current flows on the equatorial ring replacing the Kerr ring singularity of the Kerr-Newman geometry. Interior de Sitter vacuum supplies the electron with the finite positive electromagnetic mass related the interior de Sitter vacuum of the electroweak scale and to breaking of space-time symmetry, which allows to explain the mass-square differences for neutrino and the appearance of the minimal length scale in the annihilation reaction $e^{+}e^{-}\\rightarrow\\gam...
Nonlinear Dynamic Reliability of Coupled Stay Cables and Bridge Tower
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Nonlinear vibration can cause serious problems in long span cable-stayed bridges. When the internal resonance threshold is reached between the excitation frequency and natural frequency,large amplitudes occur in the cable. Based on the current situation of lacking corresponding constraint criteria, a model was presented for analyzing the dynamic reliability of coupling oscillation between the cable and tower in a cable-stayed bridge. First of all, in the case of cable sag, the d'Alembert principle is applied to studying the nonlinear dynamic behavior of the structure, and resonance failure interval of parametric oscillation is calculated accordingly. Then the dynamic reliability model is set up using the JC method. An application of this model has been developed for the preliminary design of one cable-stayed bridge located on Hai River in Tianjin, and time histories analysis as well as reliability indexes have been obtained. When frequency ratio between the cable and tower is approaching 1∶2, the reliability index is 0.98, indicating high failure probability. And this is consistent with theoretical derivation and experimental results in reference. This model, which is capable of computing the reliability index of resonance failure, provides theoretical basis for the establishment of corresponding rule.
Color image encryption based on Coupled Nonlinear Chaotic Map
Energy Technology Data Exchange (ETDEWEB)
Mazloom, Sahar [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: sahar.mazloom@gmail.com; Eftekhari-Moghadam, Amir Masud [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: eftekhari@qazviniau.ac.ir
2009-11-15
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
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.
Study of the effect of loop inductance on the RF transmission line to cavity coupling coefficient.
Lal, Shankar; Pant, K K
2016-08-01
Coupling of RF power is an important aspect in the design and development of RF accelerating structures. RF power coupling employing coupler loops has the advantage of tunability of β, the transmission line to cavity coupling coefficient. Analytical expressions available in literature for determination of size of the coupler loop using Faraday's law of induction show reasonably good agreement with experimentally measured values of β below critical coupling (β ≤ 1) but show large deviation with experimentally measured values and predictions by simulations for higher values of β. In actual accelerator application, many RF cavities need to be over-coupled with β > 1 for reasons of beam loading compensation, reduction of cavity filling time, etc. This paper discusses a modified analytical formulation by including the effect of loop inductance in the determination of loop size for any desired coupling coefficient. The analytical formulation shows good agreement with 3D simulations and with experimentally measured values. It has been successfully qualified by the design and development of power coupler loops for two 476 MHz pre-buncher RF cavities, which have successfully been conditioned at rated power levels using these coupler loops.
Study of the effect of loop inductance on the RF transmission line to cavity coupling coefficient
Lal, Shankar; Pant, K. K.
2016-08-01
Coupling of RF power is an important aspect in the design and development of RF accelerating structures. RF power coupling employing coupler loops has the advantage of tunability of β, the transmission line to cavity coupling coefficient. Analytical expressions available in literature for determination of size of the coupler loop using Faraday's law of induction show reasonably good agreement with experimentally measured values of β below critical coupling (β ≤ 1) but show large deviation with experimentally measured values and predictions by simulations for higher values of β. In actual accelerator application, many RF cavities need to be over-coupled with β > 1 for reasons of beam loading compensation, reduction of cavity filling time, etc. This paper discusses a modified analytical formulation by including the effect of loop inductance in the determination of loop size for any desired coupling coefficient. The analytical formulation shows good agreement with 3D simulations and with experimentally measured values. It has been successfully qualified by the design and development of power coupler loops for two 476 MHz pre-buncher RF cavities, which have successfully been conditioned at rated power levels using these coupler loops.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011)]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
Model of nonlinear coupled thermo-hydro-elastodyanamics response for a saturated poroelastic medium
Institute of Scientific and Technical Information of China (English)
LIU GanBin; XIE KangHe; ZHENG RongYue
2009-01-01
Based on the Blot's wave equation and theory of thermodynamic,Darcy law of fluid and the modified Fourier law of heat conduction,a nonlinear fully coupled thermo-hydro-elastodynamic response model(THMD)for saturated porous medium is derived.The compressibility of the medium,the influence of fluid flux on the heat flux,and the influence of change of temperature on the fluid flux are considered in this model.With some simplification,the coupled nonlinear thermo-hydro-elastodynamic response model can be reduced to the thermo-elastodynamic(TMD)model based on the traditional Fourier law and,further more,to the Blot's wave equation without considering the heat phase.At last,the problem of one dimensional cylindrical cavity subjected to a time-dependent thermal/mechanical shock is analyzed by using the Laplace technique,the numerical results are used to discuss the influence of Blot's modulus M and coefficient of thermo-osmosis on displacement and to compare with the results of thermo-elastodynamic response to ascertain the validity of this model.
Model of nonlinear coupled thermo-hydro-elastodynamics response for a saturated poroelastic medium
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on the Biot’s wave equation and theory of thermodynamic, Darcy law of fluid and the modified Fourier law of heat conduction, a nonlinear fully coupled thermo-hydro-elastodynamic response model (THMD) for saturated porous medium is derived. The compressibility of the medium, the influence of fluid flux on the heat flux, and the influence of change of temperature on the fluid flux are considered in this model. With some simplification, the coupled nonlinear thermo-hydro-elastodynamic response model can be reduced to the thermo-elastodynamic (TMD) model based on the traditional Fourier law and, further more, to the Biot’s wave equation without considering the heat phase. At last, the problem of one dimensional cylindrical cavity subjected to a time-dependent thermal/mechanical shock is analyzed by using the Laplace technique, the numerical results are used to discuss the influence of Biot’s modulus M and coefficient of thermoos-mosis on displacement and to compare with the results of thermo-elastodynamic response to ascertain the validity of this model.
Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.
2016-07-01
In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.
Nonlinear optical rectification in laterally-coupled quantum well wires with applied electric field
Liu, Guanghui; Guo, Kangxian; Zhang, Zhongmin; Hassanbadi, Hassan; Lu, Liangliang
2017-03-01
Nonlinear optical rectification coefficient χ0(2) in laterally-coupled AlxGa1-xAs/GaAs quantum well wires with an applied electric field is theoretically investigated using the effective mass approximation as well as the numerical energy levels and wavefunctions of electrons. We find that χ0(2) is greatly influenced by the electric field as well as both the distance and the radius of the coupled system. A blue shift of χ0(2) with increasing electric field is exhibited while a red shift followed by a blue shift with increasing distance or radius is exhibited. A nonmonotonic behavior can be found in the resonant peak values of χ0(2) along with the increase of the electric field, the distance or the radius. One or two of the following physical mechanisms: the increased localization of the ground and first-excited states, the reduced coupling and the reduced quantum confinement effect are applied to elucidate the results above. Our results play a potential role in infrared photodetectors based on the coupled system.
Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions
Institute of Scientific and Technical Information of China (English)
FangJin－Qing; MKAli
1997-01-01
In this paper the nonlinear feedback functional method is presented for study of synchronization of spatiotemporal chaos in coupled map lattices with five connection forms.Some of nonlinear feedback functions are given.The noise effect on synchronization and sporadic nonlinear feedback are discussed.
Institute of Scientific and Technical Information of China (English)
ZHU Jia-Min; LIU Yu-Lu
2009-01-01
By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-qulntic nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.
Institute of Scientific and Technical Information of China (English)
Zhiguang Xiong; Chuanmiao Chen
2007-01-01
In this paper,n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u - uh = O(hn+2),n ≥ 2,at (n + 1)-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.
A NON-LINEAR STRUCTURE-PROPERTY MODEL FOR OCTANOL-WATER PARTITION COEFFICIENT.
Yerramsetty, Krishna M; Neely, Brian J; Gasem, Khaled A M
2012-10-25
Octanol-water partition coefficient (K(ow)) is an important thermodynamic property used to characterize the partitioning of solutes between an aqueous and organic phase and has importance in such areas as pharmacology, pharmacokinetics, pharmacodynamics, chemical production and environmental toxicology. We present a non-linear quantitative structure-property relationship model for determining K(ow) values of new molecules in silico. A total of 823 descriptors were generated for 11,308 molecules whose K(ow) values are reported in the PhysProp dataset by Syracuse Research. Optimum network architecture and its associated inputs were identified using a wrapper-based feature selection algorithm that combines differential evolution and artificial neural networks. A network architecture of 50-33-35-1 resulted in the least root-mean squared error (RMSE) in the training set. Further, to improve on single-network predictions, a neural network ensemble was developed by combining five networks that have the same architecture and inputs but differ in layer weights. The ensemble predicted the K(ow) values with RMSE of 0.28 and 0.38 for the training set and internal validation set, respectively. The ensemble performed reasonably well on an external dataset when compared with other popular K(ow) models in the literature.
Directory of Open Access Journals (Sweden)
Azita Yazdanpanah
2014-04-01
Full Text Available Continuum robot manipulators are optimized to meet best trajectory requirements. Closed loop control is a key technology that is used to optimize the system output process to achieve this goal. In order to conduct research in the area of closed loop control, a control oriented cycle-to-cycle continuum robot model, containing dynamic model information for each individual continuum robot manipulator, is a necessity. In this research, the continuum robot manipulator is modeled according to information between joint variable and torque, which is represented by the nonlinear dynamic equation. After that, a multi-input-multi-output baseline computed torque control scheme is used to simultaneously control the torque load of system to regulate the joint variables to desired levels. One of the most important challenge in control theory is on-line tuning therefore fuzzy supervised optimization is used to tune the modified baseline and computed torque control coefficient. The performance of the modified baseline computed torque controller is compared with that of a baseline proportional, integral, and derivative (PID controller.
Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures
Institute of Scientific and Technical Information of China (English)
尤福财
2012-01-01
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
Enhanced continuous-variable entanglement by a pair of nonlinearly coupled waveguides
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
We seek to analyze a three-level cascade laser with a pair of nonlinearly coupled waveguides inside the cavity. Applying the pertinent master equation, we investigate the squeezing and entanglement properties intracavity produced by our system. It is shown that with the help of nonlinearly coupled waveguides highly squeezed as well as macroscopic entangled light with high intensity can be achieved.
Measurements of complex coupling coefficients in a ring resonator of a laser gyroscope
Bessonov, A. S.; Makeev, A. P.; Petrukhin, E. A.
2017-07-01
A method is proposed for measuring complex coupling coefficients in a ring optical resonator in the absence of an active gas mixture. A setup is described on which measurements are performed in ring resonators of ring He-Ne lasers with a wavelength of 632.8 nm. A model of backscattering field interference between conservative and dissipative sources is presented. Within the framework of this model, the unusual behaviour of backscattering fields in ring resonators observed in experiments is explained: a significant difference in the moduli of coupling coefficients of counterpropagating waves and variation of the magnitude of the total phase shift in a wide range. It is proposed to use this method as a metrological method when assembling and aligning a ring resonator of a laser gyroscope.
Impulse-coupling coefficients from a pulsed-laser ablation of semiconductor GaAs
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Impulse-coupling coefficients from 1.06 - μm, 10-ns Nd:YAG pulsed-laser radiation to GaAs targets with different areas were measured using the ballistic pendulum method in the laser power density ranging from 4.0 × 108 to 5.0 × 109 W·cm-2.A detonation wave model of the plasma was established theoretically. The expansion process of plasma after the laser pulse ends is described in detail, and the impulse-coupling coefficients from pulsed laser with different energies to GaAs with different areas were calculated using the given model. It is found that the theoretical results agree well with the experimental data.
Design of Dual-Band Two-Branch-Line Couplers with Arbitrary Coupling Coefficients in Bands
Directory of Open Access Journals (Sweden)
I. Prudyus
2014-12-01
Full Text Available A new approach to design dual-band two-branch couplers with arbitrary coupling coefficients at two operating frequency bands is proposed in this article. The method is based on the usage of equivalent subcircuits input reactances of the even-mode and odd-mode excitations. The exact design formulas for three options of the dual-band coupler with different location and number of stubs are received. These formulas permit to obtain the different variants for each structure in order to select the physically realizable solution and can be used in broad range of frequency ratio and power division ratio. For verification, three different dual-band couplers, which are operating at 2.4/3.9 GHz with different coupling coefficients (one with 3/6 dB, and 10/3 dB two others are designed, simulated, fabricated and tested. The measured results are in good agreement with the simulated ones.
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.
UV Nano-Lights: Nonlinear Quantum Dot-Plasmon Coupling
2014-08-01
method is also applicable to bare nanoparticles in polar solvents. 15. SUBJECT TERMS Quantum Dots, Nonlinear Optical Materials , Energy...TERMS Quantum Dots, Nonlinear Optical Materials , Energy Conservation, Up-conversion 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT
Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
National Research Council Canada - National Science Library
Kumbhakar, Dharmadas
2012-01-01
.... The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories...
Directory of Open Access Journals (Sweden)
Yong Zhao
1997-01-01
Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.
Othman, N.; Shah, N. S. M.; Tay, K. G.; Pakarzadeh, H.; Cholan, N. A.; Talib, R.
2017-09-01
The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In short, the values of both fourth-order and sixth-order dispersion coefficients at zero-dispersion wavelength decrease when the slope increases.
Nonlinear Debye screening in strongly-coupled plasmas
Sarmah, D; Tessarotto, M
2006-01-01
An ubiquitous property of plasmas is the so-called Debye shielding of the electrostatic potential. Important aspects of Debye screening concern, in particular, the investigation of non-linear charge screening effects taking place in strongly-coupled plasmas, that imply a reduction of the effective charge characterizing the Debye-H\\"{u}ckel potential. These effects are particularly relevant in dusty plasmas which are characterized by high-Z particles. The investigation of the effective interactions of these particles has attracted interest in recent years especially for numerical simulations. In this work we intend to analyze the consistency of the traditional mathematical model for the Debye screening. In particular, we intend to prove that the 3D Poisson equation involved in the DH model does not admit strong solutions. For this purpose a modified model is proposed which takes into account the effect of local plasma sheath (i.e., the local domain near test particles where the plasma must be considered discre...
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Fully Coupled Simulation of the Plasma Liquid Interface and Interfacial Coefficient Effects
Lindsay, Alexander; Shannon, Steven
2016-01-01
There is a growing interest in the study of coupled plasma-liquid systems because of their applications to biomedicine, biological and chemical disinfection, agriculture, and other areas. Without an understanding of the near-surface gas dynamics, modellers are left to make assumptions about the interfacial conditions. For instance it is commonly assumed that the surface loss or sticking coefficient of gas-phase electrons at the interface is equal to 1. In this work we explore the consequences of this assumption and introduce a couple of ways to think about the electron interfacial condition. In one set of simulations we impose a kinetic condition with varying surface loss coefficient on the gas phase interfacial electrons. In a second set of simulations we introduce a Henry's law like condition at the interface in which the gas-phase electron concentration is assumed to be in thermodynamic equilibrium with the liquid-phase electron concentration. It is shown that for a range of electron Henry coefficients spa...
Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide
Valovik, D. V.; Smol'kin, E. Yu.
2017-08-01
The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies ωe and ωm and two propagation constants {\\widehat γ _e} and {\\widehat γ _m}. The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues ({\\widehat γ _e}, {\\widehat γ _m}) in proven and intervals of their localization are determined.
Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model
Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.
2009-01-01
Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.
Institute of Scientific and Technical Information of China (English)
Wen-zhi ZHANG; Pei-yan HUANG
2014-01-01
Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob-lems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma-trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series
Cizek, Pavel; Koo, Chao
2017-01-01
An important and widely used class of semiparametric models is formed by the varyingcoefficient models. Although the varying coefficients are traditionally assumed to be smooth functions, the varying-coefficient model is considered here with the coefficient functions containing a finite set of disco
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Dmitriev, Mikhail G.; Makarov, Dmitry A.
2016-08-01
We carried out analysis of near optimality of one computationally effective nonlinear stabilizing control built for weakly nonlinear systems with coefficients depending on the state and the formal small parameter. First investigation of that problem was made in [M. G. Dmitriev, and D. A. Makarov, "The suboptimality of stabilizing regulator in a quasi-linear system with state-depended coefficients," in 2016 International Siberian Conference on Control and Communications (SIBCON) Proceedings, National Research University, Moscow, 2016]. In this paper, another optimal control and gain matrix representations were used and theoretical results analogous to cited work above were obtained. Also as in the cited work above the form of quality criterion on which this close-loop control is optimal was constructed.
Line photon transport in a non-homogeneous plasma using radiative coupling coefficients
Energy Technology Data Exchange (ETDEWEB)
Florido, R.; Gil, J.M.; Rodriguez, R.; Rubiano, J.G.; Martel, P. [Las Palmas de Gran Canaria Univ., Dept. de Fisica (Spain); Florido, R.; Gil, J.M.; Rodriguez, R.; Rubiano, J.G.; Martel, P.; Minguez, E. [Madrid Univ. Politecnica, Instituto de Fusion Nuclear-DENIM (Spain)
2006-06-15
We present a steady-state collisional-radiative model for the calculation of level populations in non-homogeneous plasmas with planar geometry. The line photon transport is taken into account following an angle- and frequency-averaged escape probability model. Several models where the same approach has been used can be found in the literature, but the main difference between our model and those ones is that the details of geometry are exactly treated in the definition of coupling coefficients and a local profile is taken into account in each plasma cell. (authors)
Energy Technology Data Exchange (ETDEWEB)
Tang, Bo [School of Science, Xi' an Jiaotong University, Xi' an 710049 (China); He, Yinnian, E-mail: heyn@mail.xjtu.edu.cn [School of Science, Xi' an Jiaotong University, Xi' an 710049 (China); Wei, Leilei; Wang, Shaoli [School of Science, Xi' an Jiaotong University, Xi' an 710049 (China)
2011-09-05
In this Letter, a variable-coefficient discrete ((G{sup '})/G )-expansion method is proposed to seek new and more general exact solutions of nonlinear differential-difference equations. Being concise and straightforward, this method is applied to the (2+1)-dimension Toda equation. As a result, many new and more general exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear differential-difference equations in mathematical physics. -- Highlights: → We propose a novel method for non-linear differential-difference equations. → Some new exact traveling wave solutions of Toda equation are obtained. → Some solutions develop a singularity at a finite point. → It appears that these singular solutions will model the physical phenomena.
Semiclassical mode-coupling factorizations of coherent nonlinear optical response
Jansen, TL; Mukamel, S
2003-01-01
The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an h expansion of Liouville space generating functions, we show how to factorize multitime nonlinear response functions into products o
Zhao, Xiong-Tao; Tang, Feng; Han, Bing; Ni, Xiao-Wu
2016-12-01
A calibrated pendulum measuring device and a dimensionless analysis method were used to measure the impulse coupling coefficient at different laser intensities with aluminum, steel, and iron targets. The experiment was performed with a pulsed laser with the wavelength of 1.06 μm and the pulse duration of 7 ns. The experimental measurements of the variation of the impulse coupling coefficient versus the laser energy density agree with the theoretical prediction, and the optimum laser energy density correlated with the maximum impulse coupling coefficient corresponding to the theoretical predictions. The impulse coupling coefficients with laser incidence angles of 0 ° and 45 ° are compared for understanding of the effects of the ablation plume on the impulse coupling effect, and the experimental result shows that the impulse coupling effect grows as the incidence angle changes from 0 ° to 45 ° . Furthermore, the transmittance of the incident laser through the ablation plume in front of the target is deduced from the impulse measurements, and the effect of the ablation plume on the impulse coupling at high laser intensity is discussed. In order to investigate the weak impulse coupling effect, which is difficult to obtain from the experiments, the impulse coupling coefficient at low laser energy density was calculated by the finite element simulation.
Energy Technology Data Exchange (ETDEWEB)
Mvogo, Alain, E-mail: mvogal_2009@yahoo.fr [Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Ben-Bolie, G.H., E-mail: gbenbolie@yahoo.fr [Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); Kofané, T.C., E-mail: tckofane@yahoo.com [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); The Abdus Salam International Center for Theoretical Physics, P.O. Box 586, Strada Costiera 11, I-34014 Trieste (Italy)
2014-07-04
An improved quantum model for exciton–phonon dynamics in an α-helix is investigated taking into account the interspine coupling and the influence of power-law long-range exciton–exciton interactions. Having constructed the model Hamiltonian, we derive the lattice equations and employ the Fourier transforms to go in continuum space showing that the long-range interactions (LRI) lead to a nonlocal integral term in the equations of motion. Indeed, the non-locality originating from the LRI results in the dynamic equations with space derivatives of fractional order. New theoretical frameworks are derived, such that: fractional generalization of coupled Zakharov equations, coupled nonlinear fractional Schrödinger equations, coupled fractional Ginzburg–Landau equations, coupled Hilbert–Zakharov equations, coupled nonlinear Hilbert–Ginzburg–Landau equations, coupled nonlinear Schrödinger equations and coupled nonlinear Hilbert–Schrödinger equations. Through the F-expansion method, we derive a set of exact Jacobian solutions of coupled nonlinear Schrödinger equations. These solutions include Jacobian periodic solutions as well as bright and dark soliton which are important in the process of energy transport in the molecule. We also discuss of the impact of LRI on the energy transport in the molecule.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities
Directory of Open Access Journals (Sweden)
Gong-Ming Wei
2008-04-01
Full Text Available In this paper we study the existence of nontrivial solutions of elliptic systems with critical nonlinearities and subcritical nonlinear coupling interactions, under Dirichlet or Neumann boundary conditions. These equations are motivated from solitary waves of nonlinear Schrodinger systems in physics. Using minimax theorem and by estimates on the least energy, we prove the existence of nonstandard least energy solutions, i.e. solutions with least energy and each component is nontrivial.
Thompson, Stephen C; Meyer, Richard J; Markley, Douglas C
2014-01-01
Tonpilz acoustic transducers for use underwater often include a stack of piezoelectric material pieces polarized along the length of the stack and having alternating polarity. The pieces are interspersed with electrodes, bonded together, and electrically connected in parallel. The stack is normally much shorter than a quarter wavelength at the fundamental resonance frequency so that the mechanical behavior of the transducer is not affected by the segmentation. When the transducer bandwidth is less than a half octave, as has conventionally been the case, for example, with lead zirconate titanate (PZT) material, stack segmentation has no significant effect on the mechanical behavior of the device in its normal operating band near the fundamental resonance. However, when a high coupling coefficient material such as lead magnesium niobate-lead titanate (PMN-PT) is used to achieve a wider bandwidth with the tonpilz, the performance difference between a segmented stack and a similar piezoelectric section with electrodes only at the two ends can be significant. This paper investigates the effects of stack segmentation on the performance of wideband underwater tonpilz acoustic transducers. Included is a discussion of a particular tonpilz transducer design using single crystal piezoelectric material with high coupling coefficient compared with a similar design using more traditional PZT ceramics.
New Exact Solutions for a Class of Nonlinear Coupled Differential Equations
Institute of Scientific and Technical Information of China (English)
ZHAO Hong; GUO Jun; BAI Cheng-Lin; HAN Ji-Guang
2005-01-01
More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.
On the importance of nonlinear couplings in large-scale neutrino streams
Dupuy, Hélène
2015-01-01
We propose a procedure to evaluate the impact of nonlinear couplings on the evolution of massive neutrino streams in the context of large-scale structure growth. Such streams can be described by general nonlinear conservation equations, derived from a multiple-flow perspective, which generalize the conservation equations of non-relativistic pressureless fluids. The relevance of the nonlinear couplings is quantified with the help of the eikonal approximation applied to the subhorizon limit of this system. It highlights the role played by the relative displacements of different cosmic streams and it specifies, for each flow, the spatial scales at which the growth of structure is affected by nonlinear couplings. We found that, at redshift zero, such couplings can be significant for wavenumbers as small as $k=0.2\\,h$/Mpc for most of the neutrino streams.
Fully coupled simulation of the plasma liquid interface and interfacial coefficient effects
Lindsay, Alexander D.; Graves, David B.; Shannon, Steven C.
2016-06-01
There is a growing interest in the study of coupled plasma-liquid systems because of their applications to biomedicine, biological and chemical disinfection, agriculture, and other areas. Optimizing these applications requires a fundamental understanding of the coupling between phases. Though much progress has been made in this regard, there is still more to be done. One area that requires more research is the transport of electrons across the plasma-liquid interface. Some pioneering works (Rumbach et al 2015 Nat. Commun. 6, Rumbach et al 2015 J. Phys. D: Appl. Phys. 48 424001) have begun revealing the near-surface liquid characteristics of electrons. However, there has been little work to determine the near-surface gas phase electron characteristics. Without an understanding of the near-surface gas dynamics, modellers are left to make assumptions about the interfacial conditions. For instance it is commonly assumed that the surface loss or sticking coefficient of gas-phase electrons at the interface is equal to 1. In this work we explore the consequences of this assumption and introduce a couple of ways to think about the electron interfacial condition. In one set of simulations we impose a kinetic condition with varying surface loss coefficient on the gas phase interfacial electrons. In a second set of simulations we introduce a Henry’s law like condition at the interface in which the gas-phase electron concentration is assumed to be in thermodynamic equilibrium with the liquid-phase electron concentration. It is shown that for a range of electron Henry coefficients spanning a range of known hydrophilic specie Henry coefficients, the gas phase electron density in the anode can vary by orders of magnitude. Varying reflection of electrons by the interface also has consequences for the electron energy profile; increasing reflection may lead to increasing thermalization of electrons depending on choices about the electron energy boundary condition. This variation
Indian Academy of Sciences (India)
Edmund Chadwick; Ali Hatam; Saeed Kazem
2016-02-01
A new approach, named the exponential function method (EFM) is used to obtain solutions to nonlinear ordinary differential equations with constant coefficients in a semi-infinite domain. The form of the solutions of these problems is considered to be an expansion of exponential functions with unknown coefficients. The derivative and product operational matrices arising from substituting in the proposed functions convert the solutions of these problems into an iterative method for finding the unknown coefficients. The method is applied to two problems: viscous flow due to a stretching sheet with surface slip and suction; and mageto hydrodynamic (MHD) flow of an incompressible viscous fluid over a stretching sheet. The two resulting solutions are compared against some standard methods which demonstrates the validity and applicability of the new approach.
Institute of Scientific and Technical Information of China (English)
Zongyao SUN; Yungang LIU
2007-01-01
In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper,without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Energy Technology Data Exchange (ETDEWEB)
Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com [Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi 110016 (India)
2014-07-15
The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.
Directory of Open Access Journals (Sweden)
Alrijadjis .
2014-12-01
Full Text Available The proportional integral derivative (PID controllers have been widely used in most process control systems for a long time. However, it is a very important problem how to choose PID parameters, because these parameters give a great influence on the control performance. Especially, it is difficult to tune these parameters for nonlinear systems. In this paper, a new modified particle swarm optimization (PSO is presented to search for optimal PID parameters for such system. The proposed algorithm is to modify constriction coefficient which is nonlinearly decreased time-varying for improving the final accuracy and the convergence speed of PSO. To validate the control performance of the proposed method, a typical nonlinear system control, a continuous stirred tank reactor (CSTR process, is illustrated. The results testify that a new modified PSO algorithm can perform well in the nonlinear PID control system design in term of lesser overshoot, rise-time, settling-time, IAE and ISE. Keywords: PID controller, Particle Swarm Optimization (PSO,constriction factor, nonlinear system.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Matsuda, Nobuyuki; Kato, Takumi; Harada, Ken-Ichi; Takesue, Hiroki; Kuramochi, Eiichi; Taniyama, Hideaki; Notomi, Masaya
2011-10-10
We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.
Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling.
Rosenblum, Michael; Pikovsky, Arkady
2007-02-09
We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incommensurate to theirs. The self-organized onset of quasiperiodicity is illustrated with Landau-Stuart oscillators and a Josephson junction array with a nonlinear coupling.
Report from LHC MD 1399: Effect of linear coupling on nonlinear observables in the LHC.
Maclean, Ewen Hamish; Giovannozzi, Massimo; Persson, Tobias Hakan Bjorn; Tomas Garcia, Rogelio; CERN. Geneva. ATS Department
2017-01-01
Simulation work during Run 1 established that linear coupling had a large impact on nonlinear observables such as detuning with amplitude and dynamic aperture. Linear coupling is generally taken to be the largest single source of uncertainty in the modelling of the LHC’s nonlinear single particle dynamics. ThisMD sought to verify that such behaviour, to this point only observed in simulation, translated into the real machine.
Tchakui, Murielle Vanessa; Woafo, Paul
2016-11-01
This work deals with the dynamics of three unidirectionally coupled Duffing oscillators and that of three coupled piezoelectric actuators, considering the special case of inchworm motors. Two configurations of the network are studied: ring configuration and chain configuration. The effects of the coupling coefficient and the time delay are analyzed through different bifurcation diagrams and phase difference variation. It is shown that varying the coupling coefficient and the time delay leads to the appearance of different dynamical behaviors: steady states, periodic and quasiperiodic oscillations, chaos, and phase synchronization.
2017-04-03
Naftaly NPL MANAGEMENT LTD Final Report 04/02/2017 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR)/ IOE...ADDRESS(ES) NPL MANAGEMENT LTD HAMPTON RD TEDDINGTON, TW11 0LW GB 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND...refractive index and () is the incident electric field. The imaginary component of nonlinear refractive index, i.e. nonlinear or multi-photon
Variational principles for some nonlinear partial differential equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
He Jihuan E-mail: jhhe@dhu.edu.cn
2004-03-01
Variational principles for generalized Korteweg-de Vries equation and nonlinear Schroedinger's equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonlinear problems. Comparison with the results obtained by the Noether's theorem is made, revealing the present theorem is a straightforward and attracting mathematical tool.
ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION
Institute of Scientific and Technical Information of China (English)
Rongxing Wu; Jiashi Yang; Jianke Du; Ji Wang
2008-01-01
We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10-e which is not insignificant,and an amplitude change of the order of 10-8. The effects are expected to be stronger under real damping of 10-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.
Institute of Scientific and Technical Information of China (English)
Yuan Huiqun; Sun Huagang
2004-01-01
The electromagnetic and mechanical coupling properties of giant rare earth giant magnetostriction material TbxDy1 -xFe2 -z (0. 27 ≤x ≤ 0.3, 0 ≤ z ≤ 0.1 ) alloys were investigated by means of self-fabricated test apparatus. The effect of coupling mechanical with electromagnetic on magnetostrictive strain coefficient was discussed. The physical model of the coupling system was established. Based on the equivalent circuit of the coupling system, the magnetomechanical coupling coefficient was derived by means of impedance resistance analysis method.
Controlling of blow-up responses by nonlinear PT -symmetric coupling
Karthiga, S.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2017-03-01
We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks: (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up-type behavior for certain input power situations. We here show a nonlinear PT -symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable PT -symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above PT -symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Shivanian, Elyas; Hosseini Ghoncheh, S. J.
2017-02-01
In this paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. A method based on the traditional shooting method and the homotopy analysis method is applied, the so-called shooting homotopy analysis method (SHHAM), to the governing nonlinear differential equation. In this technique, more high-order approximate solutions are computable and multiple solutions are easily searched and discovered due to being free of the symbolic variable. It is found that the solution might be empty, unique or dual depending on the values of the parameters of the model. Furthermore, corresponding fin efficiencies with high accuracy are computed. As a consequence, a new branch solution for this nonlinear problem by a new proposed method, based on the traditional shooting method and the homotopy analysis method, is obtained.
The nonlinear chemo-mechanic coupled dynamics of the F 1 -ATPase molecular motor.
Xu, Lizhong; Liu, Fang
2012-03-01
The ATP synthase consists of two opposing rotary motors, F0 and F1, coupled to each other. When the F1 motor is not coupled to the F0 motor, it can work in the direction hydrolyzing ATP, as a nanomotor called F1-ATPase. It has been reported that the stiffness of the protein varies nonlinearly with increasing load. The nonlinearity has an important effect on the rotating rate of the F1-ATPase. Here, considering the nonlinearity of the γ shaft stiffness for the F1-ATPase, a nonlinear chemo-mechanical coupled dynamic model of F1 motor is proposed. Nonlinear vibration frequencies of the γ shaft and their changes along with the system parameters are investigated. The nonlinear stochastic response of the elastic γ shaft to thermal excitation is analyzed. The results show that the stiffness nonlinearity of the γ shaft causes an increase of the vibration frequency for the F1 motor, which increases the motor's rotation rate. When the concentration of ATP is relatively high and the load torque is small, the effects of the stiffness nonlinearity on the rotating rates of the F1 motor are obvious and should be considered. These results are useful for improving calculation of the rotating rate for the F1 motor and provide insight about the stochastic wave mechanics of F1-ATPase.
Mynard, Jonathan; Penny, Daniel J; Smolich, Joseph J
2008-12-05
Local reflection coefficients (R) provide important insights into the influence of wave reflection on vascular haemodynamics. Using the relatively new time-domain method of wave intensity analysis, R has been calculated as the ratio of the peak intensities (R(PI)) or areas (R(CI)) of incident and reflected waves, or as the ratio of the changes in pressure caused by these waves (R(DeltaP)). While these methods have not yet been compared, it is likely that elastic non-linearities present in large arteries will lead to changes in the size of waves as they propagate and thus errors in the calculation of R(PI) and R(CI). To test this proposition, R(PI), R(CI) and R(DeltaP) were calculated in a non-linear computer model of a single vessel with various degrees of elastic non-linearity, determined by wave speed and pulse amplitude (DeltaP(+)), and a terminal admittance to produce reflections. Results obtained from this model demonstrated that under linear flow conditions (i.e. as DeltaP(+)-->0), R(DeltaP) is equivalent to the square-root of R(PI) and R(CI) (denoted by R(PI)(p) and R(CI)(p)). However for non-linear flow, pressure-increasing (compression) waves undergo amplification while pressure-reducing (expansion) waves undergo attenuation as they propagate. Consequently, significant errors related to the degree of elastic non-linearity arise in R(PI) and R(CI), and also R(PI)(p) and R(CI)(p), with greater errors associated with larger reflections. Conversely, R(Delta)(P) is unaffected by the degree of non-linearity and is thus more accurate than R(PI) and R(CI).
A new variable coefficient algebraic method and non-traveling wave solutions of nonlinear equations
Institute of Scientific and Technical Information of China (English)
Lu Bin; Zhang Hong-Qing
2008-01-01
In this paper,a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projective Riccati equation method.In order to illustrate the validity and the advantages of the method,(2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained.This algorithm can also be applied to other nonlinear differential equations.
Thompson, Stephen C; Markley, Douglas C
2013-01-01
Underwater acoustic transducers often include a stack of thickness polarized piezoelectric material pieces of alternating polarity interspersed with electrodes, bonded together and electrically connected in parallel. The stack is normally much shorter than a quarter wavelength at the fundamental resonance frequency, so that the mechanical behavior of the transducer is not affected by the segmentation. When the transducer bandwidth is less than a half octave, as has conventionally been the case, stack segmentation has no significant effect on the mechanical behavior of the device. However, when a high coupling coefficient material such as PMN-PT is used to achieve a wider bandwidth, the difference between a segmented stack and a similar piezoelectric section with electrodes only at the two ends can be significant. This paper investigates the effects of stack segmentation on the performance of wideband underwater acoustic transducers, particularly tonpilz transducer elements. Included is discussion of transduce...
Coupling coefficients and kinetic equation for Rossby waves in multi-layer ocean
Directory of Open Access Journals (Sweden)
T. Soomere
2003-01-01
Full Text Available The kinetic description of baroclinic Rossby waves in multi-layer model ocean is analysed. Explicit analytical expressions for the coupling coefficients describing energy exchange intensity between different modes are obtained and their main properties are established for the three-layer model. It is demonstrated that several types of interactions vanish in the case of simple vertical structures of the ocean, e.g. when all layers have equal depth. These cases correspond to a zero component of the eigenvectors of the potential vorticity equations. The kinetic equation always possesses a fully barotropic solution. If energy is concentrated in the baroclinic modes, the barotropic mode will necessarily be generated. Motion systems consisting of a superposition of the barotropic and a baroclinic mode always transfer energy to other baroclinic modes.
Towards Ultrafast Communications: Nonlinear Coupling Dynamics and Light-Semiconductor Interaction
Wang, W.
2007-01-01
This thesis deals with some specific problems concerning the processing of ultrashort optical pulses and their interaction with semiconductors. It includes the investigation of the ultrashort optical pulse propagation and coupling dynamics in the nonlinear coupled waveguide, and the coherent and in
Towards Ultrafast Communications: Nonlinear Coupling Dynamics and Light-Semiconductor Interaction
Wang, W.
2007-01-01
This thesis deals with some specific problems concerning the processing of ultrashort optical pulses and their interaction with semiconductors. It includes the investigation of the ultrashort optical pulse propagation and coupling dynamics in the nonlinear coupled waveguide, and the coherent and
A Solvable Model in Two-Dimensional Gravity Coupled to a Nonlinear Matter Field
Institute of Scientific and Technical Information of China (English)
YAN Jun; WANG Shun-Jin; TAO Bi-You
2001-01-01
The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.``
New Doubly Periodic Solutions for the Coupled Nonlinear Klein-Gordon Equations
Institute of Scientific and Technical Information of China (English)
LIU Chun-Ping
2005-01-01
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
Pinning Synchronization of Delayed Neural Networks with Nonlinear Inner-Coupling
Directory of Open Access Journals (Sweden)
Yangling Wang
2011-01-01
Full Text Available Without assuming the symmetry and irreducibility of the outer-coupling weight configuration matrices, we investigate the pinning synchronization of delayed neural networks with nonlinear inner-coupling. Some delay-dependent controlled stability criteria in terms of linear matrix inequality (LMI are obtained. An example is presented to show the application of the criteria obtained in this paper.
Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators
Institute of Scientific and Technical Information of China (English)
CHEN Hai-Ling; YANG Jun-Zhong
2009-01-01
In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.
Thermal entanglement in 1D optical lattice chains with nonlinear coupling
Institute of Scientific and Technical Information of China (English)
Zhou Ling; Yi Xue-Xi; Song He-Shan; Guo Yan-Qing
2005-01-01
he thermal entanglement of spin-1 atoms with nonlinear coupling in an optical lattice chain is investigated for two-particle and multi-particle systems. It is found that the relation between linear coupling and nonlinear coupling is the key to determine thermal entanglement, which shows in what kinds of atoms thermal entanglement exists. This result is true both for two-particle and multi-particle systems. For multi-particle systems, the thermal entanglement does not decrease greatly, and the critical temperature decreases only slightly.
UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
nanomaterials systems for nonlinear optics. PROJECT TIMELINE The project timeline was segmented into 3 monthly intervals. The PhD students, assisted by...technique to remove the scattering component of light from the fluorescence emission with commonly-used fluorometers [Shortell, Optics Express...nanostructure light interaction and also has helped understand and remove unwanted signal contamination through optical element interference effects as
On the Nonlinear Behavior of the Piezoelectric Coupling on Vibration-Based Energy Harvesters
Directory of Open Access Journals (Sweden)
Luciana L. Silva
2015-01-01
Full Text Available Vibration-based energy harvesting with piezoelectric elements has an increasing importance nowadays being related to numerous potential applications. A wide range of nonlinear effects is observed in energy harvesting devices and the analysis of the power generated suggests that they have considerable influence on the results. Linear constitutive models for piezoelectric materials can provide inconsistencies on the prediction of the power output of the energy harvester, mainly close to resonant conditions. This paper investigates the effect of the nonlinear behavior of the piezoelectric coupling. A one-degree of freedom mechanical system is coupled to an electrical circuit by a piezoelectric element and different coupling models are investigated. Experimental tests available in the literature are employed as a reference establishing the best matches of the models. Subsequently, numerical simulations are carried out showing different responses of the system indicating that nonlinear piezoelectric couplings can strongly modify the system dynamics.
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical......Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Directory of Open Access Journals (Sweden)
Khaled Zaki
2016-12-01
Full Text Available We establish the existence of solutions for the nonlinear parabolic problem with Dirichlet homogeneous boundary conditions, $$ \\frac{\\partial u}{\\partial t} - \\sum_{i=1}^N\\frac{\\partial}{\\partial x_i} \\Big( d_i(u\\frac{\\partial u}{\\partial x_i} \\Big =\\mu,\\quad u(t=0=u_0, $$ in a bounded domain. The coefficients $d_i(s$ are continuous on an interval $]-\\infty,m[$, there exists an index p such that $d_p(u$ blows up at a finite value m of the unknown u, and $\\mu$ is a diffuse measure.
Energy Technology Data Exchange (ETDEWEB)
He, J.S. [Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211 (China); Charalampidis, E.G., E-mail: charalamp@math.umass.edu [School of Civil Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124 (Greece); Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2014-01-24
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schrödinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose–Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue wave solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations to the exact rogue wave solutions is also discussed.
Coupled Nonlinear Schr(o)dinger Equations and the Miura Transformation
Institute of Scientific and Technical Information of China (English)
LOU Yan; ZHU Jun-Yi
2011-01-01
@@ A wide class of coupled nonlinear Schr?dinger(NLS)equations are derived by virtue of the dressing method,and the associated parametric solutions are discussed.As an illustration,the explicit solution of the coupled NLS-type equation associated with σ1 is given.The Miura transformation for a AKNS-type hierarchy is established,from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.%A wide class of coupled nonlinear Schrodinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with O\\ is given. The Miura transformation for a AKNS-type hierarchy is established, from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.
Garai, S.; Janaki, M. S.; Chakrabarti, N.
2016-09-01
The nonlinear propagation of low frequency waves, in a collisionless, strongly coupled dusty plasma (SCDP) with a density dependent viscosity, has been studied with a proper Galilean invariant generalized hydrodynamic (GH) model. The well known reductive perturbation technique (RPT) has been employed in obtaining the solutions of the longitudinal and transverse perturbations. It has been found that the nonlinear propagation of the acoustic perturbations govern with the modified Korteweg-de Vries (KdV) equation and are decoupled from the sheared fluctuations. In the regions, where transversal gradients of the flow exists, coupling between the longitudinal and transverse perturbations occurs due to convective nonlinearity which is true for the homogeneous case also. The results, obtained here, can have relative significance to astrophysical context as well as in laboratory plasmas.
Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential
Gizzi, A.; Loppini, A.; Ruiz-Baier, R.; Ippolito, A.; Camassa, A.; La Camera, A.; Emmi, E.; Di Perna, L.; Garofalo, V.; Cherubini, C.; Filippi, S.
2017-09-01
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
Nonlinear quantum optics in the (ultra)strong light-matter coupling
Sánchez-Burillo, Eduardo; García-Ripoll, Juan José; Martín-Moreno, Luis; Zueco, David
2014-01-01
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of $N$, $M$, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the Matrix Product States technique. Both the time evolution for the field and qubits is com...
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Senthilkumar, D. V.; Muruganandam, P.; Lakshmanan, M.; Kurths, J.
2010-01-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by siz...
Energy Technology Data Exchange (ETDEWEB)
Ben Mahrsia, R.; Choubani, M., E-mail: mohsenchoubani3@yahoo.fr; Bouzaiene, L.; Maaref, H.
2016-06-25
In this paper we explore the structure parameters, hydrostatic pressure and temperature effects on Nonlinear optical rectification (NOR) in an asymmetric vertically coupled lens-shaped InAs/GaAs quantum dots. During epitaxial growth, lens-shaped quantum dots (QDs) are formed on the wetting layer (WL). Many theoretical works have neglected WL and its effect on nonlinear optical properties of QD-based systems for sake of simplicity. However, in this work the WL has been shown to be so influential in the intersubband energy and nonlinear optical rectification magnitude. Also, a detailed and comprehensive study of the nonlinear optical rectification is theoretical investigated within the framework of the compact density-matrix approach and finite difference method (FDM). It's found that nonlinear optical rectification coefficient is strongly affected not only by the WL, but also by the pressure, temperature and the coupled width between the QDs. Obtained results revealed that a red or a blue shift cane be observed. This behavior in the NOR gives a new degree of freedom in regions of interest for device applications. - Highlights: • Vertically coupled lens-shaped InAs/GaAs quantum dots is investigated. • Photon energy shifts towards the red with increasing pressure. • Photon energy shifts towards the blue with increasing temperature. • Intersubband energy decreases with increasing the wetting layer width. • Nonlinear optical rectification magnitude is controlled and adjusted.
PT-symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
Avinash Khare
2015-11-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
Athanassoulis 2002) problems, over variable bathymetry regions. Using the local-mode expansion in conjunction with the variational principle the original problem is reformulated as an infinite, coupled-mode system of second-order differential equations in the propagation (horizontal) space, fully accounting for the effects of non-linearity and dispersion. Various simplified equations, like Boussinesq-type models, in shallow water depth, and non-linear mild-slope models, in intermediate depth, can be obtained as limiting forms. As a first step towards the solution of fully nonlinear coupled-mode system, the system is simplified keeping only up to second-order terms in the system coefficients, and the derived weakly non-linear model has been applied to water waves propagating over a flat bottom and over an arbitrary bathymetry. This model is solved numerically in the frequency and in the time domain, providing very good results in a wide range of water depths. In the case of monochromatic waves propagating over a flat bottom, it is shown that the present model correctly treats the dispersion effects in the whole range of relative water depths from practically deep to shallow water. In the same case, it is also shown that the present model reproduces correctly the second-order Stokes solutions. In the general case, the solution of the coupled-mode system is obtained numerically by truncating the local-mode series into a finite number of terms, and using finite differences for approximating the derivatives on the horizontal plane. Numerical results presented for a smooth underwater shoaling with a steep bottom slope, demonstrate that the rate of decay of the modal-amplitude functions is very fast, in conformity with similar behaviour in the linear case (Athanassoulis and Belibassakis 1999). This means that a small number of modes (up to 5 or 7) are sufficient for precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included
On a mixed problem for a coupled nonlinear system
Directory of Open Access Journals (Sweden)
Marcondes R. Clark
1997-03-01
Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.
Directory of Open Access Journals (Sweden)
Sobczyk Tadeusz J.
2015-09-01
Full Text Available Energy based approach was used in the study to formulate a set of functions approximating the magnetic flux linkages versus independent currents. The simplest power series that approximates field co-energy and linked fluxes for a two winding core of an induction machine are described by a set of common unknown coefficients. The authors tested three algorithms for the coefficient estimation using Weighted Least-Squared Method for two different positions of the coils. The comparison of the approximation accuracy was accomplished in the specified area of the currents. All proposed algorithms of the coefficient estimation have been found to be effective. The algorithm based solely on the magnetic field co-energy values is significantly simpler than the method based on the magnetic flux linkages estimation concept. The algorithm based on the field co-energy and linked fluxes seems to be the most suitable for determining simultaneously the coefficients of power series approximating linked fluxes and field co-energy.
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
Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; MEI Jian-Qin; ZHANG Hong-Qing
2009-01-01
Complete group classification of a class of variable coefficient (1 + 1)-dimensional wave equations is performed.The possible additional equivalence transformations between equations from the class under consideration and the conditional equivalence groups are also investigated. These allow simplification of the results of the classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of special forms of these equations via the classical Lie method. Nonclassical symmetries of the wave equations are discussed.
Energy Technology Data Exchange (ETDEWEB)
Knapp, R. B.; Kasameyer, P. W.
1988-01-01
Constitutive relationships for electrochemical and thermoelectric cross-coupling coefficients are derived using ionic mobilities, applying a general derivative of chemical potential and employing the zero net current condition. The general derivative of chemical potential permits thermal variations which give rise to the thermoelectric effect. It also accounts for nonideal solution behavior. An equation describing electric field strength is similarly derived with the additional assumption of electrical neutrality in the fluid Planck approximation. The Planck approximation implies that self-potential (SP) is caused only by local sources and also that the electric field strength has only first order spatial variations. The derived relationships are applied to the NaCl-KCl concentration cell with predicted and measured voltages agreeing within 0.4 mV. The relationships are also applied to the Long Valley and Yellowstone geothermal systems. There is a high degree of correlation between predicted and measured SP response for both systems, giving supporting evidence for the validity of the approach. Predicted SP amplitude exceeds measured in both cases; this is a possible consequence of the Planck approximation. Electrochemical sources account for more than 90% of the predicted response in both cases while thermoelectric mechanisms account for the remaining 10%; electrokinetic effects are not considered. Predicted electrochemical and thermoelectric voltage coupling coefficients are comparable to values measured in the laboratory. The derived relationships are also applied to arbitrary distributions of temperature and fluid composition to investigate the geometric diversity of observed SP anomalies. Amplitudes predicted for hypothetical saline spring and hot spring environments are less than 40 mV. In contrast, hypothetical near surface steam zones generate very large amplitudes, over 2 V in one case. These results should be viewed with some caution due to the uncertain
Electrets in soft materials: nonlinearity, size effects, and giant electromechanical coupling.
Deng, Qian; Liu, Liping; Sharma, Pradeep
2014-07-01
Development of soft electromechanical materials is critical for several tantalizing applications such as soft robots and stretchable electronics, among others. Soft nonpiezoelectric materials can be coaxed to behave like piezoelectrics by merely embedding charges and dipoles in their interior and assuring some elastic heterogeneity. Such so-called electret materials have been experimentally shown to exhibit very large electromechanical coupling. In this work, we derive rigorous nonlinear expressions that relate effective electromechanical coupling to the creation of electret materials. In contrast to the existing models, we are able to both qualitatively and quantitatively capture the known experimental results on the nonlinear response of electret materials. Furthermore, we show that the presence of another form of electromechanical coupling, flexoelectricity, leads to size effects that dramatically alter the electromechanical response at submicron feature sizes. One of our key conclusions is that nonlinear deformation (prevalent in soft materials) significantly enhances the flexoelectric response and hence the aforementioned size effects.
Nonlinear regime of the mode-coupling instability in 2D plasma crystals
Röcker, T B; Zhdanov, S K; Nosenko, V; Ivlev, A V; Thomas, H M; Morfill, G E
2014-01-01
The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect could not be reproduced in simulations employing a simple point-like wake model. This shows that at the nonlinear stage of the MCI a heating mechanism is working which was not considered so far.
THERMOELASTICALLY COUPLED AXISYMMETRIC NONLINEAR VIBRATION OF SHALLOW SPHERICAL AND CONICAL SHELLS
Institute of Scientific and Technical Information of China (English)
王永岗; 戴诗亮
2004-01-01
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines
Institute of Scientific and Technical Information of China (English)
Eric Tala-Tebue; Aurelien Kenfack-Jiotsa; Marius Hervé Tatchou-Ntemfack; Timoléon Crépin Kofané
2013-01-01
In this work,we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines.Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch.Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing.On one hand,the difference between the two lines induced the fission for only one mode of propagation.This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton,leading to a possible increasing of the bit rate.On the other hand,the dissymmetry of the two lines converts the network into a good amplifier for the w_ mode which corresponds to the regime admitting low frequencies.
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks
Barranca, Victor J.; Zhou, Douglas; Cai, David
2016-06-01
Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks.
Barranca, Victor J; Zhou, Douglas; Cai, David
2016-06-01
Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
Institute of Scientific and Technical Information of China (English)
WEN Guochun; HUANG Sha; QIAO Yuying
2001-01-01
In 1988, Yu. A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for linear uniformly parabolic equations with measurable coefficients where the coefficients satisfy the condition In this paper, we try to generalize the results of Alkhutov and Mamedov to nonlinear uni-formly parabolic systems of second order equations with measurable coefficients; moreover,we also discuss the solvability of the Neumann problem for the above systems.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
Optimizing nonlinear beam coupling in low-symmetry crystals.
Shumelyuk, A; Volkov, A; Odoulov, S; Grabar, A; Stoyka, I; Evans, D R
2014-10-01
The purpose of this paper is to find the polarizations and spatial orientations of the two interacting counterpropagating coherent light waves which ensure the largest beam coupling in monoclinic photorefractive crystal. The results of calculations are presented that are verified experimentally with Sn₂P₂S₆.
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
Hesketh, Graham D
2015-01-01
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\\chi_2$ type nonlinearity as well as two mode systems coupled via cubic $\\chi_3$ type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum and difference frequency generation, polarization dynamics, parity-time dynamics and optical processing applications.
Nonlinear Propagation of Coupling Optical Pulse under Compton Scattering in Laser Medium
Institute of Scientific and Technical Information of China (English)
HAO Dong-shan; ZHANG Xiao-fu
2006-01-01
After considering Kerr nonlinear effect,group velocity dispersion of host and gain distribution of active particle in laser amplifying medium,a basic equation describing propagation of the coupling optical pulse under the multi-photon nonlinear Compton scattering in the laser amplifying medium has been deduced. Besides,the profile and power spectrum of a picosecond-level super-Gaussian coupling pulse in the laser amplifying medium have been discussed when its central frequency coincides with the gain peak frequency of the laser amplifying medium.
EXACT EXPLICIT SOLUTIONS OF THE NONLINEAR SCHR(O)DINGER EQUATION COUPLED TO THE BOUSSINESQ EQUATION
Institute of Scientific and Technical Information of China (English)
姚若侠; 李忠斌
2003-01-01
A system comprised of the nonlinear Schrodinger equation coupled to theBoussinesq equation (S-B equations) which dealing with the stationary propagation of cou-pled non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed.To examine its solitary wave solutions, a reduced set of ordinary differential equations areconsidered by a simple traveling wave transformation. It is then shown that several newsolutions (either functional or parametrical) can be obtained systematically, in addition torederiving all known ones by means of our simple and direct algebra method with the helpof the computer algebra system Maple.
Franchi, A; Vanbavinkhove, G; CERN. Geneva. BE Department
2010-01-01
In this note we show how to compute the Resonance Driving Term (RDT) f1001, the local resonance term chi 1010 and the coupling coefficient C from the spectrum of turn-by-turn single-BPM data. The harmonic analysis of real coordinate x(y) is model independent, conversely to the the analysis of the complex Courant-Snyder coordinate hx,- = x-ipx. From the computation of f1001 along the ring is closely related to the global coupling coefficient C, but it is affected by an intrinsic error, discussed in this note.
Energy Technology Data Exchange (ETDEWEB)
Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik
2000-05-01
This paper studies nonlinear degenerate parabolic equations where the flux function does not depend Lipshitz continuously on the spatial position x. By properly adapting the 'doubling of variable' device due to Kruzkov and Carrillo, the authors prove a uniqueness result within the class of entropy solutions for the initial value problem. They also prove a result concerning the continuous dependence on the initial data and the flux function for degenerate parabolic equations with flux function of the form k(x)f(u), where k(x) is a vector-valued function and f(u) is a scalar function of the unknown scalar function u(x,t) which is sought.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems.
Wang, Zi-Peng; Wu, Huai-Ning; Li, Han-Xiong
2017-09-01
In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.
Energy Technology Data Exchange (ETDEWEB)
Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
Existence of solutions for a Schrödinger system with linear and nonlinear couplings
Li, Kui; Zhang, Zhitao
2016-08-01
We study an important system of Schrödinger equations with linear and nonlinear couplings arising from Bose-Einstein condensates. We use the Nehari manifold to prove the existence of a ground state solution; moreover, we give the sign of the solutions depending on linear coupling; by using index theory and Nehari manifold, we prove that there exist infinitely many positive bound state solutions.
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Indian Academy of Sciences (India)
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems
Zheng, Zhigang; Hu, Bambi; Hu, Gang
1998-01-01
Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become...
Enhanced continuous-variable entanglement by a pair of nonlinearly coupled waveguides
Institute of Scientific and Technical Information of China (English)
WANG KeQuan; FAN QiuBo
2009-01-01
We seek to analyze a three-level cascade laser with a pair of non,nearly coupled waveguides inside the cavity.Applying the pertinent master equation,we investigate the squeezing and entanglement prop-erties intracavity produced by our system.It is shown that with the help of nonlinearly coupled waveguides highly squeezed as well as macroscopic entangled light with high intensity can be achieved.
Directory of Open Access Journals (Sweden)
Anatoly V. Klyuchevskii
2013-11-01
Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Energy Technology Data Exchange (ETDEWEB)
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.
Coupled nonlinear-diffusion color image sharpening based on the chromaticity-brightness model
Saito, Takahiro; Nosaka, Reina; Komatsu, Takashi
2006-01-01
Previously we have presented a selective image sharpening method based on the coupled nonlinear diffusion process composed of a nonlinear diffusion term, a fidelity term and an isotropic peaking term, and it can sharpen only blurred edges without increasing the noise visibility. Our previously presented prototypal color-image sharpening methods based on the coupled nonlinear-diffusion process have been formulated on the linear color models, namely, the channel-bychannel model and the 3D vectorial model. Our prototypal methods can sharpen blurred color step edges, but they do not necessarily enhance contrasts of signal variations in complex texture image regions so well as in simple step-edge regions. To remedy the drawback, this paper extends our coupled nonlinear-diffusion color-image sharpening method to the nonlinear non-flat color model, namely, the chromaticity-brightness model, which is known to be closely relating to human color perception. We modify our time-evolution PDE's for the non-flat space of the chromaticity vector and present its digital implementations. Through experimental simulations, we compare our new color-image sharpening method based on the chromaticity-brightness model with our prototypal color-image sharpening methods based on the linear color models.
Energy Technology Data Exchange (ETDEWEB)
Samet Y. Kadioglu; Robert R. Nourgaliev; Vincent A. Mousseau
2008-03-01
We perform a comparative study for the harmonic versus arithmetic averaging of the heat conduction coefficient when solving non-linear heat transfer problems. In literature, the harmonic average is the method of choice, because it is widely believed that the harmonic average is more accurate model. However, our analysis reveals that this is not necessarily true. For instance, we show a case in which the harmonic average is less accurate when a coarser mesh is used. More importantly, we demonstrated that if the boundary layers are finely resolved, then the harmonic and arithmetic averaging techniques are identical in the truncation error sense. Our analysis further reveals that the accuracy of these two techniques depends on how the physical problem is modeled.
Directory of Open Access Journals (Sweden)
Qiang Zhang
2015-01-01
Full Text Available An analytical model on electromechanical coupling coefficient and the length optimization of a bending piezoelectric ultrasonic transducer are proposed. The piezoelectric transducer consists of 8 PZT elements sandwiched between four thin electrodes, and the PZT elements are clamped by a screwed connection between fore beam and back beam. Firstly, bending vibration model of the piezoelectric transducer is built based on the Timoshenko beam theory. Secondly, the analytical model of effective electromechanical coupling coefficient is built based on the bending vibration model. Energy method and electromechanical equivalent circuit method are involved in the modelling process. To validate the analytical model, sandwich type piezoelectric transducer example in second order bending vibration mode is analysed. Effective electromechanical coupling coefficient of the transducer is optimized with simplex reflection technique, and the optimized ratio of length of the transducers is obtained. Finally, experimental prototypes of the sandwich type piezoelectric transducers are fabricated. Bending vibration mode and impedance of the experimental prototypes are tested, and electromechanical coupling coefficient is obtained according to the testing results. Results show that the analytical model is in good agreement with the experimental model.
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.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Tang, Ze; Park, Ju H.; Lee, Tae H.
2016-10-01
This paper is devoted to the cluster synchronization issue of nonlinearly coupled Lur'e networks under the distributed adaptive pinning control strategy. The time-varying delayed networks consisted of identical and nonidentical Lur'e systems are discussed respectively by applying the edge-based pinning control scheme. In each cluster, the edges belonging to the spanning tree are pinned. In view of the nonlinearly couplings of the networks, for the first time, an efficient distributed nonlinearly adaptive update law based on the local information of the dynamical behaviors of node is proposed. Sufficient criteria for the achievement of cluster synchronization are derived based on S-procedure, Kronecker product and Lyapunov stability theory. Additionally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical results.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
SHARP CRITERIONS OF GLOBAL EXISTENCE AND COLLAPSE FOR COUPLED NONLINEAR SCHR(O)DINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gan Zaihui; Zhang Jian
2004-01-01
In this paper, a series of sharp criterions of global existence and collapse for coupled nonlinear Schrodinger equations are derived out in terms of the characteristics of the ground state and the local theories. And the conclusion that how small the initial data are, the global solutions exist is proved.
Geometry and transport in a model of two coupled quadratic nonlinear waveguides
DEFF Research Database (Denmark)
Stirling, James R.; Bang, Ole; Christiansen, Peter Leth;
2008-01-01
This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the pha...
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Indian Academy of Sciences (India)
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems
Taverniers, Søren; Tartakovsky, Daniel M.
2017-02-01
Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton-Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.
Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity.
Srinivasan, K; Senthilkumar, D V; Murali, K; Lakshmanan, M; Kurths, J
2011-06-01
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.
Institute of Scientific and Technical Information of China (English)
Li WANG; Jixiu WANG
2014-01-01
Let B1 ⊂ RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients:-div(|∇u|p-2∇u)=|x|s|u|p*(s)-2u+λ|x|t|u|p-2u, x∈B1, u|∂B1 =0, where t, s>-p, 2≤pp(p-1)t+p(p2-p+1) andλ∈(0,λ1,t), whereλ1,t is the first eigenvalue of-∆p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ (ps+p) min{1, p+tp+s}+p2p-(p-1) min{1, p+tp+s} andλ>0 is small.
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.
Directory of Open Access Journals (Sweden)
Matej URBANSKÝ
2014-12-01
Full Text Available In order to continuous tuning of the torsional oscillating mechanical system during its operation, we are making use of application of the pneumatic flexible shaft couplings, developed by us. By the gaseous medium pressure change in pneumatic couplings we can change its torsional stiffness and thereby the dynamics of whole system too. In term of dynamics is necessary to know the transitional effects of mechanical system, which are arising at its continuous tuning. For the numerical computation of these transitional effects it is necessary to know the values of flow resistance coefficients at gaseous medium flow into the compression space of pneumatic coupling from the pressure tank and out of compression space into the atmosphere. For that reason presents this paper theoretic and experimental procedure of given coefficients determination.
Solution of Nonlinear Coupled Heat and Moisture Transport Using Finite Element Method
Directory of Open Access Journals (Sweden)
T. Krejčí
2004-01-01
Full Text Available This paper deals with a numerical solution of coupled of heat and moisture transfer using the finite element method. The mathematical model consists of balance equations of mass, energy and linear momentum and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressures, gas pressure and displacement. In contrast with pure mechanical problems, there are several difficulties which require special attention. Systems of algebraic equations arising from coupled problems are generally nonlinear, and the matrices of such systems are nonsymmetric and indefinite. The first experiences of solving complicated coupled problems are mentioned in this paper.
Fiber-to-fiber nonlinear coupling via a nematic liquid crystal
Nyushkov, B. N.; Trashkeev, S. I.; Ivanenko, A. V.; Kolker, D. B.; Purtov, P. A.
2017-01-01
Nonlinear optical coupling between two single-mode fibers terminated coaxially in a nematic liquid crystal (NLC) was explored for the first time. Light-induced reorientation of nematic molecules can result in the stable self-collimation of light transmitted through the gap between fibers. Thus, high coupling efficiency can be achieved despite large fiber spacing. We demonstrated a coupling efficiency of up to ∼0.7, achieved with spacing equal to four diffraction lengths. This feature opens up possibilities for the development of novel in-line fiber-optic elements based on NLCs. For instance, a polarization controller was proposed and considered.
Vierheilig, Carmen; Grifoni, Milena
2010-01-01
We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the...
Tackling excess noise from bilinear and nonlinear couplings in gravitational-wave interferometers
Bose, Sukanta; Mazumder, Nairwita; Dhurandhar, Sanjeev; Gupta, Anuradha; Lundgren, Andrew
2016-01-01
We describe a tool we improved to detect excess noise in the gravitational wave (GW) channel arising from its bilinear or nonlinear coupling with fluctuations of various components of a GW interferometer and its environment. We also describe a higher-order statistics tool we developed to characterize these couplings, e.g., by unraveling the frequencies of the fluctuations contributing to such noise, and demonstrate its utility by applying it to understand nonlinear couplings in Advanced LIGO engineering data. Once such noise is detected, it is highly desirable to remove it or correct for it. Such action in the past has been shown to improve the sensitivity of the instrument in searches of astrophysical signals. If this is not possible, then steps must be taken to mitigate its influence, e.g., by characterizing its effect on astrophysical searches. We illustrate this through a study of the effect of transient sine-Gaussian noise artifacts on a compact binary coalescence template bank.
Nonlinear Coupled Analysis of a Single Point Mooring System
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Coupled effects on a single point mooring (SPM) system subjected to the combined action of wind, waves and current are studied in this paper. Due to the complicatedness of the sea state and the huge size of the vessel, physical experimental study is both time consuming and uneconomical, whereas the numerical study is cost-effective and DNV software provides powerful SESAM software in solving the issues. This paper focuses on the modeling process of the SPM system, catenary equilibrium calculation, static analysis of the vessel in three different scenarios, and dynamic response simulation of the SPM system under environmental excitations. The three scenarios in study are as follows: the SPM is under the combined function of (a) wind, waves and current, (b) wind and waves, (c) current and waves. They are so set that one can compare the contributions of different types of loads in both static and dynamic studies. Numerical study shows that wind and current are the two major factors contributing to the mooring line tension, and surge and sway are the two dominant motions of the moored vessel subjected to environmental excitations.
Nonlinear local electrovascular coupling. II: From data to neuronal masses.
Riera, J J; Jimenez, J C; Wan, X; Kawashima, R; Ozaki, T
2007-04-01
In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.
Micro-/nanoscale multi-field coupling in nonlinear photonic devices
Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu
2017-08-01
The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.
Directory of Open Access Journals (Sweden)
Da-Guang Zhang
2015-10-01
Full Text Available For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao, E-mail: zhouhm@cjlu.edu.cn [College of Information Engineering, China Jiliang University, 310018, Hangzhou (China)
2015-10-15
For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Directory of Open Access Journals (Sweden)
Liang Hu
2016-10-01
Full Text Available A nonlinear coupled dynamic model of a rod fastening rotor under rub-impact and initial permanent deflection was developed in this paper. The governing motion equation was derived by the D’Alembert principle considering the contact characteristic between disks, nonlinear oil-film force, rub-impact force, unbalance mass, etc. The contact effects between disks was modeled as a flexural spring with cubical nonlinear stiffness. The coupled nonlinear dynamic phenomena of the rub-impact rod fastening rotor bearing system with initial permanent deflection were investigated by the fourth-order Runge-Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that the coupled dynamic responses of the rod fastening rotor bearing system under rub-impact and initial permanent deflection exhibit a rich nonlinear dynamic diversity, synchronous periodic-1 motion, multiple periodic motion, quasi-periodic motion and chaotic motion can be observed under certain conditions. Larger radial stiffness of the stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. With the increase of initial permanent deflection length, the instability speed of the system gradually rises, and the chaotic motion region gets smaller and smaller. The corresponding results can provide guidance for the fault diagnosis of a rub-impact rod fastening rotor with initial permanent deflection and contribute to the further understanding of the nonlinear dynamic characteristics of the rod fastening rotor bearing system.
Baldi, Marco
2010-01-01
We present a complete numerical study of cosmological models with a time dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid. Depending on the functional form of the coupling strength, these models show a range of possible intermediate behaviors between the standard LCDM background evolution and the widely studied case of interacting dark energy models with a constant coupling. These different background evolutions play a crucial role in the growth of cosmic structures, and determine strikingly different effects of the coupling on the internal dynamics of nonlinear objects. By means of a suitable modification of the cosmological N-body code GADGET-2 we have performed a series of high-resolution N-body simulations of structure formation in the context of interacting dark energy models with variable couplings. Depending on the type of background evolution, the halo density profiles are found to be either less or more...
Bitencourt, Ana Carla P; Littlejohn, Robert G; Anderson, Roger; Aquilanti, Vincenzo
2014-01-01
The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.
Institute of Scientific and Technical Information of China (English)
Shitao LIU; Roberto TRIGGIANI
2011-01-01
The authors study the inverse problem of recovering damping coefficients for two coupled hyperbolic PDEs with Neumann boundary conditions by means of an additional measurement of Dirichlet boundary traces of the two solutions on a suitable,explicit subportion Γ1 of the boundary Γ,and over a computable time interval T ＞ 0.Under sharp conditions on Γ0 =Γ\\Γ1,T ＞ 0,the uniqueness and stability of the damping coefficients are established.The proof uses critically the Carleman estimate due to Lasiecka et al.in 2000,together with a convenient tactical route "post-Carleman estimates" suggested by Isakov in 2006.
Energy Technology Data Exchange (ETDEWEB)
Assadi, S.
1994-01-01
Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ``sawtooth oscillations,`` have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma.
1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
陈予恕; 杨彩霞; 吴志强; 陈芳启
2001-01-01
The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in 1: 2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the 4-dimension bifurcation equations were reduced to 3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.
Zhu, Chengjie; Huang, Guoxiang
2011-11-07
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
SHAPE STABILITY OF OPTIMAL CONTROL PROBLEMS IN COEFFICIENTS FOR COUPLED SYSTEM OF HAMMERSTEIN TYPE
Directory of Open Access Journals (Sweden)
P. I. Kogut
2014-01-01
Full Text Available In this paper we consider an optimal control problem (OCP for the coupledsystem of a nonlinear monotone Dirichlet problem with matrix-valued L∞(Ω;RN×N-controls in coecients and a nonlinear equation of Hammerstein type, where solution nonlinearly depends on L∞ -control. Since problems of this type have no solutions in general, we make a special assumption on the coecients of the state equations and introduce the class of so-called solenoidal admissible controls. Using the direct method in calculus of variations, we prove the existence of an optimal control. We also study the stability of the optimal control problem with respect to the domain perturbation. In particular, we derive the sucient conditions of the Mosco-stability for the given class of OCPs.
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system
Energy Technology Data Exchange (ETDEWEB)
Zeng, Zaiping; Garoufalis, Christos S.; Baskoutas, Sotirios, E-mail: bask@upatras.gr
2014-07-18
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system have been theoretically studied. In general, we find that the structure parameters of the coupled system significantly affect the optical susceptibilities. The enhancement of the coupling effects between the dot and ring is found to increase considerably the optical susceptibilities and redshift drastically the transition energies. Comparing to the linear susceptibility, the nonlinear optical susceptibility is found to be more sensitive to the variation of the structure parameters. A comprehensive analysis of the electron probability density movement with respect to the modification of the structure parameters is provided, which offers a unique perspective of the ground-state localization. - Highlights: • Optical susceptibilities in a quantum-dot–quantum-ring system are studied. • The structure parameters significantly affect the optical susceptibilities. • The enhancement of the coupling effects increases the optical susceptibilities. • The nonlinear susceptibility is more sensitive to the change in structure parameters. • A comprehensive analysis of the electron probability density movement is provided.
A three-dimensional coupled numerical model of nonlinear waves in a harbor
Institute of Scientific and Technical Information of China (English)
L.G.THAM
2008-01-01
A 3-D time-domain numerical coupled model for nonlinear waves acting on a ship in a harbor has been developed in the present study.The whole domain is divided into the inner domain and the outer domain.The inner domain is the area around the ship,where the flow is expressed by the Laplace equation and numerically solved by the finite element method.The other area is the outer domain,where the flow is described by the higher-order Boussinesq equations and numerically solved by the finite difference method.The matching conditions on the interfaces between the inner domain and the outer domain,the procedure of coupled solution,the length of common domain and the mesh generation in the inner domain are discussed in detail.The other coupled model with the flow in the inner domain governed by the simplified linear Euler equations and relevant physical experiment are adopted to validate the present coupled model,and it is shown that the numerical results of the present model agree with the experimental data,so the present model can be used for the study on the effect of nonlinear waves acting on a fixed ship in a large area and provide a reference for the time-domain simulation of nonlinear wave forces on an arbitrary object in a large harbor and the 3-D district computation in the future.
Effective tunneling coefficient of a coupled double-well system modulated
Tsukada,Noriaki; Yoshida, H.; Suzuki, T.
2008-01-01
We numerically study coherent tunneling oscillations of the particles between two levels in a double-well potential in the presence of anharmonic periodic potentials. Extremely short driving pulses modify the tunneling coefficient to ef f= cos A, where is the bare tunneling coefficient without the driving field and A is the pulse area of the driving wave form. The modulation amplitude of the ef f gradually decreases as the driving wave form becomes broad and is given by ef f...
Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2+Crystal
Institute of Scientific and Technical Information of China (English)
ZHENG Wen-Chen; WU Shao-Yi
2001-01-01
According to a uniform and simple method of calculating spin-lattice coupling coefficients and the pert1rbation formulas of gi factors and hyperfine structure constants Ai based on the cluster approach for 3d7 ions in cubic,tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients Fij (F11, Fl2, F44), Zij (Z11, Z12,Z44) and also g factor and hyperfine constant A for MgO:Co2+ are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values.The difiiculty in explaining the coeficients Fij and Zij is therefore removed.``
Impurity Diffusion Coefficients of Al and Zn in Mg Determined from Solid-to-Solid Diffusion Couples
Energy Technology Data Exchange (ETDEWEB)
Kammerer, Catherine [University of Central Florida, Orlando; Kulkarni, Nagraj S [ORNL; Warmack, Robert J Bruce [ORNL; Perry, Kelly A [ORNL; Belova, Irina [University of Newcastle, NSW, Australia; Murch, Prof. Graeme [University of Newcastle, NSW, Australia; Sohn, Yong Ho [University of Central Florida
2013-08-01
Increasing use and development of lightweight Mgalloys have led to the desire for more fundamental research in and understanding of Mg-based systems. As property enhancing components, Al and Zn are two of the most important and common alloying elements for Mg-alloys. We have investigated the concentration dependent interdiffusion of Al and Zn in Mg using diffusion couples of pure polycrystalline Mg mated to Mg solid solutions containing either <9 at.% Al or <3 at.% Zn. Concentration profiles were determined by electron micro-probe microanalysis of the diffusion zone. The interdiffusion coefficients were determined by the classical Boltzmann-Matano method within the Mg solid solution. As the concentration of Al or Zn approaches the dilute ends, we employ an analytical approach based on the Hall method to estimate the impurity diffusion coefficients. Results of Al and Zn impurity diffusion in Mg are reported and compared to published impurity diffusion coefficients typically determined by thin film techniques.
Nonlinear electromagnetic fields in 0.5 MHz inductively coupled plasmas
DEFF Research Database (Denmark)
Ostrikov, K.N.; Tsakadze, E.L.; Xu, S.
2003-01-01
Radial profiles of magnetic fields in the electrostatic (E) and electromagnetic (H) modes of low-frequency (similar to500 kHz) inductively coupled plasmas have been measured using miniature magnetic probes. In the low-power (similar to170 W) E-mode, the magnetic field pattern is purely linear......, with the fundamental frequency harmonics only. After transition to higher-power (similar to1130 W) H-mode, the second-harmonic nonlinear azimuthal magnetic field B-phi(2omega) that is in 4-6 times larger than the fundamental frequency component B-phi(omega), has been observed. A simplified plasma fluid model...... explaining the generation of the second harmonics of the azimuthal magnetic field in the plasma source is proposed. The nonlinear second harmonic poloidal (r-z) rf current generating the azimuthal magnetic field B-phi(2omega) is attributed to nonlinear interactions between the fundamental frequency radial...
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.
2016-09-01
This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.
Chen, Yao; Ho, Daniel W C; Lü, Jinhu; Lin, Zongli
2016-01-01
Multiagent systems (MASs) are ubiquitous in our real world. There is an increasing attention focusing on the consensus (or synchronization) problem of MASs over the past decade. Although there are numerous results reported on the convergence of a discrete-time MAS based on the infinite products of matrices, few results are on the convergence rate. Because of the switching topology, the traditional eigenvalue analysis and the Lyapunov function methods are both invalid for the convergence rate analysis of an MAS with a switching topology. Therefore, the estimation of the convergence rate for a discrete-time MAS with time-varying delays remains a difficult problem. To overcome the essential difficulty of switching topology, this paper aims at developing a contractive-set approach to analyze the convergence rate of a discrete-time MAS in the presence of time-varying delays and generalized coupling coefficients. Using the proposed approach, we obtain an upper bound of the convergence rate under the condition of joint connectivity. In particular, the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients, which have been widely applied in the existing works on this topic. As an application of the main results, we will show that the classical Vicsek model with time delays can realize synchronization if the initial topology is connected.
Directory of Open Access Journals (Sweden)
Min Zhang
2015-10-01
Full Text Available In order to study the effects of uneven adhesion coefficient and crosswind on alignment design indexes, a six-axle semi-trailer is selected as the typical vehicle model to investigate the effects of uneven adhesion coefficient caused by superelevation under the condition of rainfall on the truck's lateral stability, quantifying the crosswind using TruckSim. Based on the basic theory of vehicle dynamics, vehicle safety driving model is established. Also, the minimum radius is calculated with the consideration of uneven adhesion coefficient and crosswind. The results show that the effects of uneven adhesion coefficient and crosswind on the truck's lateral stability increase with the increasing of the truck's speed. Truck's lateral slide instability begins to appear when crosswind grade grows up to 9 or above. According to sensitive analysis, speed, rainfall, crosswind, and the interaction of the speed and rainfall have significant influences on the truck's lateral stability. The results quantify the effects of uneven adhesion coefficient and crosswind on truck's lateral stability. The advised index for horizontal curve design control is proposed, which provides a good reference for road safety design and safety protective measures. It can also provide theoretical basis and guidelines for highway safe operation in the windy and rainy areas.
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Breathers and rogue waves: Demonstration with coupled nonlinear Schrödinger family of equations
Indian Academy of Sciences (India)
N Vishnu Priya; M Senthilvelan; M Lakshmanan
2015-03-01
Different types of breathers and rogue waves (RWs) are some of the important coherent structures which have been recently realized in several physical phenomena in hydrodynamics, nonlinear optics, Bose–Einstein condensates, etc. Mathematically, they have been deduced in non-linear Schrödinger (NLS) equations. Here we show the existence of general breathers, Akhmediev breathers, Ma soliton and rogue wave solutions in coupled Manakov-type NLS equations and coupled generalized NLS equations representing four-wave mixing. We deduce their explicit forms using Hirota bilinearization procedure and bring out their exact structures and important properties. We also show the method to deduce the various breather solutions from rogue wave solutions using factorization form and the so-called imbricate series.
Directory of Open Access Journals (Sweden)
Ahmad Bashir
2010-01-01
Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.
Stochastic Analysis of Nonlinear Coupled Heave-Pitch Motion for the Truss Spar Platform
Institute of Scientific and Technical Information of China (English)
Wenjun Shen; Yougang Tang
2011-01-01
Considering the static stability and the change of the displacement volume,including the influences of higher order nonlinear terms and the instantaneous wave surface,the nonlinear coupled heave-pitch motion was established in stochastic waves.The responses of heave-pitch coupling motion for the Truss Spar platform were investigated.It was found that,when the characteristic frequency of a stochastic wave is close to the natural heave frequency,the large amplitude pitch motion is induced under the parametric-forced excitation,which is called the Mathieu instability.It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent.In addition,the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.
Nonlinear analysis on the coupling process of electromagnetic vibrator and earth
Institute of Scientific and Technical Information of China (English)
CHEN; Zubin; TENG; Jiwen; LIN; Jun; ZHANG; Linhang; JIANG
2005-01-01
The linear model based on the hydraulic pressure vibrator has been no longer adaptable to the electromagnetic vibrator. In order to realize the effective transmission of the limited energy from the vibrator to the ground, it is important to study the coupling model of the electromagnetic vibrator and the earth. In this paper, a nonlinear restore term was introduced to the coupling model because of the existence of a large amount of harmonics in the vibrator baseplate. The nonlinear vibration analysis was applied to the model by the multiscale method. In the course of energy transmission from the vibrator to the ground, ultraharmonic resonance was used to explain the generation of harmonics. An improved scheme was advanced to select the cross correlation reference signal in the vibrator seismic exploration. Good application results were obtained in field experiments.
A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schr(o)dinger system
Institute of Scientific and Technical Information of China (English)
Cai Jia-Xiang; Wang Yu-Shun
2013-01-01
We derive a new method for a coupled nonlinear Schr(o)dinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative.We prove the proposed method preserves the charge and energy conservation laws exactly.In numerical tests,we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions.Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws.These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.
Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals
Yeh, Chien-Hung; Lo, Men-Tzung; Hu, Kun
2016-07-01
Recent studies of brain activities show that cross-frequency coupling (CFC) plays an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies - cross-frequency amplitude-amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstationarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.
Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space
Indian Academy of Sciences (India)
Li Zhang; Shutang Liu; Chenglong Yu
2014-06-01
In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces.
Photon antibunching and nonlinear effects for a quantum dot coupled to a semiconductor cavity
Bello, F.; Whittaker, D. M.
2010-09-01
The models presented simulate pumping techniques that can be used on modern semiconductor devices which are capable of coupling a quantum dot and cavity mode in order to determine a more efficient method of producing a single-photon emitter while taking into consideration typical parameters which are achievable given today’s standards of coupling strength. Cavity quantum electrodynamics are incorporated in the calculations as we compare various pumping schemes for the system that either use on-resonant laser excitation or nonresonant excitation due to a wetting layer. In particular, we look to study how antibunching effects change for each method as the cavity finesse is increased toward the strong coupling regime. Experimentally these studies are equivalent to nonlinear pump-probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam.
Optical transistor action by nonlinear coupling of stimulated emission and coherent scattering
Andrews, David L.; Bradshaw, David S.
2010-08-01
In the pursuit of improved platforms for computing, communications and internet connectivity, all-optical systems offer excellent prospects for a speed and fidelity of data transmission that will greatly surpass conventional electronics, alongside the anticipated benefits of reduced energy loss. With a diverse range of sources and fiber optical connections already in production, much current effort is being devoted towards forging optical components for signal switching, such as an all-optical transistor. Achievement of the desired characteristics for any practicable device can be expected to depend crucially on the engagement of a strongly nonlinear optical response. The innovative scheme proposed in the present work is based upon a third-order nonlinearity - its effect enhanced by stimulated emission - operating within a system designed to exploit the highly nonlinear response observed at the threshold for laser emission. Here, stimulated emission is strongly driven by coupling to the coherent scattering of a signal input beam whose optical frequency is purposely off-set from resonance. An electrodynamical analysis of the all-optical coupling process shows that the signal beam can significantly modify the kinetics of emission, and so lead to a dramatically enhanced output of resonant radiation. The underlying nonlinear optical mechanism is analyzed, model calculations are performed for realizable three-level laser systems, and the results exhibited graphically. The advantages of implementing this all-optical transistor scheme, compared to several previously envisaged proposals, are then outlined.
Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system
Samanta, C.; Yasasvi Gangavarapu, P. R.; Naik, A. K.
2015-10-01
Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances.
Smith, David D.
2002-01-01
This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.
Asymptotic Spreading Fastened by Inter-Specific Coupled Nonlinearities: a Cooperative System
Lin, Guo
2010-01-01
This paper is concerned with the asymptotic spreading of a Lotka-Volterra cooperative system. Utilizing the theory developed by Berestycki et al. [Asymptotic spreading in heterogeneous diffusive excitable media, J. Funct. Anal. \\textbf{255} (2008), 2146-2189] for nonautonomous scalar equations, the lower bounds of spreading speeds of unknown functions formulated by a coupled system are estimated. Our results imply that the asymptotic spreading of one species can be significantly fastened by introducing a mutual species, which indicates the role of cooperation described by the coupled nonlinearities.
Numerical Solutions of a New Type of Fractional Coupled Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
WANG Ling; CHEN Yong; DONG Zhong-Zhou; AN Hong-Li
2008-01-01
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the frac-tional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method.
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.
Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application
MA,LI; Lin ZHAO
2007-01-01
We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a s...
ORBITAL INSTABILITY OF STANDING WAVES FOR THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gan Zaihui; Guo Boling; Zhang Jian
2008-01-01
This paper deals with a type of standing waves for the coupled nonlin-ear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.
Periodic wavetrains for systems of coupled nonlinear Schrödinger equations
Indian Academy of Sciences (India)
Kwok W Chow; Derek W C Lal
2001-11-01
Exact, periodic wavetrains for systems of coupled nonlinear Schrödinger equations are obtained by the Hirota bilinear method and theta functions identities. Both the bright and dark soliton regimes are treated, and the solutions involve products of elliptic functions. The validity of these solutions is veriﬁed independently by a computer algebra software. The long wave limit is studied. Physical implications will be assessed.
Singular solitons and other solutions to a couple of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term
Bağcı, Mahmut; Bakırtaş, İlkay; Antar, Nalan
2017-01-01
Wave collapse is arrested in the self-focusing nonlinear Schrödinger equation with coupling to a mean term (NLSM) by adding an external potential (lattice) to the governing equation. It is numerically demonstrated that collapse will eventually occur in a lattice-free system and it can be suppressed by adding an external periodic lattice to the governing system. It is numerically shown that lattice depth provides great controllability on soliton stability and more robust solitons can be obtained.
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
2013-04-01
We consider a (possibly) nonlinear interface problem in 2D and 3D, which is solved by use of various adaptive FEM-BEM coupling strategies, namely the Johnson-Nédélec coupling, the Bielak-MacCamy coupling, and Costabel's symmetric coupling. We provide a framework to prove that the continuous as well as the discrete Galerkin solutions of these coupling methods additionally solve an appropriate operator equation with a Lipschitz continuous and strongly monotone operator. Therefore, the original coupling formulations are well-defined, and the Galerkin solutions are quasi-optimal in the sense of a Céa-type lemma. For the respective Galerkin discretizations with lowest-order polynomials, we provide reliable residual-based error estimators. Together with an estimator reduction property, we prove convergence of the adaptive FEM-BEM coupling methods. A key point for the proof of the estimator reduction are novel inverse-type estimates for the involved boundary integral operators which are advertized. Numerical experiments conclude the work and compare performance and effectivity of the three adaptive coupling procedures in the presence of generic singularities.
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-01-01
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear soliton matching between optical fibers
DEFF Research Database (Denmark)
Agger, Christian; Sørensen, Simon Toft; Thomsen, Carsten L.
2011-01-01
In this Letter, we propose a generic nonlinear coupling coefficient, η2 NL ¼ ηjγ=β2jfiber2=jγ=β2jfiber1, which gives a quantitative measure for the efficiency of nonlinear matching of optical fibers by describing how a fundamental soliton couples from one fiber into another. Specifically, we use η...
Directory of Open Access Journals (Sweden)
Gui Mu
2013-01-01
Full Text Available The existence of the exponential attractors for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities with periodic initial boundary is obtained by showing Lipschitz continuity and the squeezing property.
Directory of Open Access Journals (Sweden)
Yongle Li
2015-01-01
Full Text Available Compared with medium and small span bridges, very limited attention has been paid on the research of the impact coefficient of long-span railway bridges. To estimate the impact effects of long-span railway bridges subjected to moving vehicles, a real long-span railway cable-stayed bridge is regarded as the research object in this study, and a coupled model of vehicle-bridge system is established. The track irregularities are taken as the system excitation and the dynamic responses of the vehicle-bridge system are calculated. The impact effects on main girder, stayed cable, bearings, and bridge tower are discussed at various vehicle speeds. The results show that different components of the long-span railway cable-stayed bridge have different impact coefficients. Even for each part, the impact coefficient is also different at different local positions. It reveals that the impact coefficients in the actual situation may have significant differences with the related code clauses in the present design codes.
A Non-Hermitian Approach to Non-Linear Switching Dynamics in Coupled Cavity-Waveguide Systems
DEFF Research Database (Denmark)
Heuck, Mikkel; Kristensen, Philip Trøst; Mørk, Jesper
2012-01-01
We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations.......We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations....
Fiber-coupled nanophotonic devices for nonlinear optics and cavity QED
Barclay, Paul Edward
2007-10-01
The sub-wavelength optical confinement and low optical loss of nanophotonic devices dramatically enhances the interaction between light and matter within these structures. When nanophotonic devices are combined with an efficient optical coupling channel, nonlinear optical behavior can be observed at low power levels in weakly-nonlinear materials. In a similar vein, when resonant atomic systems interact with nanophotonic devices, atom-photon coupling effects can be observed at a single quanta level. Crucially, the chip based nature of nanophotonics provides a scalable platform from which to study these effects. This thesis addresses the use of nanophotonic devices in nonlinear and quantum optics, including device design, optical coupling, fabrication and testing, modeling, and integration with more complex systems. We present a fiber taper coupling technique that allows efficient power transfer from an optical fiber into a photonic crystal waveguide. Greater than 97% power transfer into a silicon photonic crystal waveguide is demonstrated. This optical channel is then connected to a high-Q (> 40,000), ultra-small mode volume (V 44% of the photons input to a fiber. This permits the observation of optical bistability in silicon for sub-mW input powers at telecommunication wavelengths. To port this technology to cavity QED experiments at near-visible wavelengths, we also study silicon nitride microdisk cavities at wavelengths near 852 nm, and observe resonances with Q > 3 million and V device with an atom chip, creating an "atom-cavity chip" which can magnetically trap laser cooled atoms above the microcavity. Calculations of the microcavity single atom sensitivity as a function of Q/V are presented and compared with numerical simulations. Taking into account non-idealities, these cavities should allow detection of single laser cooled cesium atoms.
Linear and nonlinear heavy ion-acoustic waves in a strongly coupled plasma
Energy Technology Data Exchange (ETDEWEB)
Ema, S. A., E-mail: ema.plasma@gmail.com; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh); Hossen, M. R. [Deparment of Natural Sciences, Daffodil International University, Sukrabad, Dhaka-1207 (Bangladesh)
2015-09-15
A theoretical study on the propagation of linear and nonlinear heavy ion-acoustic (HIA) waves in an unmagnetized, collisionless, strongly coupled plasma system has been carried out. The plasma system is assumed to contain adiabatic positively charged inertial heavy ion fluids, nonextensive distributed electrons, and Maxwellian light ions. The normal mode analysis is used to study the linear behaviour. On the other hand, the well-known reductive perturbation technique is used to derive the nonlinear dynamical equations, namely, Burgers equation and Korteweg-de Vries (K-dV) equation. They are also numerically analyzed in order to investigate the basic features of shock and solitary waves. The adiabatic effects on the HIA shock and solitary waves propagating in such a strongly coupled plasma are taken into account. It has been observed that the roles of the adiabatic positively charged heavy ions, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features (viz., polarity, amplitude, width, etc.) of the HIA solitary/shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the linear as well as nonlinear phenomena associated with the HIA waves both in space and laboratory plasmas.
Castro López, R.; Sun, Guo-Hua; Camacho-Nieto, O.; Yáñez-Márquez, C.; Dong, Shi-Hai
2017-09-01
We present analytical matter-wave solutions to a generalized Gross-Pitaevskii (GGP) equation with several new time and space varying nonlinearity coefficients and external fields. This is realized by taking a suitable similarity transformation to the GGP equation which makes the original partial differential equation into a stationary and ordinary differential equation. We report a few families of analytical solutions of the GGP equation with several new time and space varying nonlinearity interactions, in which some physically relevant soliton solutions are found. The profile features of the evolution wave functions depend on the different choices of the composite functions ξ.
Institute of Scientific and Technical Information of China (English)
Xin-yu Lai; Nan-rong Zhao
2013-01-01
Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts.A generalized Langevin equation is adopted to describe the diffusion dynamics.Mode-coupling theory is employed to calculate the memory kernel of friction.For simplicity,only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism.The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure.The effect of nanoparticle size and that of the polymer size are clarified explicitly.The structural functions,the friction kernel,as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length.We find that for small nanoparticles or short chain polymers,the characteristic short time non-Markov diffusion dynamics becomes more prominent,and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant.This constant due to the microscopic contributions will decrease with the increase of nanoparticle size,while increase with polymer size.Furthermore,our result of diffusion constant from modecoupling theory is compared with the value predicted from the Stokes-Einstein relation.It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers.Inversely,when nanonparticle is big,or polymer chain is short,the hydrodynamic contribution might play a significant role.
Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang
2017-04-01
Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.
DEFF Research Database (Denmark)
Marschler, Christian; Vollmer, Jürgen
2014-01-01
, the Reynolds number for pipe flow, and with transitions from bounded chaotic patches to an invasion of space of irregular motion. Dynamical systems models are unique tools in this respect because they can provide insight into the origin of the very long lifetime of puffs, and the dynamical mechanism leading......Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest in identifying mechanisms that generate chaotic transients with superexponential growth of lifetime as a function of a control parameter...... to the transition from puffs to slugs in pipe flow. The present paper contributes to this enterprise by introducing a unidirectionally coupled map lattice. It mimics three of the salient features of pipe-flow turbulence: (i) the transition from laminar flow to puffs, (ii) a superexponential scaling of puff lifetime...
Marschler, Christian
2014-01-01
Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential growth of lifetime as a function of a control parameter, the Reynolds number for pipe flow, and with transitions from bounded chaotic patches to an invasion of space of irregular motion. Dynamical systems models are unique tools in this respect because they can provide insight into the origin of the very long life time of puffs, and the dynamical mechanism leading to the transition from puffs to slugs in pipe flow. The present paper contributes to this enterprise by introducing a unidirectionally coupled map lattice. It mimics three of the salient features of pipe-flow turbulence: (i) the transition from laminar flow to puffs, (ii) a super-exponential scaling of puff lifetime, and (iii) the transition from puffs to slugs by an unbinding transition in an intermittency scenario. ...
Yongle Li; Shifu Dong; Yulong Bao; Kejian Chen; Shizhong Qiang
2015-01-01
Compared with medium and small span bridges, very limited attention has been paid on the research of the impact coefficient of long-span railway bridges. To estimate the impact effects of long-span railway bridges subjected to moving vehicles, a real long-span railway cable-stayed bridge is regarded as the research object in this study, and a coupled model of vehicle-bridge system is established. The track irregularities are taken as the system excitation and the dynamic responses of the vehi...
Murrell, J K J
2001-01-01
previously unexplored regions of parameter space. We show that these calculations predict a range of previously unreported dynamical I-V characterises for SQUID rings in the strongly hysteretic regime. Finally, we present the successful realisation of a novel experimental technique that permits the weak link of a SQUID to be probed independently of the associated ring structure by mechanically opening and closing the ring. We demonstrate that this process can be completed during the same experimental run without the need for warming and re-cooling of the sample. This thesis is concerned with the investigation of the non-linear behaviour of a Superconducting Quantum Interference Device (SQUID) coupled to a RF tank circuit. We consider two regimes, one where the underlying SQUID behaviour is non-hysteretic with respect to an externally applied magnetic flux, and the other where hysteretic (dissipative) behaviour is observed. We show that, by following non-linearities induced in the tank circuit response, the un...
Mukamel, Shaul
2003-08-01
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
Nonlinear localized flat-band modes with spin-orbit coupling
Gligorić, G.; Maluckov, A.; Hadžievski, Lj.; Flach, Sergej; Malomed, Boris A.
2016-10-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The no-scalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the General Relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
Scalar-tensor black holes coupled to Euler-Heisenberg nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler-Heisenberg type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. In comparison to the corresponding solution in General Relativity the presented solution has a simpler causal structure the reason for which is the presence of the scalar field. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
Directory of Open Access Journals (Sweden)
El Aroudi A.
2014-01-01
Full Text Available Nonlinearities have been shown to play an important role in increasing the extracted energy of energy harvesting devices at the macro and micro scales. Vibration-based energy harvesting on the nano scale has also received attention. In this paper, we characterize the nonlinear dynamical behavior of an array of three coupled strained nanostructured graphene for its potential use in energy harvesting applications. The array is formed by three compressed vibrating membrane graphene sheet subject to external vibrational noise excitation. We present the continuous time dynamical model of the system in the form of a double-well three degree of freedom system. Random vibrations are considered as the main ambient energy source for the system and its performances in terms of the probability density function, RMS or amplitude value of the position, FFT spectra and state plane trajectories are presented in the steady state non-equilibrium regime when the noise level is considered as a control parameter.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
Geometry effect on energy transfer rate in a coupled-quantum-well structure: nonlinear regime
Salavati-fard, T.; Vazifehshenas, T.
2014-12-01
We study theoretically the effect of geometry on the energy transfer rate at nonlinear regime in a coupled-quantum-well system using the balance equation approach. To investigate comparatively the effect of both symmetric and asymmetric geometry, different structures are considered. The random phase approximation dynamic dielectric function is employed to include the contributions from both quasiparticle and plasmon excitations. Also, the short-range exchange interaction is taken into account through the Hubbard approximation. Our numerical results show that the energy transfer rate increases by increasing the well thicknesses in symmetric structures. Furthermore, by increasing spatial asymmetry, the energy transfer rate decreases for the electron temperature range of interest. From numerical calculations, it is obtained that the nonlinear energy transfer rate is proportional to the square of electron drift velocity in all structures and also, found that the influence of Hubbard local field correction on the energy transfer rate gets weaker by increasing the strength of applied electric field.
A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations
Oruç, Ömer; Esen, Alaattin; Bulut, Fatih
2016-04-01
In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.
Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.
Jiang, Zhongzheng; Zhao, Wenwen
2016-01-01
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computational model, namely the nonlinear coupled constitutive relations(NCCR),was developed by R.S.Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are fistly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows,a modified solution is developed for the NCCR model. Finally, the modified solu...
Institute of Scientific and Technical Information of China (English)
LI Hua-Mei
2003-01-01
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.
Nonlinear Peltier effect in semiconductors
Zebarjadi, Mona; Esfarjani, Keivan; Shakouri, Ali
2007-09-01
Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar
2016-07-01
We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the
Fartoukh, Stéphane David
2002-01-01
The control of the mechanical and dynamic aperture of the LHC requires a tight control of linear optics parameters such as the tune, the beta-functions and the linear coupling resonance driving terms. This report presents a non-standard measurement method of these parameters based on a transverse excitation of the beam in "AC-dipole" mode, that is at one or several frequencies close to but outside the eigenfrequency spectrum of the beam. After having derived the general expression of the beam response in four dimensions, the measurement protocol and different possible hardware configurations will be described and simulation results obtained for the LHC will be presented.
Energy Technology Data Exchange (ETDEWEB)
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
Energy Technology Data Exchange (ETDEWEB)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato.minamitsuji@ist.utl.pt, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Coupled Nonlinear Schr(o)dinger Equation: Symmetries and Exact Solutions
Institute of Scientific and Technical Information of China (English)
LIU Ping; LOU Sen-Yue
2009-01-01
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schr(o)dinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Lennart; García-Morales, Vladimir [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching (Germany); Schönleber, Konrad; Krischer, Katharina, E-mail: krischer@tum.de [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)
2014-03-15
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
Directory of Open Access Journals (Sweden)
Helge Holden
2003-04-01
Full Text Available We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general $L^p$ compactness criterion. The uniqueness proof is an adaption of Kruzkov's ``doubling of variables'' proof. We also present a numerical example motivated by biodegradation in porous media.
Wang, Wenbo; Mayrhofer, Patrick M.; He, Xingli; Gillinger, Manuel; Ye, Zhi; Wang, Xiaozhi; Bittner, Achim; Schmid, Ulrich; Luo, J. K.
2014-09-01
AlN and AlScN thin films with 27% scandium (Sc) were synthesized by DC magnetron sputtering deposition and used to fabricate surface acoustic wave (SAW) devices. Compared with AlN-based devices, the AlScN SAW devices exhibit much better transmission properties. Scandium doping results in electromechanical coupling coefficient, K2, in the range of 2.0% ˜ 2.2% for a wide normalized thickness range, more than a 300% increase compared to that of AlN-based SAW devices, thus demonstrating the potential applications of AlScN in high frequency resonators, sensors, and high efficiency energy harvesting devices. The coupling coefficients of the present AlScN based SAW devices are much higher than that of the theoretical calculation based on some assumptions for AlScN piezoelectric material properties, implying there is a need for in-depth investigations on the material properties of AlScN.
Institute of Scientific and Technical Information of China (English)
WU YUE-XIANG; HUO YAN-MEI; WU YA-KUN
2012-01-01
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method.Some new existence results are obtained.
Wang, Lei; Qi, Feng-Hua; Tang, Bing; Shi, Yu-Ying
2016-12-01
Under investigation in this paper is a variable-coefficient AB (vcAB) system, which describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. The modulation instability analysis of solutions with variable coefficients in the presence of a small perturbation is studied. The modified Darboux transformation (mDT) of the vcAB system is constructed via a gauge transformation. The first-order non-autonomous rogue wave solutions of the vcAB system are presented based on the mDT. It is found that the wave amplitude of B exhibits two types of structures, i.e. the double-peak structure appears if the plane-wave solution parameter ω is equal to zero, while selecting ω≠0 yields a single-peak one. Effects of the variable coefficients on the rogue waves are graphically discussed in detail. The periodic rogue wave and composite rogue wave are obtained with different inhomogeneous parameters. Additionally, the nonlinear tunneling of the rogue waves through a conventional hyperbolic nonlinear well and barrier are investigated.
Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling.
García-Morales, Vladimir; Orlov, Alexander; Krischer, Katharina
2010-12-01
A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.
Institute of Scientific and Technical Information of China (English)
Cai-Wan Chang-Jian; Her-Terng Yau
2007-01-01
This study performs a dynamic analysis of a rotor supported by two squeeze couple stress fluid film journal bearings with nonlinear suspension. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the dimensionless parameter l*. It is found that the system is more stable with higher dimensionless parameter l*.Thus it can conclude that the rotor-bearing system lubricated with the couple stress fluid is more stable than that with the conventional Newtonian fluid. The modeling results thus obtained by using the method proposed in this paper can be used to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.
Nonlinear coupled dynamics of liquid-filled spherical container in microgravity
Institute of Scientific and Technical Information of China (English)
YUE Bao-zeng
2008-01-01
Nonlinear coupled dynamics of a liquid-filled spherical container in micro- gravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the vari- ational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid free surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filed container are derived using the Lagrange's method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.
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.
Localized waves in three-component coupled nonlinear Schrödinger equation
Xu, Tao; Chen, Yong
2016-09-01
We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
The Relationship between Tsallis Statistics, the Fourier Transform, and Nonlinear Coupling
Nelson, Kenric P
2008-01-01
Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \\to q$ . The essence of this translation is to improve the mathematical symmetry of the q-algebra and make q directly proportional to the nonlinear coupling. A conjugate transformation is defined $\\hat q \\equiv \\frac{{- 2q}}{{2 + q}}$ which provides a dual mapping between the heavy-tail q-Gaussian distributions, whose translated q parameter is between $ - 2 < q < 0$, and the compact-support q-Gaussians, between $0 < q < \\infty $ . This conjugate transformation is used to extend the definition of the q-Fourier transform to the domain of compact support. A conjugate q-Fourier transform is proposed which transforms a q-Gaussian into a conjugate $\\hat q$ -Gaussian, which has the same exponential decay as the Fourier transform of a power-law function. The nonlinear statistical coupling is defined such that the conjugate ...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Elnaggar, Sameh Y; Tervo, Richard; Mattar, Saba M
2014-05-01
A cavity (CV) with a dielectric resonator (DR) insert forms an excellent probe for the use in electron paramagnetic resonance (EPR) spectrometers. The probe's coupling coefficient, κ, the quality factor, Q, and the filling factor, η are vital in assessing the EPR spectrometer's performance. Coupled mode theory (CMT) is used to derive general expressions for these parameters. For large permittivity the dominating factor in κ is the ratio of the DR and CV cross sectional areas rather than the dielectric constant. Thus in some cases, resonators with low dielectric constant can couple much stronger with the cavity than do resonators with a high dielectric constant. When the DR and CV frequencies are degenerate, the coupled η is the average of the two uncoupled ones. In practical EPR probes the coupled η is approximately half of that of the DR. The Q of the coupled system generally depends on the eigenvectors, uncoupled frequencies (ω1,ω2) and the individual quality factors (Q1,Q2). It is calculated for different probe configurations and found to agree with the corresponding HFSS® simulations. Provided there is a large difference between the Q1, Q2 pair and the frequencies of DR and CV are degenerate, Q is approximately equal to double the minimum of Q1 and Q2. In general, the signal enhancement ratio, Iwithinsert/Iempty, is obtained from Q and η. For low loss DRs it only depends on η1/η2. However, when the DR has a low Q, the uncoupled Qs are also needed. In EPR spectroscopy it is desirable to excite only a single mode. The separation between the modes, Φ, is calculated as a function of κ and Q. It is found to be significantly greater than five times the average bandwidth. Thus for practical probes, it is possible to excite one of the coupled modes without exciting the other. The CMT expressions derived in this article are quite general and are in excellent agreement with the lumped circuit approach and finite numerical simulations. Hence they can also be
Sanagi, Mohd Marsin; Miskam, Mazidatulakmam; Wan Ibrahim, Wan Aini; Hermawan, Dadan; Aboul-Enein, Hassan Y
2010-07-01
A three-phase hollow fiber liquid-phase microextraction method coupled with CE was developed and used for the determination of partition coefficients and analysis of selected nitrophenols in water samples. The selected nitrophenols were extracted from 14 mL of aqueous solution (donor solution) with the pH adjusted to pH 3 into an organic phase (1-octanol) immobilized in the pores of the hollow fiber and finally backextracted into 40.0 microL of the acceptor phase (NaOH) at pH 12.0 located inside the lumen of the hollow fiber. The extractions were carried out under the following optimum conditions: donor solution, 0.05 M H(3)PO(4), pH 3.0; organic solvent, 1-octanol; acceptor solution, 40 microL of 0.1 M NaOH, pH 12.0; agitation rate, 1050 rpm; extraction time, 15 min. Under optimized conditions, the calibration curves for the analytes were linear in the range of 0.05-0.30 mg/L with r(2)>0.9900 and LODs were in the range of 0.01-0.04 mg/L with RSDs of 1.25-2.32%. Excellent enrichment factors of up to 398-folds were obtained. It was found that the partition coefficient (K(a/d)) values were high for 2-nitrophenol, 3-nitrophenol, 4-nitrophenol, 2,4-dinitrophenol and 2,6-dinitrophenol and that the individual partition coefficients (K(org/d) and K(a/org)) promoted efficient simultaneous extraction from the donor through the organic phase and further into the acceptor phase. The developed method was successfully applied for the analysis of water samples.
Energy Technology Data Exchange (ETDEWEB)
Gambhir, Monica, E-mail: monica.gambhir@yahoo.com [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Kumar, Manoj [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Jha, P.K. [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Deen Dayal Upadhyaya College, University of Delhi, Delhi 110015 (India); Mohan, Man [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India)
2013-11-15
The linear and nonlinear optical absorption coefficients and changes in the refractive index in GaAs/AlGaAs quantum disk in the form of a flat cylinder are investigated theoretically in the presence of a static magnetic and a laser field within the framework of the compact-density matrix approach. It is found that the absorption coefficients and the refractive index changes depend not only on the optical wave intensity but also on the strength of the static magnetic field. The intersubband relaxation time, also, has an important influence on the linear and nonlinear optical properties of a quantum disk. -- Highlights: • The study is carried out in a quantum disk having quantum dot geometry. • The linear and non-linear optical properties are studied using density matrix approach. • The study is carried out in the presence of a laser field and a magnetic field. • Influence of incident photon energy and static magnetic field is analyzed. • The optical properties are found to be greatly influenced by the relaxation time.
Wang, Luyun; Li, Lu; Li, Zhonghao; Zhou, Guosheng; Mihalache, Dumitru
2005-09-01
The generalized nonlinear Schrödinger model with distributed dispersion, nonlinearity, and gain or loss is considered and the explicit, analytical solutions describing the dynamics of bright solitons on a continuous-wave background are obtained in quadratures. Then, the generation, compression, and propagation of pulse trains are discussed in detail. The numerical results show that solitons can be compressed by choosing the appropriate control fiber system, and pulse trains generated by modulation instability can propagate undistorsted along fibers with distributed parameters by controlling appropriately the energy of each pulse in the pulse train.
Bartels, Robert E.
2002-01-01
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
Gomes, Jay
A power measurement system has been designed for an ultra-high temperature inductively heated molten oxide electrolysis (MOE) reactor. The work presented in this research contributes to three different aspects of the induction heated MOE reactor facility: mathematical modeling of coil-to-workpiece power transfer, numerical modeling of heat transfer within the reactor, and experiments to measure the total hemispherical emittance of potential crucible materials. Facility-specific coupling coefficients for various samples have been experimentally determined for the MOE reactor facility. An analytical model coupling the predicted power input with heat transfer software was developed using COMSOL Multiphysics, and validated with experimental measurements of the steady state temperature gradient inside the reactor. These models were used to support the design of an experiment to measure the total hemispherical emissivity (epsilon) of conductive samples using a transient calorimetric technique. Results of epsilon are presented over a wide range of temperatures for copper, nickel, graphite and molybdenum. Furthermore, an investigation into optimizing the reactor system for heating will be discussed.
Directory of Open Access Journals (Sweden)
Xiaoyan Lei
2016-01-01
Full Text Available A model for dynamic analysis of the vehicle-track nonlinear coupling system is established by the finite element method. The whole system is divided into two subsystems: the vehicle subsystem and the track subsystem. Coupling of the two subsystems is achieved by equilibrium conditions for wheel-to-rail nonlinear contact forces and geometrical compatibility conditions. To solve the nonlinear dynamics equations for the vehicle-track coupling system, a cross iteration algorithm and a relaxation technique are presented. Examples of vibration analysis of the vehicle and slab track coupling system induced by China’s high speed train CRH3 are given. In the computation, the influences of linear and nonlinear wheel-to-rail contact models and different train speeds are considered. It is found that the cross iteration algorithm and the relaxation technique have the following advantages: simple programming; fast convergence; shorter computation time; and greater accuracy. The analyzed dynamic responses for the vehicle and the track with the wheel-to-rail linear contact model are greater than those with the wheel-to-rail nonlinear contact model, where the increasing range of the displacement and the acceleration is about 10%, and the increasing range of the wheel-to-rail contact force is less than 5%.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-02-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Dymnikova, Irina
2015-01-01
In nonlinear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have obligatory de Sitter centre. By the G\\"urses-G\\"ursey algorithm they are transformed to spinning electrically charged solutions asymptotically Kerr-Newman for a distant observer. Rotation transforms de Sitter center into de Sitter vacuum surface which contains equatorial disk $r=0$ as a bridge. We present general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.
Low-Dimensional Models for Physiological Systems: Nonlinear Coupling of Gas and Liquid Flows
Staples, A. E.; Oran, E. S.; Boris, J. P.; Kailasanath, K.
2006-11-01
Current computational models of biological organisms focus on the details of a specific component of the organism. For example, very detailed models of the human heart, an aorta, a vein, or part of the respiratory or digestive system, are considered either independently from the rest of the body, or as interacting simply with other systems and components in the body. In actual biological organisms, these components and systems are strongly coupled and interact in complex, nonlinear ways leading to complicated global behavior. Here we describe a low-order computational model of two physiological systems, based loosely on a circulatory and respiratory system. Each system is represented as a one-dimensional fluid system with an interconnected series of mass sources, pumps, valves, and other network components, as appropriate, representing different physical organs and system components. Preliminary results from a first version of this model system are presented.
The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
Linander, Hampus
2016-01-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using $F=0$ to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this n...
Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicate...
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
Hajjaj, Amal Z.
2017-01-30
We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
Directory of Open Access Journals (Sweden)
A. Sheykhi
2016-01-01
Full Text Available We construct a new class of charged rotating black brane solutions in the presence of logarithmic nonlinear electrodynamics with complete set of the rotation parameters in arbitrary dimensions. The topology of the horizon of these rotating black branes is flat, while due to the presence of the dilaton field the asymptotic behavior of them is neither flat nor (anti-de Sitter [(AdS]. We investigate the physical properties of the solutions. The mass and angular momentum of the spacetime are obtained by using the counterterm method inspired by AdS/CFT correspondence. We derive temperature, electric potential, and entropy associated with the horizon and check the validity of the first law of thermodynamics on the black brane horizon. We study thermal stability of the solutions in both canonical and grand-canonical ensemble and disclose the effects of the rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions. We find the solutions are thermally stable for α1 the solutions may encounter an unstable phase, where α is dilaton-electromagnetic coupling constant.
Wang, Lei; Zhang, Jian-Hui; Liu, Chong; Li, Min; Qi, Feng-Hua
2016-06-01
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W -shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W -shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
All-electrical nonlinear fano resonance in coupled quantum point contacts
Xiao, Shiran
This thesis is motivated by recent interest in the Fano resonance (FR). As a wave-interference phenomenon, this resonance is of increasing importance in optics, plasmon-ics, and metamaterials, where its ability to cause rapid signal modulations under variation of some suitable parameter makes it desirable for a variety of applications. In this thesis, I focus on a novel manifestation of this resonance in systems of coupled quantum point contacts (QPCs). The major finding of this work is that the FR in this system may be ma-nipulated by applying a nonlinear DC bias to the system. Under such conditions, we are able to induce significant distortions of resonance lineshape, providing a pathway to all-electrical manipulation of the FR. To interpret this behavior we apply a recently-developed model for a three-path FR, involving an additional "intruder" continuum. We have previously used this model to account for the magnetic-field induced distortions of the FR observed in coupled QPCs, and show here that this model also provides a frame-work for understanding the observed nonlinear behavior. Our work therefore reveals a new manifestation of the FR that can be sensitively tailored by external control, a finding that may eventually allow the application of this feature to nanoelectronics. Since the in-terference scheme involves in this thesis is a completely general one, it should be broadly applicable across a variety of different wave-based systems, including those in both pho-tonics and electronics and opening up the possibility of new applications in areas such as chemical and biological sensing and secure communications.
You, Bin Di; Wen, Jian Min; Zhao, Yang
2014-03-01
In this paper, a nonlinear dynamic modeling method for a rigid-flexible coupling satellite antenna system composed of laminated shell reflector is proposed undergoing a large overall motion. For the study of the characteristics of the reflector using laminated shell structure, the displacement field description of a point in a 3-noded shell element is acquired in conjunction with the length stretch, lateral bending and torsional deformation. Hence, a nonlinear dynamic model of the satellite antenna system is deduced based on Lagrange's equations. The complete expressions of nonlinear terms of elastic deformation and coupling terms between rigid motion and large deflection are considered in the dynamic equations, and the dynamic behavior of the rigid-flexible coupling system is analyzed using linear model and nonlinear model, respectively. In order to eliminate the system vibration, the PD with vibration force feedback control strategy is used to achieve its desired angles and velocity in a much shorter duration, and can further accomplish reduction of residual vibration. Then, the asymptotic stability of the system is proved based on the Lyapunov method. Through numerical computation, the results show that the linear model cannot capture the motion-induced coupling terms and geometric nonlinearity variations. However, the nonlinear model is suitable for dealing with large deformation rigid-flexible problem undergoing large overall motions. Hence, the satellite antenna pointing accuracy would be predicted based on the nonlinear model. Furthermore, the results also show that the proposed control strategy can suppress system vibration quickly. The above conclusions would have important academic significance and engineering value.
Weavers, Paul T; Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Tryggestad, Erik J; Gunter, Jeffrey L; McGee, Kiaran P; Litwiller, Daniel V; Hwang, Ken-Pin; Bernstein, Matt A
2017-05-01
Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs. 5th) spherical harmonic coefficients for better spatial accuracy in MRI. A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems. A decrease in the root-mean-square error (RMSE) over a 50cm diameter spherical volume from 1.80mm to 0.77mm is reported here in the case of replacing the vendor's standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner. The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor
Pakhomov, A V; Babushkin, I V; Arkhipov, M V; Tolmachev, Yu A; Rosanov, N N
2016-01-01
We study the optical response of a resonant medium possessing the nonlinear coupling to external field under excitation by few-cycle pump pulses. A theoretical approach is developed, allowing to analyze unipolar half-cycle pulse generation in such a geometry. Our approach is applicable for the arbitrary coupling functions as well as arbitrarily curved pump pulse wavefronts and defines a general framework to produce unipolar pulses of desired form.
Müstecaplıoğlu, Özgür; Hardal, Ali Ümit
2014-01-01
We investigate spin squeezing, quantum entanglement, and second-order coherence in two coupled, driven, dissipative, nonlinear cavities. We compare these quantum statistical properties for the cavities coupled with either single- or two-photon exchange. Solving the quantum optical master equation of the system numerically in the steady state, we calculate the zero-time delay second-order correlation function for the coherent, genuine two-mode entanglement parameters, an optimal spin squeezing...
Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites
Khan, Kamran
2012-05-01
This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro-macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation. © 2012 Elsevier Ltd.
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.
Standing waves for coupled nonlinear Schrödinger equations with decaying potentials
Energy Technology Data Exchange (ETDEWEB)
Chen, Zhijie, E-mail: chenzhijie1987@sina.com; Zou, Wenming, E-mail: wzou@math.tsinghua.edu.cn [Department of Mathematical Sciences, Tsinghua University, Beijing 100084 (China)
2013-11-15
We study the following singularly perturbed problem for a coupled nonlinear Schrödinger system which arises in Bose-Einstein condensate: −ε{sup 2}Δu + a(x)u = μ{sub 1}u{sup 3} + βuv{sup 2} and −ε{sup 2}Δv + b(x)v = μ{sub 2}v{sup 3} + βu{sup 2}v in R{sup 3} with u, v > 0 and u(x), v(x) → 0 as |x| → ∞. Here, a, b are non-negative continuous potentials, and μ{sub 1}, μ{sub 2} > 0. We consider the case where the coupling constant β > 0 is relatively large. Then for sufficiently small ε > 0, we obtain positive solutions of this system which concentrate around local minima of the potentials as ε → 0. The novelty is that the potentials a and b may vanish at someplace and decay to 0 at infinity.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
Lehmann, G.; Spatschek, K. H.
2013-07-01
Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime.
Rury, Aaron S.
2016-06-01
This study reports experimental, computational, and theoretical evidence for a previously unobserved coherent phonon-phonon interaction in an organic solid that can be described by the application of Fano's analysis to a case without the presence of a continuum. Using Raman spectroscopy of the hydrogen-bonded charge-transfer material quinhydrone, two peaks appear near 700 cm-1 we assign as phonons whose position and line-shape asymmetry depend on the sample temperature and light scattering excitation energy. Density functional theory calculations find two nearly degenerate phonons possessing frequencies near the values found in experiment that share similar atomic motion out of the aromatic plane of electron donor and acceptor molecules of quinhydrone. Further analytical modeling of the steady-state light scattering process using the Peierls-Hubbard Hamiltonian and time-dependent perturbation theory motivates assignment of the physical origin of the asymmetric features of each peak's line shape to an interaction between two discrete phonons via nonlinear electron-phonon coupling. In the context of analytical model results, characteristics of the experimental spectra upon 2.33 eV excitation of the Raman scattering process are used to qualify the temperature dependence of the magnitude of this coupling in the valence band of quinhydrone. These results broaden the range of phonon-phonon interactions in materials in general while also highlighting the rich physics and fundamental attributes specific to organic solids that may determine their applicability in next generation electronics and photonics technologies.
Beninato, A.; Emery, T.; Baglio, S.; Andò, B.; Bulsara, A. R.; Jenkins, C.; Palkar, V.
2013-12-01
Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi0.7Dy0.3FeO3 shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi0.7Dy0.3FeO3, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a "blueprint" for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or "target" B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.
Liu, Shuang; Zhao, Shuang-Shuang; Wang, Zhao-Long; Li, Hai-Bin
2015-01-01
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results. Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).
Chen, Shi; Zhang, Yinhong; Lin, Shuyu; Fu, Zhiqiang
2014-02-01
The electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices is investigated by the transfer matrix method. Research results show the high electromechanical coupling coefficient can be obtained in these systems. The optimization design of it is also discussed fully. It is significantly influenced by electrical boundary conditions on interfaces, thickness ratios of piezoelectric and non-piezoelectric layers, and material parameters (such as velocities of pure longitudinal and transversal bulk waves in non-piezoelectric layers). In order to obtain higher electromechanical coupling coefficient, shorted interfaces, non-piezoelectric materials with large velocities of longitudinal and transversal bulk waves, and proper thickness ratios should be chosen.
Sellami, Amira; Kchaou, Mohamed; Elleuch, Riadh; Desplanques, Yannick
2016-09-01
Aiming to provide a better understanding of thermal phenomena occurring in a sliding contact under tribological solicitation, a numerical model of pad-on-disc tribometer has been proposed. This study deals with an inverse problem concerning the identification of the heat exchange coefficient "h". The method used allows the sequential estimation of the thermal boundary conditions by minimizing an error function between numerical and experimental temperature values. Coupled with the identification of the heat flux partition coefficient, the proposed model is validated.
Lee, Shiu-Hang; Nagataki, Shigehiro
2012-01-01
To better model the efficient production of cosmic rays (CRs) in supernova remnants (SNRs) with the associated coupling between CR production and SNR dynamics, we have generalized an existing cr-hydro-NEI code (i.e., Ellison et al. 2012) to include the following processes: (1) an explicit calculation of the upstream precursor structure including the position dependent flow speed, density, temperature, and magnetic field strength; (2) a momentum and space dependent CR diffusion coefficient; (3) an explicit calculation of magnetic field amplification (MFA); (4) calculation of the maximum CR momentum using the amplified magnetic field; (5) a finite Alfven speed for the particle scattering centers; and (6) the ability to accelerate a superthermal seed population of CRs as well as the ambient thermal plasma. While a great deal of work has been done modeling SNRs, most work has concentrated on either the continuum emission from relativistic electrons or ions, or the thermal emission from the shock heated plasma. Ou...
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong
2017-04-01
We investigate the defocusing coupled nonlinear Schrödinger equations from a 3 ×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
Energy Technology Data Exchange (ETDEWEB)
Macias-Diaz, J.E. [Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Aguascalientes, Ags. 20100 (Mexico) and Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: jemacias@correo.uaa.mx; Puri, A. [Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: apuri@uno.edu
2007-07-02
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information.
Institute of Scientific and Technical Information of China (English)
Song Wei
2009-01-01
We have investigated the intrinsic decoherence on the entanglement of a two-qutrit one-dimensional (1D) optical lattice chain with nonlinear coupling.As a measure of the entanglement,the negativity of the system is calculated.It is shown that the influence of intrinsic decoherence on the entanglement varies in different initial systems.
Nonlinear effects caused by coupling misalignment in rotors equipped with journal bearings
Pennacchi, Paolo; Vania, Andrea; Chatterton, Steven
2012-07-01
Misalignment is one of the most common sources of trouble of rotating machinery when rigid couplings connect the shafts. Ideal alignment of the shafts is difficult to be obtained and rotors may present angular and/or parallel misalignment (defined also as radial misalignment or offset). During a complete shaft revolution, a periodical change of the bearings load occurs in hyperstatic shaft-lines, if coupling misalignment between the shafts is excessive. If the rotating machine is equipped with fluid-film journal bearings, the change of the loads on the bearing causes also the variation of their instantaneous dynamic characteristics, i.e. damping and stiffness, and the complete system cannot be considered any longer as linear. Despite misalignment is often observed in the practice, there are relatively few studies about this phenomenon in literature and their results are sometimes conflicting. The authors aim at modeling accurately this phenomenon, for the first time in this paper, and giving pertinent diagnostic information. The proposed method is suitable for every type of shaft-line supported by journal bearings. A finite element model is used for the hyperstatic shaft-line, while bearing characteristics are calculated by integrating Reynolds equation as a function of the instantaneous load acting on the bearings, caused also by the coupling misalignment. The results obtained by applying the proposed method are shown by means of the simulation, in the time domain, of the dynamical response of a hyperstatic shaft-line. Nonlinear effects are highlighted and the spectral components of the system response are analyzed, in order to give diagnostic information about the signature of this type of fault.
Barseghyan, Manuk G; Restrepo, Ricardo L; Mora-Ramos, Miguel E; Kirakosyan, Albert A; Duque, Carlos A
2012-09-28
: The linear and nonlinear intraband optical absorption coefficients in GaAs three-dimensional single quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and electric field, applied along the growth direction of the heterostructure, the energies of the ground and first excited states of a donor impurity have been found using the effective mass approximation and a variational method. The energies of these states are examined as functions of the dimensions of the structure, electric field, and hydrostatic pressure. We have also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as a function of incident photon energy for several configurations of the system. It is found that the variation of distinct sizes of the structure leads to either a redshift and/or a blueshift of the resonant peaks of the intraband optical spectrum. In addition, we have found that the application of an electric field leads to a redshift, whereas the influence of hydrostatic pressure leads to a blueshift (in the case of on-ring-center donor impurity position) of the resonant peaks of the intraband optical spectrum.
Xue, Hongqi; Wu, Hulin; 10.1214/09-AOS784
2010-01-01
This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge--Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurement error. The B-spline is used to approximate the time-varying coefficients, and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach. Our results show that if the maximum step size of the $p$-order numerical algorithm goes to zero at a rate faster than $n^{-1/(p\\wedge4)}$, the numerical error is negligible compared to the measurement error. This result provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. Moreover, we h...
Unlocking the full potential of wave-matter nonlinear coupling in the epsilon-near-zero regime
Ciattoni, Alessandro; Marini, Andrea; Di Falco, Andrea; Faccio, Daniele; Scalora, Michael
2015-01-01
In recent years, unconventional metamaterial properties have triggered a revolution of electromagnetic research which has unveiled novel scenarios of wave-matter interaction. A very small dielectric permittivity is a leading example of such unusual features, since it produces an exotic static-like regime where the electromagnetic field is spatially slowly-varying over a physically large region. The so-called epsilon-near-zero metamaterials thus offer an ideal platform where to manipulate the inner details of the "stretched" field. Here we theoretically prove that a standard nonlinearity is able to operate such a manipulation to the point that even a thin slab produces a dramatic nonlinear pulse transformation, if the dielectric permittivity is very small within the field bandwidth. The predicted non-resonant releasing of full nonlinear coupling produced by the epsilon-near-zero condition does not resort to any field enhancement mechanisms and opens novel routes to exploiting matter nonlinearity for steering t...
Energy Technology Data Exchange (ETDEWEB)
Vakhnenko, Oleksiy O., E-mail: vakhnenko@bitp.kiev.ua
2016-05-27
Highlights: • The integrable nonlinear Schrödinger system on a triangular-lattice ribbon is inclined to metamorphoses. • The system under study is capable to incorporate the effect of external linear potential. • The system criticality against the background parameter reduces the number of independent field variables. • At critical point the system Poisson structure becomes degenerate. • The effect of criticality is elucidated by the system one-soliton solution. - Abstract: The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. There are at least the two types of system crucial modifications stipulated by the two types of governing parameters. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz–Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modeling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice. The multi-component structure of basic integrable system alongside with the attractive character of system nonlinearities has predetermined the logic of whole consideration.
Sabeen, A.; Masood, W.; Qureshi, M. N. S.; Shah, H. A.
2017-07-01
In this paper, linear and nonlinear coupling of kinetic Alfven and acoustic waves has been studied in a dusty plasma in the presence of trapping and self-gravitation effects. In this regard, we have derived the linear dispersion relations for positively and negatively coupled dust kinetic Alfven-acoustic waves. Stability analysis of the coupled dust kinetic Alfven-acoustic wave has also been presented. The formation of solitary structures has been investigated following the Sagdeev potential approach by using the two-potential theory. Numerical results show that the solitary structures can be obtained only for sub-Alfvenic regimes in the scenario of space plasmas.
Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model
Energy Technology Data Exchange (ETDEWEB)
Ngai, K. L. [CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy and Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)
2015-03-21
Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ{sub 1}(f), the frequency dispersion of the third-order dielectric susceptibility, χ{sub 3}(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ{sub 1}(f) and χ{sub 3}(f) is the characteristic of the many
Liu, Chuangye; Nguyen, Nghiem V.; Wang, Zhi-Qiang
2016-10-01
In this paper, we investigate the orbital stability of solitary-wave solutions for an m-coupled nonlinear Schrödinger system i /∂ ∂ t u j + /∂ 2 ∂ x 2 u j + ∑ i = 1 m b i j |" separators=" u i | 2 u j = 0 , j = 1 , … , m , where m ≥ 2, uj are complex-valued functions of (x, t) ∈ ℝ2, bjj ∈ ℝ, j = 1, 2, …, m, and bij, i ≠ j are positive coupling constants satisfying bij = bji. It will be shown that spatially synchronized solitary-wave solutions of the m-coupled nonlinear Schrödinger system exist and are orbitally stable. Here, by synchronized solutions we mean solutions in which the components are proportional to one another. Our results completely settle the question on the existence and stability of synchronized solitary waves for the m-coupled system while only partial results were known in the literature for the cases of m ≥ 3 heretofore. Furthermore, the conditions imposed on the symmetric matrix B = (bij) satisfied here are both sufficient and necessary for the m-coupled nonlinear Schrödinger system to admit synchronized ground-state solutions.
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-Ⅰ), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.
Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A
2012-03-01
We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.
Directory of Open Access Journals (Sweden)
Hideki Gotoh
2014-10-01
Full Text Available Optical nonlinear effects are examined using a two-color micro-photoluminescence (micro-PL method in a coherently coupled exciton-biexciton system in a single quantum dot (QD. PL and photoluminescence excitation spectroscopy (PLE are employed to measure the absorption spectra of the exciton and biexciton states. PLE for Stokes and anti-Stokes PL enables us to clarify the nonlinear optical absorption properties in the lowest exciton and biexciton states. The nonlinear absorption spectra for excitons exhibit asymmetric shapes with peak and dip structures, and provide a distinct contrast to the symmetric dip structures of conventional nonlinear spectra. Theoretical analyses with a density matrix method indicate that the nonlinear spectra are caused not by a simple coherent interaction between the exciton and biexciton states but by coupling effects among exciton, biexciton and continuum states. These results indicate that Fano quantum interference effects appear in exciton-biexciton systems at QDs and offer important insights into their physics.
Institute of Scientific and Technical Information of China (English)
ZHOU Shihua; SONG Guiqiu; REN Zhaohui; WEN Bangchun
2016-01-01
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
Zhou, Shihua; Song, Guiqiu; Ren, Zhaohui; Wen, Bangchun
2016-03-01
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
Institute of Scientific and Technical Information of China (English)
王悦悦; 戴朝卿
2012-01-01
With the help of the similarity transformation connected the variable-eoeicient （3＋1）-dimensionai nonlin- ear Sehroedinger equation with the standard nonlinear Schr6dinger equation, we firstly obtain first-order and second-order rogue wave solutions. Then, we investigate the controllable behaviors of these rogue waves in the hyperbolic dispersion decreasing profile. Our results indicate that the integral relation between the accumulated time T and the reai time t is the basis to realize the control and manipulation of propagation behaviors of rogue waves, such as sustainment and restraint. We can modulate the value To to achieve the sustained and restrained spatiotemporai rogue waves. Moreover, the controllability for position of sustainment and restraint for spatiotemporai rogue waves can aiso be realized by setting different values of Xo.
Hamedi, H. R.; Ruseckas, J.; Juzeliūnas, G.
2017-09-01
We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N-type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell-Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.
Energy Technology Data Exchange (ETDEWEB)
Martínez-Orozco, J.C. [Unidad Académica de Física. Universidad Autónoma de Zacatecas, Calzada Solidaridad esquina con Paseo la Bufa S/N, C.P. 98060. Zacatecas, Zac. (Mexico); Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia)
2014-11-01
The conduction band states of GaAs-based vertically coupled double triangular quantum dots in two dimensions are investigated within the effective mass and parabolic approximation, using a diagonalization procedure to solve the corresponding Schrödinger-like equation. The effect of an externally applied static electric field is included in the calculation, and the variation of the lowest confined energy levels as a result of the change of the field strength is reported for different geometrical setups. The linear and nonlinear optical absorptions and the relative change of the refractive index, associated with the energy transition between the ground and the first excited state in the system, are studied as a function of the incident light frequency for distinct configurations of inter-dot distance and electric field intensities. The blueshift of the resonant absorption peaks is detected as a consequence of the increment in the field intensity, whereas the opposite effect is obtained from the increase of inter-dot vertical distance. It is also shown that for large enough values of the electric field there is a quenching of the optical absorption due to field-induced change of symmetry of the first excited state wavefunction, in the case of triangular dots of equal shape and size.
Coupled force-balance and scattering equations for nonlinear transport in quantum wires
Huang, Danhong; Gumbs, Godfrey
2009-07-01
The coupled force-balance and scattering equations have been derived and applied to study nonlinear transport of electrons subjected to a strong dc electric field in an elastic-scattering-limited quantum wire. Numerical results have demonstrated both field-induced heating-up and cooling-down behaviors in the nonequilibrium part of the total electron-distribution function by varying the impurity density or the width of the quantum wire. The obtained asymmetric distribution function in momentum space invalidates the application of the energy-balance equation to our quantum-wire system in the center-of-mass frame. The experimentally observed suppression of mobility by a driving field for the center-of-mass motion in the quantum-wire system has been reproduced [see K. Tsubaki , Electr. Lett. 24, 1267 (1988); M. Hauser , Sci. Technol. 9, 951 (1994)]. In addition, the thermal enhancement of mobility in the elastic-scattering-limited system has been demonstrated, in accordance with a similar prediction made for graphene nanoribbons [see T. Fang , Phys. Rev. B 78, 205403 (2008)]. This thermal enhancement has been found to play a more and more significant role with higher lattice temperature and becomes stronger for a low-driving field.
Takatsuka, Kazuo
Nonlinear dynamics and chaos are studied in a system for which a complete set of equations of motion such as equations of Newton, Navier-Stokes and Van der Pol, is not available. As a very general system as such, we consider coupled classical spins (pendulums), each of which is under control by a fuzzy system that is designed to align the spin to an unstable fixed point. The fuzzy system provides a deterministic procedure to control an object without use of a differential equation. The positions and velocities of the spins are monitored periodically and each fuzzy control gives a momentum to its associated spin in the reverse directions. If the monitoring is made with an interval short enough, the spin-spin interactions are overwhelmed by the fuzzy control and the system converges to a state as designed. However, a long-interval monitoring induces dynamics of “too-late response”, and thereby results in chaos. A great variety of dynamics are generated under very delicate balance between the fuzzy control and the spin-spin interaction, in which two independent mechanisms of creating negative and positive “Liapunov exponents” interact with each other.
Nonlinear coupled rotor-fuselage helicopter vibration studies with higher harmonic control
Friedmann, P. P.; Venkatesan, C.; Papavassiliou, I.
1990-01-01
This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible-fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition, it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs, was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.
A nonlinear electromechanical coupling model for electropore expansion in cell electroporation
Deng, Peigang; Lee, Yi-Kuen; Zhang, Tong-Yi
2014-11-01
Under an electric field, the electric tractions acting on a cell membrane containing a pore-nucleus are investigated by using a nonlinear electromechanical coupling model, in which the cell membrane is treated as a hyperelastic material. Iterations between the electric field and the structure field are performed to reveal the electrical forces exerting on the pore region and the subsequent pore expansion process. An explicit exponential decay of the membrane’s edge energy as a function of pore radius is defined for a hydrophilic pore and the transition energy as a hydrophobic pore converts to a hydrophilic pore during the initial stage of pore formation is investigated. It is found that the edge energy for the creation of an electropore edge plays an important role at the atomistic scale and it determines the hydrophobic-hydrophilic transition energy barrier. Various free energy evolution paths are exhibited, depending on the applied electric field, which provides further insight towards the electroporation (EP) phenomenon. In comparison with previous EP models, the proposed model has the ability to predict the metastable point on the free energy curve that is relevant to the lipid ion channel. In addition, the proposed model can also predict the critical transmembrane potential for the activation of an effective electroporation that is in a good agreement with previously published experimental data.
Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation
Kiessling, A; Heavens, A F
2011-01-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Eucl...
Classical defects in higher-dimensional Einstein gravity coupled to nonlinear σ -models
Prasetyo, Ilham; Ramadhan, Handhika S.
2017-09-01
We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear σ -model with cosmological constant. The σ -model can be perceived as exterior configuration of a spontaneously-broken SO(D-1) global higher-codimensional "monopole". Here we allow the kinetic term of the σ -model to be noncanonical; in particular we specifically study a quadratic-power-law type. This is some possible higher-dimensional generalization of the Bariola-Vilenkin (BV) solutions with k-global monopole studied recently. The solutions can be perceived as the exterior solution of a black hole swallowing up noncanonical global defects. Even in the absence of comological constant its surrounding spacetime is asymptotically non-flat; it suffers from deficit solid angle. We discuss the corresponding horizons. For Λ >0 in 4 d there can exist three extremal conditions (the cold, ultracold, and Nariai black holes), while in higher-than-four dimensions the extremal black hole is only Nariai. For Λ <0 we only have black hole solutions with one horizon, save for the 4 d case where there can exist two horizons. We give constraints on the mass and the symmetry-breaking scale for the existence of all the extremal cases. In addition, we also obtain factorized solutions, whose topology is the direct product of two-dimensional spaces of constant curvature (M_2, dS_2, or AdS_2) with (D-2)-sphere. We study all possible factorized channels.
A nonlinear electromechanical coupling model for electropore expansion in cell electroporation
Deng, Peigang
2014-10-15
Under an electric field, the electric tractions acting on a cell membrane containing a pore-nucleus are investigated by using a nonlinear electromechanical coupling model, in which the cell membrane is treated as a hyperelastic material. Iterations between the electric field and the structure field are performed to reveal the electrical forces exerting on the pore region and the subsequent pore expansion process. An explicit exponential decay of the membrane\\'s edge energy as a function of pore radius is defined for a hydrophilic pore and the transition energy as a hydrophobic pore converts to a hydrophilic pore during the initial stage of pore formation is investigated. It is found that the edge energy for the creation of an electropore edge plays an important role at the atomistic scale and it determines the hydrophobic-hydrophilic transition energy barrier. Various free energy evolution paths are exhibited, depending on the applied electric field, which provides further insight towards the electroporation (EP) phenomenon. In comparison with previous EP models, the proposed model has the ability to predict the metastable point on the free energy curve that is relevant to the lipid ion channel. In addition, the proposed model can also predict the critical transmembrane potential for the activation of an effective electroporation that is in a good agreement with previously published experimental data.
A Robust Hash Function Using Cross-Coupled Chaotic Maps with Absolute-Valued Sinusoidal Nonlinearity
Directory of Open Access Journals (Sweden)
Wimol San-Um
2016-01-01
Full Text Available This paper presents a compact and effective chaos-based keyed hash function implemented by a cross-coupled topology of chaotic maps, which employs absolute-value of sinusoidal nonlinearity, and offers robust chaotic regions over broad parameter spaces with high degree of randomness through chaoticity measurements using the Lyapunov exponent. Hash function operations involve an initial stage when the chaotic map accepts initial conditions and a hashing stage that accepts input messages and generates the alterable-length hash values. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. The results of hashing performances show that the mean changed probabilities are very close to 50%, and the mean number of bit changes is also close to a half of hash value lengths. The collision tests reveal the mean absolute difference of each character values for the hash values of 128, 160 and 256 bits are close to the ideal value of 85.43. The proposed keyed hash function enhances the collision resistance, comparing to MD5 and SHA1, and the other complicated chaos-based approaches. An implementation of hash function Android application is demonstrated.
Song, Byeongju; Park, Byeongjin; Sohn, Hoon; Lim, Cheol-Woo; Park, Jae-Roung
2015-04-01
Rotating shafts in drop lifts of manufacturing facilities are susceptible to fatigue cracks as they are under repetitive heavy loading and high speed spins. However, it is challenging to use conventional contact transducers to monitor these shafts as they are continuously spinning with a high speed. In this study, a noncontact crack detection technique for a rotating shaft is proposed using air-coupled transducers (ACTs). (1) Low frequency (LF) and high frequency (HF) sinusoidal inputs are simultaneously applied to a shaft using two ACTs, respectively. A fatigue crack can provide a mechanism for nonlinear ultrasonic modulation and create spectral sidebands at the modulation frequencies, which are the sum and difference of the two input frequencies Then LF and HF inputs are independently applied to the shaft using each ACT. These three ultrasonic responses are measured using another ACT. (2) The damage index (DI) is defined as the energy of the first sideband components, which corresponding to the frequency sum and difference between HF and LF inputs. (3) Steps 1 and 2 are repeated with various combinations of HF and LF inputs. Crack existence is detected through an outlier analysis of the DIs. The effectiveness of the proposed technique is investigated using a steel shaft with a real fatigue crack.
Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators
Energy Technology Data Exchange (ETDEWEB)
Franchi, A.
2006-07-01
In this thesis a beam-based method has been developed to measure the strength and the polarity of corrector magnets (skew quadrupoles and sextupoles) in circular accelerators. The algorithm is based on the harmonic analysis (via FFT) of beam position monitor (BPM) data taken turn by turn from an accelerator in operation. It has been shown that, from the differences of the spectral line amplitudes between two consecutive BPMs, both the strength and the polarity of non-linear elements placed in between can be measured. The method has been successfully tested using existing BPM data from the SPS of CERN. A second beam-based method has been studied for a fast measurement and correction of betatron coupling driven by skew quadrupole field errors and tilted focusing quadrupoles. In this thesis it has been shown how the correction for minimizing the coupling stop band C can be performed in a single machine cycle from the harmonic analysis of multi-BPM data. The method has been successfully applied to RHIC. A third theoretical achievement is a new description of the betatron motion close to the difference resonance in presence of linear coupling. New formulae describing the exchange of RMS resonances have been derived here making use of Lie algebra providing a better description of the emittance behavior. A new way to decouple the equations of motion and explicit expressions for the individual single particle invariants have been found. For the first time emittance exchange studies have been carried out in the SIS-18 of GSI. Applications of this manipulation are: emittance equilibration under consideration for future operations of the SIS-18 as booster for the SIS-100; emittance transfer during multi-turn injection to improve the efficiency and to protect the injection septum in high intensity operations, by shifting part of the horizontal emittance into the vertical plane. Multi-particle simulations with 2D PIC space-charge solver have been run to infer heuristic scaling
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Hammer, Hans; Lou, Jijie; Wang, Yaqi; Ortensi, Javier; Gleicher, Frederick; Baker, Benjamin; DeHart, Mark; Martineau, Richard
2016-11-01
The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA
Energy Technology Data Exchange (ETDEWEB)
Nazari, M.; Karimi, M.J., E-mail: karimi@sutech.ac.ir; Keshavarz, A.
2013-11-01
In this study, the linear, the third-order nonlinear and total optical absorption coefficients and refractive index changes of a modulation-doped GaAs/Al{sub x}Ga{sub 1−x}As quantum well are investigated numerically. In the effective-mass approximation, the electronic structure of modulation-doped quantum well is calculated by solving the Schrödinger and Poisson equations self-consistently. Optical properties are obtained using the compact density matrix approach. The effects of structure parameters, the applied magnetic field and the hydrostatic pressure on the optical properties of the modulation-doped quantum well are studied. Results show that the resonant peaks shift toward the higher (lower) energies with the increase in the magnetic field (pressure). The magnitude of the resonant peaks of the optical properties decreases with the increasing magnetic field or pressure.
Energy Technology Data Exchange (ETDEWEB)
Rojas-Briseño, J.G.; Martínez-Orozco, J.C.; Rodríguez-Vargas, I. [Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calzada Solidaridad esquina con Paseo la Bufa S/N, C.P. 98060, Zacatecas, Zac. (Mexico); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia)
2013-09-01
In this work we are reporting the energy level spectrum for a quantum system consisting of an n-type double δ-doped quantum well with a Schottky barrier potential in a Gallium Arsenide matrix. The calculated states are taken as the basis for the evaluation of the linear and third-order nonlinear contributions to the optical absorption coefficient and to the relative refractive index change, making particular use of the asymmetry of the potential profile. These optical properties are then reported as a function of the Schottky barrier height (SBH) and the separation distance between the δ-doped quantum wells. Also, the effects of the application of hydrostatic pressure are studied. The results show that the amplitudes of the resonant peaks are of the same order of magnitude of those obtained in the case of single δ-doped field effect transistors; but tailoring the asymmetry of the confining potential profile allows the control the resonant peak positions.
Horton, Rebecca B; McConico, Morgan; Landry, Currie; Tran, Tho; Vogt, Frank
2012-10-09
Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. 'Predictor Surfaces' were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables. As proof-of-principle for the Predictor Surfaces' capabilities, an application from environmental analytical chemistry was chosen. Microalgae cells are known to sensitively adapt to changes in environmental parameters such as pollution and/or nutrient availability and thus have potential as novel in situ sensors for environmental monitoring. These adaptations of the microalgae cells are reflected in their chemical signatures which were then acquired by means of FT-IR spectroscopy. In this study, the concentrations of three nutrients, namely inorganic carbon and two nitrogen containing ions, were chosen. Biological considerations predict that changes in nutrient availability produce a nonlinear response in the cells' biomass composition; it is also known that microalgae need certain nutrient mixes to thrive. The nonlinear Predictor Surfaces were demonstrated to be more accurate in predicting the values of these nutrients' concentrations than principal component regression. For qualitative chemical studies of biological systems, the Predictor Surfaces themselves are a novel tool as they visualize
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which axe coincident with the ones in literature.
Ekşioğlu, Yasa; Güven, Kaan
2011-01-01
We propose that a weakly-coupled nonlinear dielectric waveguide -- surface-plasmon system can be formulated as a new type of Josephson junction. Such a system can be realized along a metal - dielectric interface where the dielectric medium hosts a nonlinear waveguide (e.g. fiber) for soliton propagation. We demonstrate that the system is in close analogy to the bosonic Josephson-Junction (BJJ) of atomic condensates at very low temperatures, yet exhibits different dynamical features. In particular, the inherently dynamic coupling parameter between soliton and surface-plasmon generates self-trapped oscillatory states at nonzero fractional populations with zero and $\\pi$ time averaged phase difference. The salient features of the dynamics are presented in the phase space.
Toutounji, Mohamad
2005-03-22
While an optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed-phase systems was derived by Toutounji [J. Chem. Phys. 121, 2228 (2004)], the corresponding analytical optical line shape is derived. The respective nonlinear correlation functions are also derived. Model calculations involving photon-echo, pump-probe, and hole-burning signals of model systems with both linear and quadratic coupling are provided. Hole-burning formula of Hayes-Small is compared to that of Mukamel in mixed quantum-classical systems.
Institute of Scientific and Technical Information of China (English)
Gongming WEI
2008-01-01
A 2-coupled nonlinear Schr(o)dinger equations with bounded varying potentials and strongly attractive interactions is considered.When the attractive interaction is strong enough,the existence of a ground state for sufficiently small Planck constant is proved.As the Planck constant approaches zero,it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.
Global Well-posedness of a System of Nonlinearly Coupled KdV equations of Majda and Biello
Guo, Yanqiu; Titi, Edriss S
2013-01-01
This paper addresses the problem of global well-posedness of a coupled system of Korteweg-de Vries equations, derived by Majda and Biello in the context of nonlinear resonant interaction of Rossby waves, in a periodic setting in homogeneous Sobolev spaces $\\dot H^s$, for $s\\geq 0$. Our approach is based on a successive time-averaging method developed by Babin, Ilyin and Titi [1].
Qin, Meng; Ge, Xing; Zhai, Xiao-Yue; Liu, Cui-Cui; Wang, Bi-Li
2011-03-01
This paper investigates the entanglement of a two-qutrit Heisenberg XXX chain with nonlinear couplings under an inhomogeneous magnetic field. By the concept of negativity, we find that the critical temperature increases with the increase of inhomogeneous magnetic field b. Our study indicates that for any |K| > |J|, or |K| < |J| entanglement always exists for certain regions. We also find that at the critical point, the entanglement becomes a nonanalytic function of B and a quantum phase transition occurs.
A Novel All-Optical Switch in a Double-Loop Sagnac Ring Coupled with a Nonlinear Ring Resonator
Institute of Scientific and Technical Information of China (English)
LI Jun-Qing; LI Li; ZHAO Jia-Qun; LI Chun-Fei
2004-01-01
@@ We propose a novel configuration of all-optical switch based on a double-loop Sagnac ring coupled with a nonlinear ring resonator. In the case of self-phase modulation, the reducing switching threshold power down to mW is predicted, which is the improvement of earlier works on all-optical switches. The switch optimization is analysed.A way to increase the response speed of all-optical switches is suggested.
Khoa, Doan Quoc; Phuong, Le Thi Thu; Hoi, Bui Dinh
2017-03-01
A quantum kinetic equation for electrons interacting with confined phonons is used to investigate the nonlinear absorption of an intense electromagnetic wave by electrons in cylindrical GaAs/AlAs quantum wires. The analytic expression for absorption coefficient is calculated for three models of confined optical phonons: the dielectric continuum (DC), hydrodynamic continuum (HC), and Huang-Zhu (HZ) models. The absorption coefficient depends on the square of the electromagnetic wave amplitude. The electrophonon resonance and optically detected electrophonon resonance (ODEPR) are observed through the absorption spectrum. The full width at half maximum (the line-width) of the ODEPR peaks is obtained by a computational method. The line-width is found to increase with increasing temperature and decrease with increasing the quantum wire radius. In particular, numerical results show that the DC and HZ models lead to a similar behaviour of electron - confined phonon interaction whereas the HC model results in a quite different one, especially at small quantum wire radius. For large quantum wire radii, above mentioned phonon models have equivalent contributions to the ODEPR line-width.
Sheng, Shiqi; Tu, Z C
2015-02-01
We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation for nonlinear response accurate up to the quadratic order is derived from the stalling condition and the symmetry argument. By applying this generic nonlinear constitutive relation to finite-time thermodynamics, we obtain the necessary and sufficient condition for the universality of efficiency at maximum power, which states that a tight-coupling heat engine takes the universal efficiency at maximum power up to the quadratic order if and only if either the engine symmetrically interacts with two heat reservoirs or the elementary thermal energy flowing through the engine matches the characteristic energy of the engine. Hence we solve the following paradox: On the one hand, the quadratic term in the universal efficiency at maximum power for tight-coupling heat engines turned out to be a consequence of symmetry [Esposito, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009); Sheng and Tu, Phys. Rev. E 89, 012129 (2014)]; On the other hand, typical heat engines such as the Curzon-Ahlborn endoreversible heat engine [Curzon and Ahlborn, Am. J. Phys. 43, 22 (1975)] and the Feynman ratchet [Tu, J. Phys. A 41, 312003 (2008)] recover the universal efficiency at maximum power regardless of any symmetry.
Dynamics and Nonlinearities of the Electro-Mechanical Coupling in Inertial MEMS
Machado da Rocha, L.A.
2005-01-01
The study of the nonlinear dynamics of electrostatically actuated MEMS devices is essential for proper device operation and for the actual exploitation of the dynamic aspects of MEMS. Accurate static and dynamic models and nonlinear analysis provide the tools to achieve a better understanding of the
Zamani, A.; Azargoshasb, T.; Niknam, E.
2017-10-01
Effects of applied magnetic field, temperature and dimensions on the optical absorption coefficients (AC) and refractive index (RI) changes of a GaAs quantum ring are investigated in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI). To this end, the finite difference method (FDM) is used in order to numerically calculate the energy eigenvalues and eigenstates of the system while the compact density matrix approach is hired to calculate the optical properties. It is shown that application of magnetic field, temperature as well as the geometrical size in the presence of spin-orbit interactions, alter the electronic structure and consequently influence the linear and third-order nonlinear optical absorption coefficients as well as the refractive index changes of the system. Results show an obvious blue shift in optical curves with enhancing external magnetic field and temperature while the increment of dimensions result in red shift.
Sosnowska, Anita; Barycki, Maciej; Gajewicz, Agnieszka; Bobrowski, Maciej; Freza, Sylwia; Skurski, Piotr; Uhl, Stefanie; Laux, Edith; Journot, Tony; Jeandupeux, Laure; Keppner, Herbert; Puzyn, Tomasz
2016-06-01
This work focuses on determining the influence of both ionic-liquid (IL) type and redox couple concentration on Seebeck coefficient values of such a system. The quantitative structure-property relationship (QSPR) and read-across techniques are proposed as methods to identify structural features of ILs (mixed with LiI/I2 redox couple), which have the most influence on the Seebeck coefficient (Se ) values of the system. ILs consisting of small, symmetric cations and anions with high values of vertical electron binding energy are recognized as those with the highest values of Se . In addition, the QSPR model enables the values of Se to be predicted for each IL that belongs to the applicability domain of the model. The influence of the redox-couple concentration on values of Se is also quantitatively described. Thus, it is possible to calculate how the value of Se will change with changing redox-couple concentration. The presence of the LiI/I2 redox couple in lower concentrations increases the values of Se , as expected.
Metzger, Bernd; Hentschel, Mario; Nesterov, Maxim; Schumacher, Thorsten; Lippitz, Markus; Giessen, Harald
2016-04-01
We investigate the polarization-resolved linear and third-order optical response of plasmonic nanostructure arrays that consist of orthogonally coupled gold nanoantennas. By rotating the incident light polarization direction, either one of the two eigenmodes of the coupled system or a superposition of the eigenmodes can be excited. We find that when an eigenmode is driven by the external light field, the generated third-harmonic signals exhibit the same polarization direction as the fundamental field. In contrast, when a superposition of the two eigenmodes is excited, third-harmonic can efficiently be radiated at the perpendicular polarization direction. Furthermore, the interference of the coherent third-harmonic signals radiated from both nanorods proves that the phase between the two plasmonic oscillators changes in the third-harmonic signal over 3π when the laser is spectrally tuned over the resonance, rather than over π as in the case of the fundamental field. Finally, almost all details of the linear and the nonlinear spectra can be described by an anharmonic coupled oscillator model, which we discuss in detail and which provides deep insight into the linear and the nonlinear optical response of coupled plasmonic nanoantennas.
Institute of Scientific and Technical Information of China (English)
CHEN Zhen; LI Hong-Lang; YAN Li; CHEN Xiao-Yang; LU Da-Cheng; WANG Xiao-Hui; LIU Xiang-Lin; HAN Pei-De; YUAN Hai-Rong; WANG Du; WANG Zhan-Guo; HE Shi-Tang
2001-01-01
High-quality and high-resistivity GaN films were grown on (0001) sapphire face by metal-organic vapour phase epitaxy. To measure the surface acoustic wave properties accurately, we deposited metallized interdigital trans ducers on the GaN surface. The acoustic surface wave velocity and electromechanical coupling coefficient were measured, respectively, to be 5667m/s and 1.9% by the pulse method.
Comprehensive analysis of the optical Kerr coefficient of graphene
Soh, Daniel B. S.; Hamerly, Ryan; Mabuchi, Hideo
2016-08-01
We present a comprehensive analysis of the nonlinear optical Kerr effect in graphene. We directly solve the S -matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh-type crystal wave functions. We then convert to the nonlinear refractive index coefficients through the Kramers-Kronig relation. In this formalism, the source of Kerr nonlinearity is the interplay of optical fields that cooperatively drive the transition from valence to conduction band. This formalism makes it possible to identify and compute the rates of distinct nonlinear processes that contribute to the Kerr nonlinear refractive index coefficient. The four identified mechanisms are two-photon absorption, Raman transition, self-coupling, and quadratic ac Stark effect. We also present a comparison of our theory with recent experimental and theoretical results.
Grimsmo, Arne L.; Parkins, Scott
2014-03-01
We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A 87, 033814 (2013), 10.1103/PhysRevA.87.033814]. For a range of the nonlinear interaction strength about a special value, degeneracies or near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity loss, gives rise to an essentially closed cycle of excitations and photon emissions within these subspaces. Consequently, the cavity output field is strongly antibunched, while over this range of nonlinear strengths the atomic population undergoes an abrupt inversion. We develop a quantum-trajectory-based description of the system that models its key properties very well, and use a simple dressed-state picture to explain the novel structure of the cavity fluorescence spectrum. We also present numerical results for a potential realization of the system using a rubidium atom coupled strongly to a high-finesse optical cavity mode.
Institute of Scientific and Technical Information of China (English)
XIAO Yong-gang; FU Yi-ming; ZHA Xu-dong
2005-01-01
Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.
Sun, Wen-Rong; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Jiang, Yan
2016-10-01
High-order rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported in this paper. Key point lies in the introduction of a limit process in the Darboux transformation, with which we obtain a family of the first- and second-order rational solutions for the purpose of modelling the rogue waves. We observe that the double-hump rogue wave in the course of evolution turns into the one-hump rogue wave, and that the dark rogue wave with four valleys in the course of evolution turns into the bright rogue wave. It is found that the second-order rogue wave can split up, giving birth to the multiple rogue waves.
Dijkstra, Arend G
2015-01-01
We study hole, electron and exciton transport in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole and exciton transfer can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states du...
Directory of Open Access Journals (Sweden)
Kanittha Yimnak
2014-01-01
Full Text Available The meshless local Pretrov-Galerkin method (MLPG with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.
Directory of Open Access Journals (Sweden)
M. Li
2012-01-01
Full Text Available This paper proposes a mathematical model of the multirotor system with a flexible coupling on spring supports on Lagrange's approach, which has taken into account the effects of dynamic angular misalignment and mass unbalance. Then its nonlinear dynamic behaviors of the system are discussed based on the method of multiple scales and numerical technique, respectively. The results show that the responses of the system in lateral directions contain a similar component to that of the mass unbalanced system on both the vibrating frequency and amplitude and involve the typical nonlinear components such as the ones from some combined frequencies; the results also reveal that the numerical agreements on the above-mentioned methods are perfect for the transient responses.
Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Sun, Yan
2017-07-01
Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.
Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power
Directory of Open Access Journals (Sweden)
Sado Danuta
2006-01-01
Full Text Available An ideal and nonideal autoparametrical system excited by DC motor with unbalanced mass is presented in this work. The system consists of the body of mass M which is hung on a nonlinear spring with a nonlinear damper, and a pendulum of the length l and mass m mounted to the body of mass M. It is assumed that the motion of the pendulum is damped by nonlinear resistive forces. Vibrations of both models (ideal and nonideal are researched. Solutions for the system response are presented for specific values of the parameters of system and the energy transfer between modes of vibrations is studied. Next excited vibrations for both models have been examined analytically and numerically. Except different kinds of periodic vibrations, there may also appear chaotic vibrations.
Institute of Scientific and Technical Information of China (English)
Kong Linghua; Wang Jinhuan; Zheng Sining
2012-01-01
This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the criterion for simultaneous blow-up of solutions,and then establish the uniform blow-up profiles of solutions near the blow-up time.It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmetric,but also the blow-up rates of the same component u (or v) may be in different levels under different dominations.
Institute of Scientific and Technical Information of China (English)
2013-01-01
In this paper, a numerical method based on a coupling between a mathematical model of nonlinear transient ship manoeu-vring motion in the horizontal plane and Mathematical Programming (MP) techniques is proposed. The aim of the proposed proce-dure is an efficient estimation of optimal ship hydrodynamic parameters in a dynamic model at the early design stage. The proposed procedure has been validated through turning circle and zigzag manoeuvres based on experimental data of sea trials of the 190 000-dwt oil tanker. Comparisons between experimental and computed data show a good agreement of overall tendency in manoeuvring trajectories.
Energy Technology Data Exchange (ETDEWEB)
Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H.
2002-04-01
We prove uniqueness and existence of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. The uniqueness proof is an adaption of Kruzkov's ''doubling of variables'' proof. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. We also present a numerical example motivated by biodegradation in porous media.
Sanbonmatsu, K. Y.; Goldman, M. V.; Newman, D. L.
A hybrid kinetic-fluid model is developed which is relevant to lower hybrid spikelets observed in the topside auroral ionosphere [Vago et al., 1992; Eriksson et al., 1994]. In contrast to previous fluid models [Shapiro et al., 1995; Tam and Chang, 1995; Seyler, 1994; Shapiro et al., 1993] our linear low frequency plasma response is magnetized and kinetic. Fluid theory is used to incorporate the nonlinear wave coupling. Performing a linear stability analysis, we calculate the growth rate for the modulational instability, driven by a lower hybrid wave pump. We find that both the magnetic and kinetic effects inhibit the modulational instability.
Institute of Scientific and Technical Information of China (English)
Yirang YUAN
2006-01-01
For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oil resources.
Sheykhi, A.; Hajkhalili, S.
2015-11-01
We study topological dilaton black holes of Einstein gravity in the presence of exponential nonlinear electrodynamics. The event horizons of these black holes can be a two-dimensional positive, zero or negative constant curvature surface. We analyze thermodynamics of these solutions by calculating all conserved and thermodynamic quantities and showing that the first law holds on the black hole horizon. Then, we perform the stability analysis in both canonical and grand canonical ensemble and disclose the effects of the dilaton and nonlinear electrodynamics on the thermal stability of the solutions. Finally, we study the phase transition points of these black holes in the thermodynamic geometry approach.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-computing is a practical and advanced tool for solving large-scale underground rock engineering problems.
Klika, Václav; Grmela, Miroslav
2013-01-01
Motivated by biological applications (e.g., bone tissue development and regeneration) we investigate coupling between mesoscopic mechanics and chemical kinetics. Governing equations of both dynamical systems are first written in a form expressing manifestly their compatibility with microscopic mechanics and thermodynamics. The same form is then required from governing equations of the coupled dynamics. The main result of the paper is an admissible form of the coupled dynamics.
Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators
Zhou, Brian B.; Roy, Rajarshi
2007-02-01
We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators, mutually coupled with a propagation delay, synchronize isochronally when both are symmetrically driven by a third Ikeda oscillator. This synchronous operation, unstable in the two delay-coupled oscillators alone, facilitates simultaneous, bidirectional communication of messages with chaotic carrier wave forms. This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multicomponent system.
Gain in regularity for a coupled nonlinear Schrödinger system
Directory of Open Access Journals (Sweden)
Octavio Vera Villagrán
2006-11-01
Full Text Available We study the gain of regularity for the initial value problem for acoupled nonlinear Schrödinger system that describes some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photo refractive media in optics and Bose-Einstein condensates. This study is motivated by the results obtained by N. Hayashi et al.
Li, Wei; Tang, Yougang; Liu, Liqin; Liu, Shuxiao; Cai, Runbo
2017-04-01
Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model. In fact, in addition to the heave and pitch which are in one plane, the nonlinear unstable motion will also occur in roll. From the results of the experiments, the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch. The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force. The nonlinear coupled equations in heave, roll and pitch are established by considering time-varying wet surface and coupling. The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency. Numerical integration of the motion equations has been performed to verify the first-order perturbation solution. The results are confirmed by model test. There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch. It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value. The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch. The energy transfers from heave to pitch and then transfers from pitch to roll. Due to the influence of the low-frequency vortex-excited force, the response of roll is more complicated than that of pitch.
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Mode competition in a system of two parametrically driven pendulums with nonlinear coupling
Banning, E.J.; Weele, van der J.P.; Ross, J.C.; Kettenis, M.M.
1997-01-01
This paper is part three in a series on the dynamics of two coupled, parametrically driven pendulums. In the previous parts Banning and van der Weele (1995) and Banning et al. (1997) studied the case of linear coupling; the present paper deals with the changes brought on by the inclusion of a nonlin
Jungnickel, F.; Chilla, E.; Makarov, S.; Fröhlich, H.-J.
1997-12-01
The use of AlAs/GaAs layered structures for SAW sensor applications is discussed with the aim of exploring the potential of the material system for the integration of SAW and electronic devices. Based on the acoustic wave spectrum on the (001) cut of GaAs the development of the Rayleigh-type mode in the [110] direction of the AlAs/GaAs structure is described. Using a transfer matrix algorithm the phase velocity and the coupling coefficient of the dispersive structure are calculated as a function of the relative layer thickness 0964-1726/6/6/009/img7, with k being the wave number and 0964-1726/6/6/009/img8 the layer thickness. Results of SAW phase velocity measurements carried out by a thermoelastic laser excitation method and a time delay technique are presented. The coupling coefficient has a maximum at kh = 1.8 being twice as high as the coefficient of bare GaAs. The temperature stabilization with 0964-1726/6/6/009/img9 and Au layers is calculated and the relation between 0964-1726/6/6/009/img10 and 0964-1726/6/6/009/img11 is determined for a vanishing temperature coefficient of delay (TCD). The mass sensitivity is increased by the application of the temperature stabilizing layers. It reaches a maximum value at 0964-1726/6/6/009/img12 and 0964-1726/6/6/009/img13. Some aspects of optimization procedures including the AlAs layer thickness are discussed.
Institute of Scientific and Technical Information of China (English)
Ahcene Boubakir; Fares Boudjema; Salim Labiod
2009-01-01
The aim of this paper is to develop a neuro-fuzzy-sliding mode controller (NFSMC) with a nonlinear sliding surface for a coupled tank system.The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation.A first-order nonlinear sliding surface is presented,on which the developed sliding mode controller (SMC) is based.Mathematical proof for the stability and convergence of the system is presented.In order to reduce the chattering in SMC,a fixed boundary layer around the switch surface is used.Within the boundary layer,where the fuzzy logic control is applied,the chattering phenomenon,which is inherent in a sliding mode control,is avoided by smoothing the switch signal.Outside the boundary,the sliding mode control is applied to drive the system states into the boundary layer.Moreover,to compute the equivalent controller,a feed-forward neural network (NN) is used.The weights of the net are updated such that the corrective control term of the NFSMC goes to zero.Then,this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain.Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.
Zhou, Hao-Miao; Li, Meng-Han; Li, Xiao-Hong; Zhang, Da-Guang
2016-08-01
For a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress, this paper proposes a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model. This model is based on the Taylor expansion of the elastic Gibbs free energy of giant magnetostrictive material and thermodynamic relations from the perspective of macro continuum mechanics. Predictions made using this model are in good agreement with experimental data for magnetization and the magnetostrictive strain curve under the collective effect of pre-stress and temperature. Additionally, the model overcomes the drawback of the existing magneto-thermo-mechanical constitutive model that cannot accurately predict the magnetization and magnetostrictive strain curve for different temperatures and pre-stresses. Furthermore, the constitutive model does not contain an implicit function and is compact, and can thus be applied in both situations of tensile and compressive stress and to both positive and negative magnetostrictive materials, and it is thus appropriate for engineering applications. Comprehensive analysis shows that the model fully describes the nonlinear coupling properties of a magnetic field, magnetostrictive strain and elasticity of a magnetostrictive material subjected to stress, a magnetic field and heat.
Energy Technology Data Exchange (ETDEWEB)
Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu
2016-02-05
We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves.
Salerno, D; Minardi, S; Trull, J; Varanavicius, A; Tamosauskas, G; Valiulis, G; Dubietis, A; Caironi, D; Trillo, S; Piskarskas, A; Di Trapani, P
2003-10-01
We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.
Wolf, Omri; Allerman, Andrew A.; Ma, Xuedan; Wendt, Joel R.; Song, Alex Y.; Shaner, Eric A.; Brener, Igal
2015-10-01
We use planar metamaterial resonators to enhance by more than two orders of magnitude the near infrared second harmonic generation obtained from intersubband transitions in III-Nitride heterostructures. The improvement arises from two factors: employing an asymmetric double quantum well design and aligning the resonators' cross-polarized resonances with the intersubband transition energies. The resulting nonlinear metamaterial operates at wavelengths where single photon detection is available, and represents a different class of sources for quantum photonics related phenomena.
Energy Technology Data Exchange (ETDEWEB)
Wolf, Omri, E-mail: owolf@sandia.gov, E-mail: ibrener@sandia.gov; Ma, Xuedan; Brener, Igal, E-mail: owolf@sandia.gov, E-mail: ibrener@sandia.gov [Center for Integrated Nanotechnologies, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Allerman, Andrew A.; Wendt, Joel R.; Shaner, Eric A. [Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185 (United States); Song, Alex Y. [Electrical Engineering Department, Princeton University, EQuad, Olden St, Princeton, New Jersy 08540 (United States)
2015-10-12
We use planar metamaterial resonators to enhance by more than two orders of magnitude the near infrared second harmonic generation obtained from intersubband transitions in III-Nitride heterostructures. The improvement arises from two factors: employing an asymmetric double quantum well design and aligning the resonators' cross-polarized resonances with the intersubband transition energies. The resulting nonlinear metamaterial operates at wavelengths where single photon detection is available, and represents a different class of sources for quantum photonics related phenomena.
Nonlinear waves in a positive-negative coupled waveguide zigzag array
Kazantseva, Elena V
2013-01-01
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest and next nearest neighboring waveguides exist. It is shown that there is a stop band in the spectrum of linear waves. The system of evolution equations for coupled waves has the steady state solution describing the electromagnetic pulse running in the array. Numerical simulation demonstrates robustness of these solitary waves.
Martinez, David
2015-11-01
We investigate on the National Ignition Facility (NIF) the ablative Rayleigh-Taylor (RT) instability in the transition from linear to highly nonlinear regimes. This work is part of the Discovery Science Program on NIF and of particular importance to indirect-drive inertial confinement fusion (ICF) where careful attention to the form of the rise to final peak drive is calculated to prevent the RT instability from shredding the ablator in-flight and leading to ablator mixing into the cold fuel. The growth of the ablative RT instability was investigated using a planar plastic foil with pre-imposed two-dimensional broadband modulations and diagnosed using x-ray radiography. The foil was accelerated for 12ns by the x-ray drive created in a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. The dependence on initial conditions was investigated by systematically changing the modulation amplitude, ablator material and the modulation pattern. For each of these cases bubble mergers were observed and the nonlinear evolution of the RT instability showed insensitivity to the initial conditions. This experiment provides critical data needed to validate current theories on the ablative RT instability for indirect drive that relies on the ablative stabilization of short-scale modulations for ICF ignition. This paper will compare the experimental data to the current nonlinear theories. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
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.
Experimental observation of multifrequency patterns in arrays of coupled nonlinear oscillators.
In, Visarath; Kho, Andy; Neff, Joseph D; Palacios, Antonio; Longhini, Patrick; Meadows, Brian K
2003-12-12
Frequency-related oscillations in coupled oscillator systems, in which one or more oscillators oscillate at different frequencies than the other oscillators, have been studied using group theoretical methods by Armbruster and Chossat [Phys. Lett. A 254, 269 (1999)] and more recently by Golubitsky and Stewart [in Geometry, Mechanics, and Dynamics, edited by P. Newton, P. Holmes, and A. Weinstein (Springer, New York, 2002), p. 243]. We demonstrate, experimentally, via electronic circuits, the existence of frequency-related oscillations in a network of two arrays of N oscillators, per array, coupled to one another. Under certain conditions, one of the arrays can be induced to oscillate at N times the frequency of the other array. This type of behavior is different from the one observed in a driven system because it is dictated mainly by the symmetry of the coupled system.
Low-frequency variability and heat transport in a low-order nonlinear coupled ocean-atmosphere model
Vannitsem, Stéphane; De Cruz, Lesley; Ghil, Michael
2014-01-01
We formulate and study a low-order nonlinear coupled ocean-atmosphere model with an emphasis on the impact of radiative and heat fluxes and of the frictional coupling between the two components. This model version extends a previous 24-variable version by adding a dynamical equation for the passive advection of temperature in the ocean, together with an energy balance model. The bifurcation analysis and the numerical integration of the model reveal the presence of low-frequency variability (LFV) concentrated on and near a long-periodic, attracting orbit. This orbit combines atmospheric and oceanic modes, and it arises for large values of the meridional gradient of radiative input and of frictional coupling. Chaotic behavior develops around this orbit as it loses its stability; this behavior is still dominated by the LFV on decadal and multi-decadal time scales that is typical of oceanic processes. Atmospheric diagnostics also reveals the presence of predominant low- and high-pressure zones, as well as of a su...
Institute of Scientific and Technical Information of China (English)
Ta Na; Qiu Jiajun; Cai Ganhua
2005-01-01
Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF and vibrations resulted by it are studied. First, calculating method of the ZMNF excited by electromagnetic in vibrational system of coupled mechanics and electrics are given from the view of magnetic energy.Laws that the ZMNF varies with active power and exciting current are obtained and are verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system is studied by considering rest eccentricity, rotating eccentricity and swing eccentricity. Using Largrange-Maxwell equation when three phases are asymmetric derives differential equation of the coupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics of resonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF will occur in turbine generators by the action of electromagnetic. Because ZMNF varies with electromagnetic parameters,resonance can occur when exciting frequency of the rotor speed is fixed whereas exciting current change. And also find that a generator is in the state of large amplitude in rated exciting current.
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.
Sheykhi, A; Zangeneh, M Kord
2016-01-01
We construct a new class of charged rotating black brane solutions in the presence of logarithmic nonlinear electrodynamics with complete set of the rotation parameters in arbitrary dimensions. The topology of the horizon of these rotating black branes are flat, while, due to the presence of the dilaton field the asymptotic behaviour of them are neither flat nor (anti)-de Sitter [(A)dS]. We investigate the physical properties of the solutions. The mass and angular momentum of the spacetime are obtained by using the counterterm method inspired by AdS/CFT correspondence. We derive temperature, electric potential and entropy associated with the horizon and check the validity of the first law of thermodynamics on the black brane horizon. We study thermal stability of the solutions in both canonical and grand canonical ensemble and disclose the effects of the rotation parameter, nonlinearity of electrodynamics and dilaton field on the thermal stability conditions. We find the solutions are thermally stable for $\\a...