Energy Technology Data Exchange (ETDEWEB)
Murkin, J.M.; Farrar, J.K.; Tweed, W.A.; McKenzie, F.N.; Guiraudon, G.
1987-09-01
Measurement of /sup 133/Xe clearance and effluent cerebral venous blood sampling were used in 38 patients to determine the effects of cardiopulmonary bypass, and of maintaining temperature corrected or noncorrected PaCO/sub 2/ at 40 mm Hg on regulation of cerebral blood flow (CBF) and flow/metabolism coupling. After induction of anesthesia with diazepam and fentanyl, mean CBF was 25 ml X 100 g-1 X min-1 and cerebral oxygen consumption, 1.67 ml X 100 g-1 X min-1. Cerebral oxygen consumption during nonpulsatile cardiopulmonary bypass at 26 degrees C was reduced to 0.42 ml X 100 g-1 X min-1 in both groups. CBF was reduced to 14-15 ml X 100 g-1 X min-1 in the non-temperature-corrected group (n = 21), was independent of cerebral perfusion pressure over the range of 20-100 mm Hg, but correlated with cerebral oxygen consumption. In the temperature-corrected group (n = 17), CBF varied from 22 to 32 ml X 100 g-1 X min-1, and flow/metabolism coupling was not maintained (i.e., CBF and cerebral oxygen consumption varied independently). However, variation in CBF correlated significantly with cerebral perfusion pressure over the pressure range of 15-95 mm Hg. This study demonstrates a profound reduction in cerebral oxygen consumption during hypothermic nonpulsatile cardiopulmonary bypass. When a non-temperature-corrected PaCO/sub 2/ of approximately 40 mm Hg was maintained, CBF was lower, and analysis of pooled data suggested that CBF regulation was better preserved, i.e., CBF was independent of pressure changes and dependent upon cerebral oxygen consumption.
International Nuclear Information System (INIS)
Murkin, J.M.; Farrar, J.K.; Tweed, W.A.; McKenzie, F.N.; Guiraudon, G.
1987-01-01
Measurement of 133 Xe clearance and effluent cerebral venous blood sampling were used in 38 patients to determine the effects of cardiopulmonary bypass, and of maintaining temperature corrected or noncorrected PaCO 2 at 40 mm Hg on regulation of cerebral blood flow (CBF) and flow/metabolism coupling. After induction of anesthesia with diazepam and fentanyl, mean CBF was 25 ml X 100 g-1 X min-1 and cerebral oxygen consumption, 1.67 ml X 100 g-1 X min-1. Cerebral oxygen consumption during nonpulsatile cardiopulmonary bypass at 26 degrees C was reduced to 0.42 ml X 100 g-1 X min-1 in both groups. CBF was reduced to 14-15 ml X 100 g-1 X min-1 in the non-temperature-corrected group (n = 21), was independent of cerebral perfusion pressure over the range of 20-100 mm Hg, but correlated with cerebral oxygen consumption. In the temperature-corrected group (n = 17), CBF varied from 22 to 32 ml X 100 g-1 X min-1, and flow/metabolism coupling was not maintained (i.e., CBF and cerebral oxygen consumption varied independently). However, variation in CBF correlated significantly with cerebral perfusion pressure over the pressure range of 15-95 mm Hg. This study demonstrates a profound reduction in cerebral oxygen consumption during hypothermic nonpulsatile cardiopulmonary bypass. When a non-temperature-corrected PaCO 2 of approximately 40 mm Hg was maintained, CBF was lower, and analysis of pooled data suggested that CBF regulation was better preserved, i.e., CBF was independent of pressure changes and dependent upon cerebral oxygen consumption
Primordial fluctuations from nonlinear couplings
International Nuclear Information System (INIS)
Calzetta, E.A.; Gonorazky, S.
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is nonlinearly 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, tilting it towards the blue. We discuss in some detail whether these fluctuations are quantum or classical in nature. copyright 1997 The American Physical Society
Phenomenology of coupled nonlinear oscillators
Estevez-Rams, E.; Estevez-Moya, D.; Aragón-Fernández, B.
2018-02-01
A recently introduced model of coupled nonlinear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns appearing in the system for different values of the control parameters. Such behaviors, resembling cellular automata, have been characterized both spatially and temporally. Information distance is used to study the stability of the system to perturbations in the initial conditions and in the control parameters. The latter is not an issue in cellular automata theory, where the rules form a numerable set, contrary to the continuous nature of the parameter space in the system studied in this contribution. The variation in the density of the digits, as a function of time is also studied. Local transitions in the control parameter space are also discussed.
Nonlinear frequency conversion in coupled ring cavities
DEFF Research Database (Denmark)
Buchhave, Preben; Abitan, Haim; Tidemand-Lichtenberg, Peter
2001-01-01
The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power and the op......The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power...... and the optical elements is solved by a numerical root find function of a commercial mathematics software. The method allows computation of the output of sequential nonlinear processes such as laser gain, second harmonic generation and optical parametric amplification as a function of the input diode pump power...
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.
Foundations of Coupled Nonlinear Dimensionality Reduction
Mohri, Mehryar; Rostamizadeh, Afshin; Storcheus, Dmitry
2015-01-01
In this paper we introduce and analyze the learning scenario of \\emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning. First, we present new generalization bounds for this scenario and, second, we introduce an algorithm that follows from these bounds. The generalization error bound is based on a careful analysis of the empirical Rademacher complexity of the relevant hypothes...
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.
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
We explore the dynamical consequences of time-varying conjugate coupling in a system of nonlinear oscillators. We analyze the behavior of coupled ... Conjugate coupling; time varying coupling. PACS Nos 05.45.Xt. 1. Introduction ..... MDS acknowledges the financial support from DST,. New Delhi. References. [1] L Glass ...
Artificial Nonlinearity Generated from Electromagnetic Coupling Metamolecule
Wen, Yongzheng; Zhou, Ji
2017-04-01
A purely artificial mechanism for optical nonlinearity is proposed based on a metamaterial route. The mechanism is derived from classical electromagnetic interaction in a metamolecule consisting of a cut-wire meta-atom nested within a split-ring meta-atom. Induced by the localized magnetic field in the split-ring meta-atom, the magnetic force drives an anharmonic oscillation of free electrons in the cut-wire meta-atom, generating an intrinsically nonlinear electromagnetic response. An explicit physical process of a second-order nonlinear behavior is adequately described, which is perfectly demonstrated with a series of numerical simulations. Instead of "borrowing" from natural nonlinear materials, this novel mechanism of optical nonlinearity is artificially dominated by the metamolecule geometry and possesses unprecedented design freedom, offering fascinating possibilities to the research and application of nonlinear optics.
Measurement of nonlinear mode coupling of tearing fluctuations
International Nuclear Information System (INIS)
Assadi, S.; Prager, S.C.; Sidikman, K.L.
1992-03-01
Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum
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...... increases with the coupling strength. The results are compared with SPECTRE RF simulations....
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.
Superposed nonlinear waves in coherently coupled Bose–Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Babu Mareeswaran, R.; Kanna, T., E-mail: kanna_phy@bhc.edu.in
2016-09-23
We study the dynamics of superposed nonlinear waves in coherently coupled Gross–Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity coefficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schrödinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev–Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient. - Highlights: • Coherently coupled Gross–Pitaevskii equations with constant and time-dependent nonlinearities are considered. • Novel superposed nonlinear structures are reported. • Breather collision and nontrivial twin-peak rogue wave are explored. • Co-existing breathers and rogue waves are observed. • Creeping solitons and compression mechanism, respectively for periodically modulated and kink-like nonlinearity are identified.
Nonlinear vibrations analysis of rotating drum-disk coupling structure
Chaofeng, Li; Boqing, Miao; Qiansheng, Tang; Chenyang, Xi; Bangchun, Wen
2018-04-01
A dynamic model of a coupled rotating drum-disk system with elastic support is developed in this paper. By considering the effects of centrifugal and Coriolis forces as well as rotation-induced hoop stress, the governing differential equation of the drum-disk is derived by Donnell's shell theory. The nonlinear amplitude-frequency characteristics of coupled structure are studied. The results indicate that the natural characteristics of the coupling structure are sensitive to the supporting stiffness of the disk, and the sensitive range is affected by rotating speeds. The circumferential wave numbers can affect the characteristics of the drum-disk structure. If the circumferential wave number n = 1 , the vibration response of the drum keeps a stable value under an unbalanced load of the disk, there is no coupling effect if n ≠ 1 . Under the excitation, the nonlinear hardening characteristics of the forward traveling wave are more evident than that of the backward traveling wave. Moreover, because of the coupling effect of the drum and the disk, the supporting stiffness of the disk has certain effect on the nonlinear characteristics of the forward and backward traveling waves. In addition, small length-radius and thickness-radius ratios have a significant effect on the nonlinear characteristics of the coupled structure, which means nonlinear shell theory should be adopted to design rotating drum's parameter for its specific structural parameters.
On Coupled Rate Equations with Quadratic Nonlinearities
Montroll, Elliott W.
1972-01-01
Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013
Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime
Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying
2018-03-01
Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.
A real nonlinear integrable couplings of continuous soliton hierarchy and its Hamiltonian structure
International Nuclear Information System (INIS)
Yu Fajun
2011-01-01
Some integrable coupling systems of existing papers are linear integrable couplings. In the Letter, beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing real nonlinear integrable couplings of continuous soliton hierarchy. A direct application to the AKNS spectral problem leads to a novel nonlinear integrable couplings, then we consider the Hamiltonian structures of nonlinear integrable couplings of AKNS hierarchy with the component-trace identity. - Highlights: → We establish a scheme to construct real nonlinear integrable couplings. → We obtain a novel nonlinear integrable couplings of AKNS hierarchy. → Hamiltonian structure of nonlinear integrable couplings AKNS hierarchy is presented.
Nonlocal nonlinear coupling of kinetic sound waves
Directory of Open Access Journals (Sweden)
O. Lyubchyk
2014-11-01
Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
In this case there are three solutions of the coupled dimer eqs (1) and (2) out of which we present two solutions now and the third one (a novel superposed solution) in the next subsection. Solution I: It is easy to check that u(t) = ±v(t) = Adn[β(t + t0), m]. (22) is an exact solution provided. (ǫ + δ)β2 = −2β2, (2 − m)β2 = −1 ± k.
Theories of quantum dissipation and nonlinear coupling bath descriptors
Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing
2018-03-01
The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.
Soliton solutions of coupled nonlinear Klein-Gordon equations
International Nuclear Information System (INIS)
Alagesan, T.; Chung, Y.; Nakkeeran, K.
2004-01-01
The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations
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.
Signatures of Nonlinear Cavity Optomechanics in the Weak Coupling Regime
Børkje, K.; Nunnenkamp, A.; Teufel, J. D.; Girvin, S. M.
2013-08-01
We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong laser drive is detuned by half the mechanical frequency, optomechanically induced transparency also occurs due to resonant two-photon processes. The cavity response to a second probe drive is in this case nonlinear in the probe power. These effects should be observable with optomechanical coupling strengths that have already been realized in experiments.
Solitons and periodic solutions to a couple of fractional nonlinear ...
Indian Academy of Sciences (India)
2014-02-26
Feb 26, 2014 ... 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 ...
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
. 995–1009. Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space. LI ZHANG1,∗, SHUTANG LIU2 and CHENGLONG YU3. 1Business School, Shandong University of Political Science and Law, Jinan ...
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
995–1009. Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space. LI ZHANG1,∗, SHUTANG LIU2 and CHENGLONG YU3. 1Business School, Shandong University of Political Science and Law, Jinan 250014, China. 2College of Control Science and Engineering, Shandong University, ...
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
Exact solutions of some coupled nonlinear diffusion-reaction equations using auxiliary equation method. RANJIT KUMAR. Department of Physics, Dyal Singh College, University of Delhi, Delhi 110 003, India. E-mail: du.ranjit@gmail.com. MS received 1 January 2012; revised 29 February 2012; accepted 10 May 2012.
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 coupling of tearing fluctuations in the Madison Symmetric Torus
International Nuclear Information System (INIS)
Sarff, J.S.; Almagri, A.F.; Cekic, M.; Den Hartog, D.J.; Fiksel, G.; Hokin, S.A.; Ji, H.; Prager, S.C.; Shen, W.; Stoneking, M.R.; Assadi, S.; Sidikman, K.L.
1992-11-01
Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in ''k-space. The strength of nonlinear three-wave interactions satisfying the sum rules m 1 + m 2 = m 3 and n 1 + n 2 = n 3 is measured by the bicoherency. In the RFP, m=l, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=l modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from MHD computation. However, in the experiment, enhanced coupling occurs in the ''crash'' phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade
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.
Positive Solutions for Coupled Nonlinear Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Wenning Liu
2014-01-01
Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.
Driven Nonlinear Dynamics of Two Coupled Exchange-Only Qubits
Directory of Open Access Journals (Sweden)
Arijeet Pal
2014-01-01
Full Text Available Inspired by the creation of a fast exchange-only qubit [Medford et al., Phys. Rev. Lett. 111, 050501 (2013], we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same as or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about 1% of their level splittings, and we calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of interqubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate the existence of an optimal range of coupling strength maintaining stability during the operational time.
Nonlinearly coupled dynamics of irregularities in the equatorial electrojet
International Nuclear Information System (INIS)
Atul, J.K.; Sarkar, S.; Singh, S.K.
2016-01-01
Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed. - Highlights: • Nonlinear influence of Farley Buneman mode on the Gradient drift mode, is investigated. • Electron collision frequency and density gradient scale length get modified. • A new quasimode gets excited due to the competition between these modes. • It seems to be important for modelling of Equatorial Electrojet current system.
Dark state in a nonlinear optomechanical system with quadratic coupling
Huang, Yue-Xin; Zhou, Xiang-Fa; Guo, Guang-Can; Zhang, Yong-Sheng
We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed. Supported by the National Fundamental Research Program of China (Grants No. 2011CB921200 and No. 2011CBA00200), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB01030200), and NSFC (Grants No. 61275122 and 11474266).
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 nonlinearity...... in the coupling transconductances, in conjunction with a finite amplitude relaxation time and de-tuning of the individual oscillators, cause close-to-carrier AM-to-PM noise conversion. A discussion is presented of how the theoretic results translate into design rules for quadrature oscillator ICs. SPECTRE RF...
Forced nonlinear resonance in a system of coupled oscillators.
Glebov, Sergei; Kiselev, Oleg; Tarkhanov, Nikolai
2011-06-01
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t∼ɛ(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.
UV Nano Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
compact optical devices with new functionalities and coupling electronic transitions directly to strongly localised optical modes is highly desirable...in the form of the localised surface plasmon resonance of the gold component of nanoparticle hybrids could enhance nonlinear emission by several...intense electric fields generated by the localised surface plasmon absorption at the Au nanoparticle interface. it was found that a significant improvement
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.
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.
Coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers.
Zhang, Junshi; Chen, Hualing; Li, Bo; McCoul, David; Pei, Qibing
2015-10-14
This article describes the development of an analytical model to study the coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers (DEs) under non-equibiaxial tensile forces by utilizing the method of virtual work. Numerically calculated results are employed to predict this nonlinear dynamic behavior. The resonant frequency (where the amplitude-frequency response curve peaks) and the amplitude-frequency response of the deformation in both in-plane directions are tuned by varying the values of tensile force. The oscillation response in the two in-plane directions exhibits strong nonlinearity and coupling with each other, and is tuned by the changing tensile forces under a specific excitation frequency. By varying the values of tensile forces, the dynamic viscoelastic creep in a certain in-plane direction can be eliminated. Phase diagrams and Poincaré maps under several values of tensile forces are utilized to study the stability evolution of the DE system under non-equibiaxial tensile forces.
Nonlinear electrodynamics coupled to teleparallel theory of gravity
Gamal, G. L. Nashed
2011-02-01
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.
Contributions of non-intrusive coupling in nonlinear structural mechanics
International Nuclear Information System (INIS)
Duval, Mickael
2016-01-01
This PhD thesis, part of the ANR ICARE project, aims at developing methods for complex analysis of large scale structures. The scientific challenge is to investigate very localised areas, but potentially critical as of mechanical systems resilience. Classically, representation models, discretizations, mechanical behaviour models and numerical tools are used at both global and local scales for simulation needs of graduated complexity. Global problem is handled by a generic code with topology (plate formulation, geometric approximation...) and behaviour (homogenization) simplifications while local analysis needs implementation of specialized tools (routines, dedicated codes) for an accurate representation of the geometry and behaviour. The main goal of this thesis is to develop an efficient non-intrusive coupling tool for multi-scale and multi-model structural analysis. Constraints of non-intrusiveness result in the non-modification of the stiffness operator, connectivity and the global model solver, allowing to work in a closed source software environment. First, we provide a detailed study of global/local non-intrusive coupling algorithm. Making use of several relevant examples (cracking, elastic-plastic behaviour, contact...), we show the efficiency and the flexibility of such coupling method. A comparative analysis of several optimisation tools is also carried on, and the interacting multiple patches situation is handled. Then, non-intrusive coupling is extended to globally non-linear cases, and a domain decomposition method with non-linear re-localization is proposed. Such methods allowed us to run a parallel computation using only sequential software, on a high performance computing cluster. Finally, we apply the coupling algorithm to mesh refinement with patches of finite elements. We develop an explicit residual based error estimator suitable for multi-scale solutions arising from the non-intrusive coupling, and apply it inside an error driven local mesh
DEFF Research Database (Denmark)
Kutluyarov, Ruslan V.; Bagmanov, Valeriy Kh; Antonov, Vyacheslav V.
2017-01-01
This paper is focused on the analysis of linear and nonlinear mode coupling in space division multiplexed (SDM) optical communications over step-index fiber in few-mode regime. Linear mode coupling is caused by the fiber imperfections, while the nonlinear coupling is caused by the Kerr-nonlineari......This paper is focused on the analysis of linear and nonlinear mode coupling in space division multiplexed (SDM) optical communications over step-index fiber in few-mode regime. Linear mode coupling is caused by the fiber imperfections, while the nonlinear coupling is caused by the Kerr...... to a significant increase of the nonlinear distortions. It is necessary to take this phenomenon into account in SDM systems with linear compensation of mode coupling, because the nonlinear distortions may sufficiently decrease the effectiveness of the compensation....
Coupled equations of electromagnetic waves in nonlinear metamaterial waveguides.
Azari, Mina; Hatami, Mohsen; Meygoli, Vahid; Yousefi, Elham
2016-11-01
Over the past decades, scientists have presented ways to manipulate the macroscopic properties of a material at levels unachieved before, and called them metamaterials. This research can be considered an important step forward in electromagnetics and optics. In this study, higher-order nonlinear coupled equations in a special kind of metamaterial waveguides (a planar waveguide with metamaterial core) will be derived from both electric and magnetic components of the transverse electric mode of electromagnetic pulse propagation. On the other hand, achieving the refractive index in this research is worthwhile. It is also shown that the coupled equations are not symmetric with respect to the electric and magnetic fields, unlike these kinds of equations in fiber optics and dielectric waveguides. Simulations on the propagation of a fundamental soliton pulse in a nonlinear metamaterial waveguide near the resonance frequency (a little lower than the magnetic resonant frequency) are performed to study its behavior. These pulses are recommended to practice in optical communications in controlled switching by external voltage, even in low power.
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.
Spectrally variable two-beam coupling nonlinear deconvolution.
Haji-Saeed, Bahareh; Sengupta, Sandip K; Goodhue, William D; Khoury, Jed; Woods, Charles L; Kierstead, John
2007-12-01
In previous work, we introduced a dynamic range compression-based technique for image correction using nonlinear deconvolution; the impulse response of the distortion function and the distorted image are jointly transformed to pump a clean reference beam in a photorefractive two-beam coupling arrangement. The Fourier transform of the pumped reference beam contains the deconvolved image and its conjugate. Here we extend our work to spectrally variable dynamic range compression. This approach allows the retrieval of distorted signals embedded in a very high noise environment and does not require one to work with a very high beam ratio as in our previous work. Resolution recovery of blurred noisy images is demonstrated for several different types of image blur.
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.
Nonlinear coupling between cortical oscillations and muscle activity during isotonic wrist flexion
Directory of Open Access Journals (Sweden)
Yuan Yang
2016-12-01
Full Text Available Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e. the contralateral primary sensorimotor areas, supplementary motor area, prefrontal area and posterior parietal cortex. For all these areas, linear coupling between EEG and EMG is present with peaks in the beta band (15-35 Hz, while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4 and non-integer (2:3 harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (supplementary motor area, prefrontal area compared to the sensory association area (posterior parietal cortex; but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.
The solution of a coupled system of nonlinear physical problems using the homotopy analysis method
International Nuclear Information System (INIS)
El-Wakil, S A; Abdou, M A
2010-01-01
In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.
A fully coupled thermal-mechanical-fluid flow model for nonlinear geologic systems
Hart, R. D.
1981-02-01
A single model is presented which describes fully coupled thermal-mechanical-fluid flow behavior of highly nonlinear, dynamic or quasistatic, porous geologic systems. The mathematical formulation for the model utilizes the continuum theory of mixtures to describe the multiphase nature of the system, and incremental linear constitutive theory to describe the path dependency of nonlinear material behavior. The model, incorporated in an explicit finite difference numerical procedure, was implemented in two different computer codes. A special-purpose one-dimensional code, SNEAKY, was written for initial validation of the coupling mechanisms and testing of the coupled model logic. A general purpose commercially available code, STEALTH, developed for modeling dynamic nonlinear thermomechanical processes, was modified to include fluid flow behavior and the coupling constitutive model. The fully explicit approach in the coupled calculation facilitated the inclusion of the coupling mechanisms and complex constitutive behavior.
Directory of Open Access Journals (Sweden)
Ren He
2015-01-01
Full Text Available Since theoretical guidance is lacking in the design and control of the integrated system of electromagnetic brake and frictional brake, this paper aims to solve this problem and explores the nonlinear coupling characteristics and dynamic characteristics of the integrated system of electromagnetic brake and frictional brake. This paper uses the power bond graph method to establish nonlinear coupling mathematical model of the integrated system of electromagnetic brake and frictional brake and conducts the contrastive analysis on the dynamic characteristics based on this mathematical model. Meanwhile, the accuracy of the nonlinear coupling mathematical model proposed above is verified on the hardware in the loop simulation platform, and nonlinear coupling characteristics of the integrated system are also analyzed through experiments.
Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input
International Nuclear Information System (INIS)
Hung, M.-L.; Yan, J.-J.; Liao, T.-L.
2008-01-01
This paper addresses the synchronization problem of drive-response chaotic gyros coupled with dead-zone nonlinear input. Using the sliding mode control technique, a novel control law is established which guarantees generalized projective synchronization even when the dead-zone nonlinearity is present. Numerical simulations are presented to verify that the synchronization can be achieved by using the proposed synchronization scheme
Dynamic coupling design for nonlinear output agreement and time-varying flow control
Buerger, Mathias; De Persis, Claudio
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances, using dynamic diffusive couplings. Necessary conditions are derived for general networks of nonlinear systems, and these conditions are explicitly interpreted as conditions
The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-05-01
Full Text Available The present paper proposes a new monotone iteration principle for the existence as well as approximations of the coupled solutions for a coupled periodic boundary value problem of second order ordinary nonlinear differential equations. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper. We claim that the method as well as the results of this paper are new to literature on nonlinear analysis and applications.
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.
He, Ren; Hu, Donghai
2015-01-01
Since theoretical guidance is lacking in the design and control of the integrated system of electromagnetic brake and frictional brake, this paper aims to solve this problem and explores the nonlinear coupling characteristics and dynamic characteristics of the integrated system of electromagnetic brake and frictional brake. This paper uses the power bond graph method to establish nonlinear coupling mathematical model of the integrated system of electromagnetic brake and frictional brake and c...
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.
2018-01-01
In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.
Sliding mode control for a two-joint coupling nonlinear system based on extended state observer.
Zhao, Ling; Cheng, Haiyan; Wang, Tao
2018-02-01
A two-joint coupling nonlinear system driven by pneumatic artificial muscles is introduced in this paper. A sliding mode controller with extended state observer is proposed to cope with nonlinearities and disturbances for the two-joint coupling nonlinear system. In addition, convergence of the extended state observer is presented and stability analysis of the closed-loop system is also demonstrated with the sliding mode controller. Lastly, some experiments are carried out to show the reality effectiveness of the proposed method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
Mode coupling in the nonlinear response of black holes
International Nuclear Information System (INIS)
Zlochower, Yosef; Gomez, Roberto; Husa, Sascha; Lehner, Luis; Winicour, Jeffrey
2003-01-01
We study the properties of the outgoing gravitational wave produced when a nonspinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes
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.
Experimental Investigation of Nonlinear Coupling of Lower Hybrid Waves on Tore Supra
Czech Academy of Sciences Publication Activity Database
Goniche, M.; Frincu, B.; Ekedahl, A.; Petržílka, Václav; Berger-By, G.; Hillairet, J.; Litaudon, X.; Preynas, M.; Voyer, D.
2012-01-01
Roč. 62, č. 2 (2012), s. 322-332 ISSN 1536-1055 R&D Projects: GA ČR GA202/07/0044 Institutional research plan: CEZ:AV0Z20430508 Keywords : LHwave * plasma * lower hybrid * wave coupling * nonlinear coupling Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.517, year: 2012
Painlevйe analysis and integrability of two-coupled non-linear ...
Indian Academy of Sciences (India)
Coupled non-linear oscillators describe a variety of self-organization phenom- ena. Examples include multi-rhythmicity of heart beating [9,10], wave in ensembles of intestinal cells [11], oscillations in chemical reactions [12,13], transition between two oscillation modes [14], wave fronts in coupled Lorentz oscillators [15] and ...
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.
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
[1] C S Bertuglia and F Vaio, Nonlinearity, chaos and complexity (The Dynamics of Natural and. Social Systems) (Oxford University Press, New York, 2005). [2] Radhey Shyam Kaushal, Structural analogy in understanding nature (Anamaya Publishers,. New Delhi, 2003). [3] S A. Khuri, Chaos, Solitons and Fractals 36, 1181 ...
Breathers and rogue waves: Demonstration with coupled nonlinear ...
Indian Academy of Sciences (India)
. ∗ and M LAKSHMANAN. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University,. Tiruchirappalli 620 024, India. ∗. Corresponding author. E-mail: velan@cnld.bdu.ac.in. DOI: 10.1007/s12043-015-0937-4; ePublication: ...
Breathers and rogue waves: Demonstration with coupled nonlinear ...
Indian Academy of Sciences (India)
Abstract. Different types of breathers and rogue waves (RWs) are some of the important coher- ent 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) ...
Regression of non-linear coupling of noise in LIGO detectors
Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.
2018-03-01
In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.
International Nuclear Information System (INIS)
Zhou, Shengxi; Cao, Junyi; Wang, Wei; Liu, Shengsheng; Lin, Jing
2015-01-01
This paper presents a nonlinear doubly magnet-coupled energy harvesting system (DMEHS) which could exhibit co-bistable and monostable dynamic characteristics. Its various characteristic responses induced by the magnetic force can be conveniently obtained using the adjustable horizontal distance between two coupled harvesters in the DMEHS. In the case of appropriate relative positions, the DMEHS appears in a co-bistable structure which is different from the traditional bistable structure. Additionally, both the inclination angle of endmost magnets and the displacement perpendicular to the vibration direction are taken into account to calculate the nonlinear magnetic force in the nonlinear electromechanical equations. The numerical investigations show good agreement with experimental results with respect to the output voltage response. Each harvester without magnetic coupling is tested independently to compare with the DMEHS. Both numerical and experimental results also demonstrate the frequency bandwidth and performance enhancements by changing the horizontal distance between the two coupled harvesters. (paper)
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...
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.
Non-linear seismic analysis of structures coupled with fluid
International Nuclear Information System (INIS)
Descleve, P.; Derom, P.; Dubois, J.
1983-01-01
This paper presents a method to calculate non-linear structure behaviour under horizontal and vertical seismic excitation, making possible the full non-linear seismic analysis of a reactor vessel. A pseudo forces method is used to introduce non linear effects and the problem is solved by superposition. Two steps are used in the method: - Linear calculation of the complete model. - Non linear analysis of thin shell elements and calculation of seismic induced pressure originating from linear and non linear effects, including permanent loads and thermal stresses. Basic aspects of the mathematical formulation are developed. It has been applied to axi-symmetric shell element using a Fourier series solution. For the fluid interaction effect, a comparison is made with a dynamic test. In an example of application, the displacement and pressure time history are given. (orig./GL)
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.
A novel real-time non-linear wavelet-based model predictive controller for a coupled tank system
Owa, K; Sharma, S; Sutton, R
2014-01-01
This article presents the design, simulation and real-time implementation of a constrained non-linear model predictive controller for a coupled tank system. A novel wavelet-based function neural network model and a genetic algorithm online non-linear real-time optimisation approach were used in the non-linear model predictive controller strategy. A coupled tank system, which resembles operations in many chemical processes, is complex and has inherent non-linearity, and hence, controlling such...
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.
Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.
Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi
2014-03-10
We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.
Nonlinear optical control of Josephson coupling in cuprates
Energy Technology Data Exchange (ETDEWEB)
Casandruc, Eliza
2017-03-15
In High-T{sub C} cuprates superconducting Cu-O planes alternate with insulating layers along the crystallographic c-axis, making the materials equivalent to Josephson junctions connected in series. The most intriguing consequence is that the out-of-plane superconducting transport occurs via Cooper pairs tunneling across the insulating layers and can be predicted by the Josephson tunneling equations. Nonlinear interaction between light fields and the superconducting carriers serves as a powerful dynamical probe of cuprates, while offering opportunities for controlling them in an analogous fashion to other stimuli such as pressure and magnetic fields. The main goal of this thesis work is to use intense transient light fields to control the interlayer superconducting transport on ultrafast time scales. This was achieved by tuning the wavelength of such light pulses to completely different ranges, in order to either directly excite Josephson Plasma Waves in the nonlinear regime, or efficiently melt the competing charge and spin order phase, which in certain cuprates quenches the Josephson tunneling at equilibrium. In a first study, I have utilized strong field terahertz transients with frequencies tuned to the Josephson plasma resonance (JPR) to coherently control the c-axis superconducting transport. The Josephson relations have a cubic nonlinearity which is exploited to achieve two related, albeit slightly different, phenomena. Depending on the driving pulse, solitonic breathers were excited with narrow-band multi-cycle pulses in La{sub 1.84}Sr{sub 0.16}CuO{sub 4} while broad-band half-cycle pulses were employed to achieve a parametric amplification of Josephson Plasma Waves in La{sub 1.905}Ba{sub 0.095}CuO{sub 4}. These experiments are supported by extensive modeling, showing exceptional agreement. A comprehensive study illustrates the strong enhancement of the nonlinear effects near the JPR frequency. Then, I turned to investigate the competition between
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
The nonlinearity measurement of charge-coupled device array spectrometer using colorful LED
Zhao, Wei-qiang; Liu, Hui; Liu, Jian
2017-11-01
A nonlinearity measurement of the charge-coupled device (CCD) array spectrometer using flux addition and comparison method is described. The light with various colors from the colorful light emitting diode (LED) light source is applied to measure the nonlinearity of the spectrometer at different wavelengths, respectively. An high-end CCD array spectrometer is tested. For colorful LED light sources, the nonlinearity factors of the CCD array spectrometer (absolute value) are as follows: kwhite light, k <1.1% for red light, k <2.2% for green light and k<4.7% for blue light. By using those quasi-monochromatic light sources, it is shown that the nonlinearity depends on the wavelength. It is important to be wariness about the spectral nonlinearity and related uncertainty evaluation when the narrow-band light source is tested.
Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines
Eric, Tala-Tebue; Aurelien, Kenfack-Jiotsa; Marius Hervé, Tatchou-Ntemfack; Timoléon Crépin, Kofané
2013-07-01
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 ω_ mode which corresponds to the regime admitting low frequencies.
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.
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.
Xiaoyan Lei; Shenhua Wu; Bin Zhang
2016-01-01
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 ...
Coupled bending and torsional vibration of a rotor system with nonlinear friction
Energy Technology Data Exchange (ETDEWEB)
Hua, Chunli; Cao, Guohua; Zhu, Zhencai [China University of Mining and Technology, Xuzhou (China); Rao, Zhushi; Ta, Na [Shanghai Jiao Tong University, Shanghai (China)
2017-06-15
Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating ma- chinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose self- excited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
International Nuclear Information System (INIS)
Hedrih, K
2008-01-01
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
Energy Technology Data Exchange (ETDEWEB)
Hedrih, K [Faculty of Mechanical Engineering University of Nis, Mathematical Institute SANU, ul. Vojvode Tankosic 3/V/22, 18000-Nis (Serbia)], E-mail: katica@masfak.ni.ac.yu, E-mail: khedrih@eunet.yu
2008-02-15
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task.
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
1Department of Physics, Central University of Rajasthan, Ajmer 305 817, India. 2The Institute of Mathematical Science, CIT Campus, .... Now, based on the choice of k1 and k2, we consider two cases, (1) C1: both k1 and k2 ... 2.5, coupled systems show multiple transitions between synchronized and unsynchronized states.
Directory of Open Access Journals (Sweden)
Shi Miao
2013-01-01
Full Text Available Distributed adaptive synchronization control for complex dynamical networks with nonlinear derivative coupling is proposed. The distributed adaptive strategies are constituted by directed connections among nodes. By means of the parameters separation, the nonlinear functions can be transformed into the linearly form. Then effective distributed adaptive techniques are designed to eliminate the effect of time-varying parameters and made the considered network synchronize a given trajectory in the sense of square error norm. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible. An example shows the applicability and feasibility of the approach.
Mode coupling in nonlinear Rayleigh--Taylor instability
International Nuclear Information System (INIS)
Ofer, D.; Shvarts, D.; Zinamon, Z.; Orszag, S.A.
1992-01-01
This paper studies the interaction of a small number of modes in the two-fluid Rayleigh--Taylor instability at relatively late stages of development, i.e., the nonlinear regime, using a two-dimensional hydrodynamic code incorporating a front-tracking scheme. It is found that the interaction of modes can greatly affect the amount of mixing and may even reduce the width of the mixing region. This interaction is both relatively long range in wave-number space and also acts in both directions, i.e., short wavelengths affect long wavelengths and vice versa. Three distinct stages of interaction have been identified, including substantial interaction among modes some of which may still be in their classical (single mode) ''linear'' phase
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.
Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field
International Nuclear Information System (INIS)
Deng Fengyan; He Xingsuo; Li Liang; Zhang Juan
2007-01-01
In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange's equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a 'stiffening beam' can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases
Nonlinear local electrovascular coupling. I: A theoretical model.
Riera, Jorge J; Wan, Xiaohong; Jimenez, Juan Carlos; Kawashima, Ryuta
2006-11-01
Here we present a detailed biophysical model of how brain electrical and vascular dynamics are generated within a basic cortical unit. The model was obtained from coupling a canonical neuronal mass and an expandable vasculature. In this proposal, we address several aspects related to electroencephalographic and functional magnetic resonance imaging data fusion: (1) the impact of the cerebral architecture (at different physical levels) on the observations; (2) the physiology involved in electrovascular coupling; and (3) energetic considerations to gain a better understanding of how the glucose budget is used during neuronal activity. The model has three components. The first is the canonical neural mass model of three subpopulations of neurons that respond to incoming excitatory synaptic inputs. The generation of the membrane potentials in the somas of these neurons and the electric currents flowing in the neuropil are modeled by this component. The second and third components model the electrovascular coupling and the dynamics of vascular states in an extended balloon approach, respectively. In the first part we describe, in some detail, the biophysical model and establish its face validity using simulations of visually evoked responses under different flickering frequencies and luminous contrasts. In a second part, a recursive optimization algorithm is developed and used to make statistical inferences about this forward/generative model from actual data. Copyright 2006 Wiley-Liss, Inc.
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.
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.
Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation
International Nuclear Information System (INIS)
Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo
2007-01-01
In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented
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.
Influence of the linear mode coupling on the nonlinear impairments in few-mode fibers
DEFF Research Database (Denmark)
Kutluyarov, R.V.; Lyubopytov, V.S.; Bagmanov, V.Kh
2017-01-01
This paper is focused on the influence of the linear mode coupling caused by the fiber bending on the nonlinear distortions in a mode-division multiplexed system. The system under test utilizes the fundamental Gaussian mode and the conjugated first-order vortex modes propagating in the step-index...
Fitting and forecasting coupled dark energy in the non-linear regime
International Nuclear Information System (INIS)
Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian; Baldi, Marco
2016-01-01
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 0z=–1.6 and wave modes below 0k=1 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 weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β 2 , with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications
Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays
International Nuclear Information System (INIS)
Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.
2005-04-01
We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)
Diffusion rate for the emittance growth due to periodic crossings of nonlinear coupled resonances
Energy Technology Data Exchange (ETDEWEB)
Shi, J. (Texas Univ., Houston, TX (United States). Dept. of Physics); Gluckstern, R.L.; Ohnuma, S. (Brookhaven National Lab., Upton, NY (United States))
1992-01-01
Assuming that many betatron oscillations occur between crossings so that the betatron phase is uncorrelated from one crossing to the next, we estimate the diffusion rate for the emittance growth due to periodic crossing of coupled nonlinear resonances. It was shown that the diffusion rate is more or less independent of the frequency, but it is inversely proportional to the modulation amplitude.
Diffusion rate for the emittance growth due to periodic crossings of nonlinear coupled resonances
Energy Technology Data Exchange (ETDEWEB)
Shi, J. [Texas Univ., Houston, TX (United States). Dept. of Physics; Gluckstern, R.L.; Ohnuma, S. [Brookhaven National Lab., Upton, NY (United States)
1992-06-01
Assuming that many betatron oscillations occur between crossings so that the betatron phase is uncorrelated from one crossing to the next, we estimate the diffusion rate for the emittance growth due to periodic crossing of coupled nonlinear resonances. It was shown that the diffusion rate is more or less independent of the frequency, but it is inversely proportional to the modulation amplitude.
Periodic wavetrains for systems of coupled nonlinear Schrödinger ...
Indian Academy of Sciences (India)
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 ...
Periodic wavetrains for systems of coupled nonlinear Schrödinger ...
Indian Academy of Sciences (India)
Abstract. 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 ...
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...
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.
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.
Wu, Hui; Hu, Liming; Wen, Qingbo
2017-06-01
Electro-osmotic consolidation is an effective method for soft ground improvement. A main limitation of previous numerical models on this technique is the ignorance of the non-linear variation of soil parameters. In the present study, a multi-field numerical model is developed with the consideration of the non-linear variation of soil parameters during electro-osmotic consolidation process. The numerical simulations on an axisymmetric model indicated that the non-linear variation of soil parameters showed remarkable impact on the development of the excess pore water pressure and degree of consolidation. A field experiment with complex geometry, boundary conditions, electrode configuration and voltage application was further simulated with the developed numerical model. The comparison between field and numerical data indicated that the numerical model coupling of the non-linear variation of soil parameters gave more reasonable results. The developed numerical model is capable to analyze engineering cases with complex operating conditions.
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.
International Nuclear Information System (INIS)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao
2015-01-01
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.
Solutions and laws of conservation for coupled nonlinear Schrödinger equations: Lie group analysis
Pulov, V. I.; Uzunov, I. M.; Chacarov, E. J.
1998-03-01
A set of two coupled nonlinear Schrödinger equations is systematically analyzed by means of Lie group technique. The physical situations under consideration include nonlinear propagation in strongly birefringent and multimode optical fibers. The most general Lie group of point symmetries, its Lie algebra, and a group of adjoint representations that correspond to the Lie algebra are identified. As a result, a complete list of group-invariant exact solutions is obtained and compared with earlier results. The corresponding laws of conservation are derived employing Noether's theorem.
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators.
Senthilkumar, D V; Muruganandam, P; Lakshmanan, M; Kurths, J
2010-06-01
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 size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength ε(c) with a scaling exponent γ. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for m couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength ε. In addition, we have found that ε(c) shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rössler and Lorenz oscillators.
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...
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
Directory of Open Access Journals (Sweden)
Goli Konan Charles Etienne
2017-12-01
Full Text Available We study the existence of solutions of the system submitted to nonlinear coupled boundary conditions on [0, T] where ∅1, ∅2: (-a, a → ℝ, with 0 < a < +∞, are two increasing homeomorphisms such that ∅1(0 = ∅2(0 = 0, and fi : [0, T] × ℝ4 → ℝ, i ∈{1, 2} are two L1-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.
Murguia, C; Fey, Rob H B; Nijmeijer, H
2015-02-01
We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delay (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functional and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. The results are illustrated by computer simulations of coupled Hindmarsh-Rose neurons.
Murguia, C.; Fey, Rob H. B.; Nijmeijer, H.
2015-02-01
We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delay (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functional and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. The results are illustrated by computer simulations of coupled Hindmarsh-Rose neurons.
A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system
International Nuclear Information System (INIS)
Cai Jia-Xiang; Wang Yu-Shun
2013-01-01
We derive a new method for a coupled nonlinear Schrödinger system by using the square of first-order Fourier spectral differentiation matrix D 1 instead of traditional second-order Fourier spectral differentiation matrix D 2 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
Directory of Open Access Journals (Sweden)
Koichi Narahara
2018-01-01
Full Text Available The leapfrogging pulses in two unbalanced electrical nonlinear transmission lines (NLTLs with capacitive couplings are investigated for efficient modulation of a pulse train. Due to the resonant interactions, the nonlinear solitary waves in the NLTLs exhibit complementary behaviors of amplitudes and phases called leapfrogging. For maximizing resonance, both solitary waves should have a common average velocity. Sharing the common velocity, the characteristic impedance can still be freely designed for two coupled solitary waves. In this study, we characterize the leapfrogging pulses developed in unbalanced NLTLs having distinct characteristic impedance. Through the soliton perturbation theory and numerical time-domain calculations, it is found that both the leapfrogging frequency and the voltage variations of pulse amplitudes increase as the difference in the characteristic impedance becomes large. These properties can improve the on/off ratio of modulated pulse train.
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.
Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved.......Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....
Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization.
Jin, Xiao-Zheng; Yang, Guang-Hong; Che, Wei-Wei
2012-09-01
This paper deals with a class of complex networks with nonideal coupling networks, and addresses the problem of asymptotic synchronization of the complex network through designing adaptive pinning control and coupling adjustment strategies. A more general coupled nonlinearity is considered as perturbations of the network, while a serious faulty network named deteriorated network is also proposed to be further study. For the sake of eliminating these adverse impacts for synchronization, indirect adaptive schemes are designed to construct controllers and adjusters on pinned nodes and nonuniform couplings of un-pinned nodes, respectively. According to Lyapunov stability theory, the proposed adaptive strategies are successful in ensuring the achievement of asymptotic synchronization of the complex network even in the presence of perturbed and deteriorated networks. The proposed schemes are physically implemented by circuitries and tested by simulation on a Chua's circuit network.
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.
Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....
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.
Weak ωNN coupling in the non-linear chiral model
International Nuclear Information System (INIS)
Shmatikov, M.
1988-01-01
In the non-linear chiral model with the soliton solution stabilized by the ω-meson field the weak ωNN coupling constants are calculated. Applying the vector dominance model for the isoscalar current the constant of the isoscalar P-odd ωNN interaction h ω (0) =0 is obtained while the constant of the isovector (of the Lagrangian of the ωNN interaction proves to be h ω (1) ≅ 1.0x10 -7
Hopf bifurcation in love dynamical models with nonlinear couples and time delays
International Nuclear Information System (INIS)
Liao Xiaofeng; Ran Jiouhong
2007-01-01
A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results
A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling
Directory of Open Access Journals (Sweden)
Jesús Cuevas-Maraver
2016-05-01
Full Text Available As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK and kink-anti-kink (KA complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively.
Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.
2015-03-01
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.
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. PMID:25762243
Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice
Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan
2018-01-01
We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.
Strong asymmetry for surface modes in nonlinear lattices with long-range coupling
International Nuclear Information System (INIS)
Martinez, Alejandro J.; Vicencio, Rodrigo A.; Molina, Mario I.
2010-01-01
We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increases (decreases) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.
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....
A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys
International Nuclear Information System (INIS)
Jin Ke; Kou Yong; Zheng Xiaojing
2012-01-01
This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops. - Highlights: ► A general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials is proposed. ► Model is thermodynamically motivated and the reversible magnetic domain rotation and irreversible domain wall motion are taken. ► The predictions are in good accordance with the experimental data including both rods and films. ► Magnetostrictive alloys are sensitive to environment temperature and pre-stress or residual stress.
A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling
Directory of Open Access Journals (Sweden)
João Paulo de Barros Cavalcante
Full Text Available Abstract The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.
Identification of nonlinear coupling in wave turbulence at the surface of water
Campagne, Antoine; Hassaini, Roumaissa; Redor, Ivan; Aubourg, Quentin; Sommeria, Joël; Mordant, Nicolas
2017-11-01
The Weak Turbulence Theory is a theory, in the limit of vanishing nonlinearity, that derive analytically statistical features of wave turbulence. The stationary spectrum for the surface elevation in the case of gravity waves, is predicted to E(k) k - 5 / 2 . This spectral exponent -5/2 remains elusive in all experiments. in which the measured exponent is systematically lower than the prediction. Furthermore in the experiments the weaker the nonlinearity the further the spectral exponent is from the prediction. In order to investigate the reason for this observation we developed an experiment in the CORIOLIS facility in Grenoble. It is a 13m-diameter circular pool filled with water with a 70 cm depth. We generate wave turbulence by using two wedge wavemakers. Surface elevation measurements are performed by a stereoscopic optical technique and by capacitive probes. The nonlinear coupling at work in this system are analyzed by computing 3- and 4-wave correlations of the Fourier wave amplitudes in frequency. Theory predicts that coupling should occur through 4-wave resonant interaction. In our data, strong 3-wave correlations are observed in addition to the 4-wave correlation. Most our observations are consistent with field observation in the Black Sea (Leckler et al. 2015). This project has received funding from the European Research Council (ERC, Grant Agreement No 647018-WATU).
Nonlinear coupling of low-n modes in PBX-M
International Nuclear Information System (INIS)
Sesnic, S.; Kaita, R.; Kaye, S.; Okabayashi, M.; Bell, R.E.; Kugel, H.W.; Leblanc, B.; Takahashi, H.; Gammel, G.M.; Holland, A.; Levinton, F.M.; Powers, E.J.; Im, S.
1994-03-01
In many of the medium and high beta discharges in PBX-M low-n modes with different n-numbers are observed. The probability of a low-n mode to be excited decreases with increasing n-number. If two modes of different frequency and n-number (ω 1 and ω 2 ; k 1 and k 2 ) are simultaneously present in the plasma, these modes interact nonlinearly and create sidebands in frequency (ω 2 ±ω 1 ) and wave-number (k 2 ±k 1 or n 2 ±n 1 and m 2 ±m 1 ). If these fundamental modes, ω 1 /k 1 and ω 2 /k 2 , contain strong harmonics, the harmonics also interact nonlinearly, creating more nonlinear products: kω 2 ±lω 1 and kk 2 ±lk 1 , where k and l are integers describing the harmonics. These modes, the products of nonlinear interaction between two fundamental modes, most probably have a kink character. During this three-wave coupling interaction, a decrease in neutron rate and an enhanced loss of medium energy ions are observed
DEFF Research Database (Denmark)
Marschler, Christian; Vollmer, Jürgen
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 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......, and (iii) the transition from puffs to slugs by an unbinding transition in an intermittency scenario. In our model all transitions and scalings are theoretically described from a dynamical systems point of view....
The role of nonlinear coupling in Human-Horse Interaction: A preliminary study.
Lanata, Antonio; Guidi, Andrea; Valenza, Gaetano; Baragli, Paolo; Scilingo, Enzo Pasquale
2017-07-01
This study focuses on the analysis of human-horse dynamic interaction using cardiovascular information exclusively. Specifically, the Information Theoretic Learning (ITL) approach has been applied to a Human-Horse Interaction paradigm, therefore accounting for the nonlinear information of the heart-heart interplay between humans and horses. Heartbeat dynamics was gathered from humans and horses during three experimental conditions: absence of interaction, visual-olfactory interaction, and brooming. Cross Information Potential, Cross Correntropy, and Correntropy Coefficient were computed to quantitatively estimate nonlinear coupling in a group of eleven subjects and one horse. Results showed a statistical significant difference on all of the three interaction phases. Furthermore, a Support Vector Machine classifier recognized the three conditions with an accuracy of 90:9%. These preliminary and encouraging results suggest that ITL analysis provides viable metrics for the quantitative evaluation of human-horse interaction.
Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report
International Nuclear Information System (INIS)
Cai, Xiao-Chuan; Yang, Chao; Pernice, Michael
2014-01-01
The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementation since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.
Numerical combination for nonlinear analysis of structures coupled to layered soils
Directory of Open Access Journals (Sweden)
Wagner Queiroz Silva
Full Text Available This paper presents an alternative coupling strategy between the Boundary Element Method (BEM and the Finite Element Method (FEM in order to create a computational code for the analysis of geometrical nonlinear 2D frames coupled to layered soils. The soil is modeled via BEM, considering multiple inclusions and internal load lines, through an alternative formulation to eliminate traction variables on subregions interfaces. A total Lagrangean formulation based on positions is adopted for the consideration of the geometric nonlinear behavior of frame structures with exact kinematics. The numerical coupling is performed by an algebraic strategy that extracts and condenses the equivalent soil's stiffness matrix and contact forces to be introduced into the frame structures hessian matrix and internal force vector, respectively. The formulation covers the analysis of shallow foundation structures and piles in any direction. Furthermore, the piles can pass through different layers. Numerical examples are shown in order to illustrate and confirm the accuracy and applicability of the proposed technique.
Deng, Zhenhua; Shang, Jing; Nian, Xiaohong
2015-11-01
In this paper, two coupling permanent magnet synchronous motors system with nonlinear constraints is studied. First of all, the mathematical model of the system is established according to the engineering practices, in which the dynamic model of motor and the nonlinear coupling effect between two motors are considered. In order to keep the two motors synchronization, a synchronization controller based on load observer is designed via cross-coupling idea and interval matrix. Moreover, speed, position and current signals of two motor all are taken as self-feedback signal as well as cross-feedback signal in the proposed controller, which is conducive to improving the dynamical performance and the synchronization performance of the system. The proposed control strategy is verified by simulation via Matlab/Simulink program. The simulation results show that the proposed control method has a better control performance, especially synchronization performance, than that of the conventional PI controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Rao, N.N.
1998-01-01
A systematic analysis of the stationary propagation of nonlinearly coupled electromagnetic and ion-acoustic waves in an unmagnetized plasma via the ponderomotive force is carried out. For small but finite amplitudes, the governing equations have a Hamiltonian structure, but with a kinetic energy term that is not positive definite. The Hamiltonian is similar to the well-known Hacute enon endash Heiles Hamiltonian of nonlinear dynamics, and is completely integrable in three regimes of the allowed parameter space. The corresponding second invariants of motion are also explicitly obtained. The integrable parameter regimes correspond to supersonic values of the Mach number, which characterizes the propagation speed of the coupled waves. On the other hand, in the sub- as well as near-sonic regimes, the coupled mode equations admit different types of exact analytical solutions, which represent nonlinear localized eigenstates of the electromagnetic field trapped in the density cavity due to the ponderomotive potential. While the density cavity has always a single-dip structure, for larger amplitudes it can support higher-order modes having a larger number of nodes in the electromagnetic field. In particular, we show the existence of a new type of localized electromagnetic wave whose field intensity has a triple-hump structure. For typical parameter values, the triple-hump solitons propagate with larger Mach numbers that are closer to the sonic limit than the single- as well as the double-hump solitons, but carry a lesser amount of the electromagnetic field energy. A comparison between the different types of solutions is carried out. The possibility of the existence of trapped electromagnetic modes having a larger number of humps is also discussed. copyright 1998 American Institute of Physics
Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory
Wang, Liming; Zheng, Shijie
2018-02-01
In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.
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.
Modeling the Synchrotron: An Exploration of Delay-Coupled Nonlinear Mathieu Equations
Bernstein, Alexander
A synchrotron is a circular particle accelerator where beams of electrons are maintained at high velocity. Each beam contains clusters of electrons called "bunches," and we model the vertical displacement of each bunch as simple harmonic motion with parametric excitation, i.e. the Mathieu equation. Different types of coupling are accounted for, including one that only takes effect after one orbit, which we model using delay terms; the resulting model is a system of delay-differential equations. Nonlinear and damping terms are also included to make the model more realistic and the dynamics more rich. Variations of this core model are examined using perturbation methods and checked against numerical integration.
Coupled tapering/uptapering of Thirring type soliton pair in nonlinear media
Prasad, Shraddha; Dutta, Manoj Kumar; Sarkar, Ram Krishna
2018-03-01
The paper investigates coupled tapering/uptapering of Thirring type soliton pair, employing Beam Propagation Method. It is seen that, the pair uptapers in presence of losses and tapers in presence of gain. When the first beam has gain and the second one has losses in the nonlinear medium, the second beam induces uptapering in the first beam, while, first beam induces tapering in the second beam. When the medium provides gain/losses to only one of the two beams, the beam undergoes tapering/uptapering and also induces tapering/uptapering to the other loss less beam; however, magnitude of tapering/uptapering are different.
A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system
International Nuclear Information System (INIS)
Zhao, Hai-qiong; Yuan, Jinyun
2016-01-01
A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N -fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit. (paper)
Directory of Open Access Journals (Sweden)
MANISH JAIN
2017-06-01
Full Text Available Recently, Samet et al. [34], by using the equivalence of the three basic metrics showed that certain coupled fixed point results can be obtained immediately from the well-known fixed point theorems. In the setting of partially ordered metric spaces, we establish a generalization of the recent coupled fixed / coincidence point results under new nonlinear contractive conditions. The signicant feature of the presented work is that, our obtained results are not the immediate consequence of the already existing results in the literature. Presented work generalizes some of the results of Bhaskar and Lakshmikantham [6], Berinde [7], Choudhury et al. [10], Harjani et al. [17], Jain et al. [21] , Karapinar et al. [22], Luong and Thuan [25], and Rasouli and Bahrampour [30].
Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions
BoŻek, Piotr
2018-03-01
The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.
International Nuclear Information System (INIS)
Chen Zhipeng; Li Hong; Liu Qiuyan; Luo Chen; Xie Jinlin; Liu Wandong
2011-01-01
A method is proposed to built up plasma based on a nonlinear enhancement phenomenon of plasma density with discharge by multiple internal antennas simultaneously. It turns out that the plasma density under multiple sources is higher than the linear summation of the density under each source. This effect is helpful to reduce the fast exponential decay of plasma density in single internal inductively coupled plasma source and generating a larger-area plasma with multiple internal inductively coupled plasma sources. After a careful study on the balance between the enhancement and the decay of plasma density in experiments, a plasma is built up by four sources, which proves the feasibility of this method. According to the method, more sources and more intensive enhancement effect can be employed to further build up a high-density, large-area plasma for different applications. (low temperature plasma)
Nonlinear spin current generation in noncentrosymmetric spin-orbit coupled systems
Hamamoto, Keita; Ezawa, Motohiko; Kim, Kun Woo; Morimoto, Takahiro; Nagaosa, Naoto
2017-06-01
Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and has been studied actively. For example, representative methods of spin-current generation include spin-polarized current injections from ferromagnetic metals, the spin Hall effect, and the spin battery. Here, we theoretically propose a mechanism of spin-current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field E induces spin current proportional to E2 in noncentrosymmetric spin-orbit coupled systems. We demonstrate that the nonlinear spin current of the proposed mechanism is supported in the surface state of three-dimensional topological insulators and two-dimensional semiconductors with the Rashba and/or Dresselhaus interaction. In the latter case, the angular dependence of the nonlinear spin current can be manipulated by the direction of the electric field and by the ratio of the Rashba and Dresselhaus interactions. We find that the magnitude of the spin current largely exceeds those in the previous methods for a reasonable magnitude of the electric field. Furthermore, we show that application of ac electric fields (e.g., terahertz light) leads to the rectifying effect of the spin current, where dc spin current is generated. These findings will pave a route to manipulate the spin current in noncentrosymmetric crystals.
Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.
2017-10-01
We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.
International Nuclear Information System (INIS)
Boutin, B.
2009-11-01
This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)
Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model
International Nuclear Information System (INIS)
Ngai, K. L.
2015-01-01
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 1 (f), the frequency dispersion of the third-order dielectric susceptibility, χ 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 1 (f) and χ 3 (f) is the characteristic of the many-body relaxation
DEFF Research Database (Denmark)
Enemark, Søren; Santos, Ilmar F.
2016-01-01
In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy......-coupling between the two orthogonal directions, especially during counter-phase motion between shaft and bearings. The clear nonlinear behaviour is facilitated by the lack of damping resulting in relatively large vibrations. The overall nonlinear dynamic behaviour is well captured by the theoretical model, thereby...
Sokhoyan, R.; Azizbekyan, H.; Leroy, C.; Ishkhanyan, A.
2011-04-01
We discuss the strong-coupling regime of the nonlinear Landau-Zener problem occurring at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation for the molecular state probability and construct an accurate approximation describing the time dynamics of the coupled atom-molecule system. The resultant solution improves the accuracy of the previous approximation [22]. The obtained results reveal a remarkable observation that in the strong-coupling limit, the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecule oscillations occurring soon after crossing the resonance are principally of a linear nature. This observation is supposedly general for all nonlinear quantum systems having the same generic quadratic nonlinearity, due to the basic attributes of the resonance crossing processes in such systems. The constructed approximation turns out to have a larger applicability range than it was initially expected, covering the whole moderate-coupling regime for which the proposed solution accurately describes ail the main characteristics of the system evolution except the amplitude of the coherent atom-molecule oscillation, which is rather overestimated.
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%.
Directory of Open Access Journals (Sweden)
Jigisha U. Pandya
2012-01-01
Full Text Available The behavior of the non-linear-coupled systems arising in axially symmetric hydromagnetics flow between two horizontal plates in a rotating system is analyzed, where the lower is a stretching sheet and upper is a porous solid plate. The equations of conservation of mass and momentum are transformed to a system of coupled nonlinear ordinary differential equations. These equations for the velocity field are solved numerically by using quintic spline collocation method. To solve the nonlinear equation, quasilinearization technique has been used. The numerical results are presented through graphs, in which the effects of viscosity, through flow, magnetic flux, and rotational velocity on velocity field are discussed.
Directory of Open Access Journals (Sweden)
Josefa Caballero
2014-01-01
Full Text Available We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D0+α[x(t/f(t,x(t,y(t]=g(t,x(t,y(t,D0+αy(t/f(t,y(t,x(t=g(t,y(t,x(t, 0
Running coupling and power corrections in nonlinear evolution at the high-energy limit
Gardi, E; Rummukainen, K; Weigert, H; Gardi, Einan; Kuokkanen, Janne; Rummukainen, Kari; Weigert, Heribert
2007-01-01
A main feature of high-energy scattering in QCD is saturation in the number density of gluons. This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have been derived at leading logarithmic accuracy. In this paper we generalize this framework to include running coupling corrections to the evolution kernel. We develop a dispersive representation of the dressed gluon propagator in the background of Weiszacker Williams fields and use it to compute O(beta_0^{n-1} alpha_s^n) corrections to the kernel to all orders in perturbation theory. The resummed kernels present infrared-renormalon ambiguities, which are indicative of the form and importance of non-perturbative power corrections. We investigate numerically the effect of the newly computed perturbative corrections as well as the power corrections on the evolution and find that at present energies they are both significant.
Optical response of two coupled optomechanical systems in the presence of nonlinear mediums
Asghari Nejad, A.; Askari, H. R.; Baghshahi, H. R.
2018-01-01
In this paper, we investigate response of a hybrid optomechanical system in different situations. This system is composed of two coupled optomechanical cavities, which one of them is filled with an optical parametric amplifier (OPA) and the other one encompasses a nonlinear Kerr medium. The Hamiltonian of the system is written in a rotating frame. The dynamics of the system is obtained by the quantum Langevin equations of motion in a steady state regime. The results show that the presence of OPA and the Kerr medium in the system can considerably change the behavior of both cavities. For this reason, we show that by choosing different values for the optical parameters of the system, one can switches the behaviors of the cavities between mono-, bi- and tristability. Also, we show that by changing the detunings of the cavities, one can obtain uncommon responses from the system. Furthermore, we show that it is possible to create proper optical multistability regions for both cavities.
Directory of Open Access Journals (Sweden)
Jinli Xu
2017-01-01
Full Text Available A spiral bevel gear system supported on thrust bearings considering the coupled bending-torsional nonlinear vibration is proposed and an eight degrees of freedom (8DOF lumped parameter dynamic model of the spiral bevel gear system combined with time-varying stiffness, static transmission error, gear backlash, and bearing clearances is investigated. The spiral bevel gear system is analyzed with the equations of motion and the dynamic response is solved using the Runge-Kutta method. The effects of mesh frequency, mesh damping coefficient, load coefficient, and gear backlash are revealed, which describe the true mesh characteristics of the spiral bevel gear system. The bifurcation characteristics as jump discontinuities, periodic windows, and chaos are obtained by studying time histories, phase plane portraits, Poincaré maps, Fourier spectra, and global bifurcation diagrams of the gear system. The results presented in this study provide some useful information for engineers in designing and controlling such gear systems.
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.
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.
Soliton interactions and complexes for coupled nonlinear Schrödinger equations.
Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Li, Min; Wang, Pan
2012-03-01
Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the N-CNLS ones (N≥3), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the N-CNLS equations (N>3). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
Athanassoulis 2002) problems, over variable bathymetry regions. Using the local-mode expansion in conjunction with the variational principle the original problem is reformulated as an infinite, coupled-mode system of second-order differential equations in the propagation (horizontal) space, fully accounting for the effects of non-linearity and dispersion. Various simplified equations, like Boussinesq-type models, in shallow water depth, and non-linear mild-slope models, in intermediate depth, can be obtained as limiting forms. As a first step towards the solution of fully nonlinear coupled-mode system, the system is simplified keeping only up to second-order terms in the system coefficients, and the derived weakly non-linear model has been applied to water waves propagating over a flat bottom and over an arbitrary bathymetry. This model is solved numerically in the frequency and in the time domain, providing very good results in a wide range of water depths. In the case of monochromatic waves propagating over a flat bottom, it is shown that the present model correctly treats the dispersion effects in the whole range of relative water depths from practically deep to shallow water. In the same case, it is also shown that the present model reproduces correctly the second-order Stokes solutions. In the general case, the solution of the coupled-mode system is obtained numerically by truncating the local-mode series into a finite number of terms, and using finite differences for approximating the derivatives on the horizontal plane. Numerical results presented for a smooth underwater shoaling with a steep bottom slope, demonstrate that the rate of decay of the modal-amplitude functions is very fast, in conformity with similar behaviour in the linear case (Athanassoulis and Belibassakis 1999). This means that a small number of modes (up to 5 or 7) are sufficient for precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
Hajjaj, Amal Z.
2017-01-30
We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
Quantum theory of a one-dimensional laser with output coupling. 2. Nonlinear theory
International Nuclear Information System (INIS)
Penaforte, J.C.; Baseia, B.
1984-01-01
A previous paper describing the quantum theory of a laser in linear approximation is here extended to the nonlinear case. Instead of the approach of conventional theory - which deals with discrete 'cavity-modes' and includes artificial mechanisms to simulates radiation field losses due to beam extraction - a more realistic model of optical cavity having output coupling is used that works entirely within the continuous spectrum, allowing one to obtain the equations for the field both inside and outside the laser cavity. Besides the quantum noise due to spontaneous emission, a noise term of classical nature due to transmission losses automatically emerges from the present treatment. For single-collective-mode operation the equations for laser field are solved exactly, yielding the transient and steady-state solutions. Inside the laser cavity, the results of nonlinear analysis agree with those found in conventional theory once the conventional 'mode-amplitude' is reinterpreted as a collective variable. Outside the cavity - unaccessible region in the conventional treatment - the solution for the laser field is also exhibited. Further considerations as concerning the role played by the noise terms in the field buildup are discussed. (Author) [pt
Diab, A; Hassan, M; Boudaoud, S; Marque, C; Karlsson, B
2013-01-01
Understanding the direction and quantity of information flowing in a complex system is a fundamental task in signal processing. Several measures have been proposed to detect the quantity of synchronization and the directionality between time series and in physiological data. In this paper we use two methods that are widely used in synchronization and directionality analysis: Nonlinear correlation coefficient (h(2)) and the general synchronization (H). The performances of both methods were tested on four dimensional coupled synthetic nonlinear Rössler models. They were then applied to a single real labor contraction uterine EMG burst with the aim of using them to detect synchronization and to plot the map of direction of information flow between the whole signal channels. The results on synthetic signal show a slight superiority of H over h(2). The results obtained on a single contraction are encouraging for the future use of these tools for resolving the open question of the directionality of uterine contractions and may provide a way of finding their source loci.
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.
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.
International Nuclear Information System (INIS)
Lo, C.-Y.; Chang-Jian, C.-W.
2008-01-01
This study presents a dynamic analysis of a rotor supported by two turbulent flow model journal bearings and lubricated with couple stress fluid under nonlinear suspension. The dynamics of the rotor center and bearing center is studied. The dynamic equations are solved using the Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincare maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The results show that the values of dimensionless parameters l* strongly influence dynamic motions of bearing and rotor centre. It is found that couple stress fluid improve the stability of the system when l* > 0.4 even if the flow of this system is turbulent. We also demonstrated that the dimensionless rotational speed ratios s and the dimensionless unbalance parameter β are also significant system parameters. The modeling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, B.A.
1987-01-01
Four levels of nonlinear hydrodynamic description are presented for a nondissipative multicondensate solution of superfluids with vorticity. First, the multivelocity superfluid (MVSF) theory is extended to the case of a multivelocity superfluid plasma (MVSP), in which some of the superfluid condensates (protons, say) are charged and coupled electromagnetically to an additional, normal, charged fluid (electrons). The resulting drag-current density is derived due to the electromagnetic coupling of the condensates with the normal fluids. For the case of one charged condensate, the MVSP equations simplify to what we call superfluid Hall magnetohydrodynamics (SHMHD) in the approximation that displacement current and electron inertia are negligible, and local charge neutrality is imposed. The contribution of the charged condensate to the Hall drift force is determined. In turn, neglecting the Hall effect in SHMHD gives the equations of superfluid magnetohydrodynamics (SMHD). Each set of equations (MVSF, MVSP, SHMHD, and SMHD) is shown to be Hamiltonian and to possess a Poisson bracket associated with the dual space of a corresponding semidirect-product Lie algebra with a generalized two-cocycle defined on it. Topological conservation laws (helicities) associated with the kernels of these Lie algebras are also discussed as well as those associated physically with generalized Kelvin theorems for conservation of superfluid circulation around closed loops moving with the normal fluid
Testing universal relations of neutron stars with a nonlinear matter-gravity coupling theory
International Nuclear Information System (INIS)
Sham, Y.-H.; Lin, L.-M.; Leung, P. T.
2014-01-01
Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.
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.
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.
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
Mechelli, A; Price, C J; Friston, K J
2001-10-01
The aim of this work was to investigate the dependence of BOLD responses on different patterns of stimulus input/neuronal changes. In an earlier report, we described an input-state-output model that combined (i) the Balloon/Windkessel model of nonlinear coupling between rCBF and BOLD signals, and (ii) a linear model of how regional flow changes with synaptic activity. In the present investigation, the input-state-output model was used to explore the dependence of simulated PET (rCBF) and fMRI (BOLD) signals on various parameters pertaining to experimental design. Biophysical simulations were used to estimate rCBF and BOLD responses as functions of (a) a prior stimulus, (b) epoch length (for a fixed SOA), (c) SOA (for a fixed number of events), and (d) stimulus amplitude. We also addressed the notion that a single neuronal response may differ, in terms of the relative contributions of early and late neural components, and investigated the effect of (e) the relative size of the late or "endogenous" neural component. We were interested in the estimated average rCBF and BOLD responses per stimulus or event, not in the statistical efficiency with which these responses are detected. The BOLD response was underestimated relative to rCBF with a preceding stimulus, increasing epoch length, and increasing SOA. Furthermore, the BOLD response showed some highly nonlinear behaviour when varying stimulus amplitude, suggesting some form of hemodynamic "rectification." Finally, the BOLD response was underestimated in the context of large late neuronal components. The difference between rCBF and BOLD is attributed to the nonlinear transduction of rCBF to BOLD signal. Our simulations support the idea that varying parameters that specify the experimental design may have differential effects in PET and fMRI. Moreover, they show that fMRI can be asymmetric in its ability to detect deactivations relative to activations when an absolute baseline is stipulated. Finally, our simulations
International Nuclear Information System (INIS)
Preynas, M.; Goniche, M.; Hillairet, J.; Litaudon, X.; Ekedahl, A.; Colas, L.
2013-01-01
To achieve steady-state operation on future fusion devices, in particular on ITER, the coupling of the lower hybrid wave must be optimized on a wide range of edge conditions. However, under some specific conditions, deleterious effects on the lower hybrid current drive (LHCD) coupling are sometimes observed on Tore Supra. 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 multi-junction (FAM) and the new passive active multi-junction (PAM) antennas. A non-linear 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 (RC) with the LHCD power is not predicted by the standard linear theory of the LH wave coupling. A theoretical model is suggested to describe the non-linear wave–plasma interaction induced by the ponderomotive effect and implemented in a new full wave LHCD code, PICCOLO-2D (ponderomotive effect in a coupling code of lower hybrid wave-2D). The code self-consistently treats the wave propagation in the antenna vicinity and its interaction with the local edge plasma density. The simulation reproduces very well the occurrence of a non-linear behaviour 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 modelling for the first time on the FAM and PAM antennas on Tore Supra. (paper)
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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.
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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.
Depolarization of the electron spin in storage rings by nonlinear spin-orbit coupling
International Nuclear Information System (INIS)
Kewisch, J.
1985-10-01
Electrons and positrons which circulate in the storage ring are polarized at the emission of synchrotron radiation by the so called Sokolov-Ternov effect. This polarization is on the one hand of large interest for the study of the weak interaction, on the other hand it can be used for the accurate measurement of the beam energy and by this of the mass of elementary particles. The transverse and longitudinal particle vibrations simultaneously excited by the synchrotron radiation however can effect that this polarization is destroyed. This effect is called spin-orbit coupling. For the calculation of the spin-orbit coupling the computer program SITROS was written. This program is a tracking program: The motion of some sample particles and their spin vectors are calculated for some thousand circulations. From this the mean depolarization and by extrapolation the degree of polarization of the equilibrium state is determined. Contrarily to the known program SLIM which is based on perturbational calculations in SITROS the nonlinear forces in the storage ring can be regarded. By this the calculation of depolarizing higher order resonances is made possible. In this thesis the equations of motion for the orbital and spin motion of the electrons are derived which form the base for the program SITROS. The functions of the program and the approximations necessary for the saving of calculational time are explained. The comparison of the SITROS results with the measurement results obtained at the PETRA storage ring shows that the SITROS program is a useful means for the planning and calculation of storage rings with polarized electron beams. (orig.) [de
International Nuclear Information System (INIS)
Hamedi, H R; Ruseckas, J; Juzeliūnas, G
2017-01-01
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. (paper)
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.
Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems
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Jorge J. Hernández-Gómez
2017-12-01
Full Text Available Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge–Kutta problems that need to be calculated. In this work we introduce a parallel implementation based on MPI (Message Passing Interface for the calculation of the Lyapunov exponents for a multidimensional dynamical system, considering a weakly coupled algorithm. Since we work on an academic high-latency cluster interconnected with a gigabit switch, the design has to be oriented to reduce the number of messages required. With the design introduced in this work, the computing time is drastically reduced, and the obtained performance leads to close to optimal speed-up ratios. The implemented parallelisation allows us to carry out many experiments for the calculation of several Lyapunov exponents with a low-cost cluster. The numerical experiments showed a high scalability, which we showed with up to 68 cores.
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.
Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators
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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
Xu, Hao; Pei, Yongmao; Li, Faxin; Fang, Daining
2018-05-01
The magnetic, electric and mechanical behaviors are strongly coupled in magnetoelectric (ME) materials, making them great promising in the application of functional devices. In this paper, the magneto-electro-mechanical fully coupled constitutive behaviors of ME laminates are systematically studied both theoretically and experimentally. A new probabilistic domain switching function considering the surface ferromagnetic anisotropy and the interface charge-mediated effect is proposed. Then a multi-scale multi-field coupling nonlinear constitutive model for layered ME composites is developed with physical measureable parameters. The experiments were performed to compare the theoretical predictions with the experimental data. The theoretical predictions have a good agreement with experimental results. The proposed constitutive relation can be used to describe the nonlinear multi-field coupling properties of both ME laminates and thin films. Several novel coupling experimental phenomena such as the electric-field control of magnetization, and the magnetic-field tuning of polarization are observed and analyzed. Furthermore, the size-effect of the electric tuning behavior of magnetization is predicted, which demonstrates a competition mechanism between the interface strain-mediated effect and the charge-driven effect. Our study offers deep insight into the coupling microscopic mechanism and macroscopic properties of ME layered composites, which is benefit for the design of electromagnetic functional devices.
Aihara, Ikkyu; Tsumoto, Kunichika
2008-01-01
Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.
International Nuclear Information System (INIS)
Krishan, S.
2007-01-01
The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment
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
Michiels, Wim; Nijmeijer, Henk
2009-09-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties
Yongcheng, J.; Wen, S.; Baohua, Z.; Dong, L.
2017-09-01
Laser-induced breakdown spectroscopy (LIBS) coupled with the nonlinear multivariate regression method was applied to analyze magnesium (Mg) contents in soil. The plasma was generated using a 100 mJ Nd:YAG pulsed laser, and the spectra were acquired using a multi-channel spectrometer integrated with a CCD detector. The line at 383.8 nm was selected as the analysis line for Mg. The calibration model between the intensity of characteristic line and the concentration of Mg was constructed. The traditional calibration curve showed that the concentration of Mg was not only related to the line intensity of itself, but also to other elements in soil. The intensity of characteristic lines for Mg (Mg I 383.8 nm), manganese (Mn) (Mn I 403.1 nm), and iron (Fe) (Fe I 407.2 nm) were used as input data for nonlinear multivariate calculation. According to the results of nonlinear regression, the ternary nonlinear regression was the most appropriate of the studied models. A good agreement was observed between the actual concentration provided by inductively coupled plasma mass spectrometry (ICP-MS) and the predicted value obtained using the nonlinear multivariate regression model. The correlation coefficient between predicted concentration and the measured value was 0.987, while the root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) were reduced to 0.017% and 0.014%, respectively. The ratio of the standard deviation of the validation to the RMSEP increased to 8.79, and the relative error was below 1.21% for nine validation samples. This indicated that the multivariate model can obtain better predicted accuracy than the calibration curve. These results also suggest that the LIBS technique is a powerful tool for analyzing the micro-nutrient elements in soil by selecting calibration and validation samples with similar matrix composition.
Energy Technology Data Exchange (ETDEWEB)
Ganguly, Jayanta [Department of Chemistry, Brahmankhanda Basapara High School, Basapara, Birbhum 731 215, West Bengal (India); Ghosh, Manas, E-mail: pcmg77@rediffmail.com [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India)
2015-02-02
Highlights: • Linear and nonlinear polarizabilities of quantum dot are studied. • Quantum dot is doped with a repulsive impurity. • Doped system is subject to Gaussian white noise. • Dopant migrates under damped condition. • Noise-damping coupling affects polarizabilities. - Abstract: We investigate the profiles of diagonal components of static and frequency-dependent linear, first, and second nonlinear polarizabilities of repulsive impurity doped quantum dot. We have considered propagation of dopant within an environment that damps the motion. Simultaneous presence of noise inherent to the system has also been considered. The dopant has a Gaussian potential and noise considered is a Gaussian white noise. The doped system is exposed to an external electric field which could be static or time-dependent. Noise undergoes direct coupling with damping and the noise-damping coupling strength appears to be a crucial parameter that designs the profiles of polarizability components. This happens because the coupling strength modulates the dispersive and asymmetric character of the system. The frequency of external field brings about additional features in the profiles of polarizability components. The present investigation highlights some useful features in the optical properties of doped quantum dots.
Manikandan, N; Radhakrishnan, R; Aravinthan, K
2014-08-01
We have constructed a dark-bright N-soliton solution with 4N+3 real parameters for the physically interesting system of mixed coupled nonlinear Schrödinger equations. Using this as well as an asymptotic analysis we have investigated the interaction between dark-bright vector solitons. Each colliding dark-bright one-soliton at the asymptotic limits includes more coupling parameters not only in the polarization vector but also in the amplitude part. Our present solution generalizes the dark-bright soliton in the literature with parametric constraints. By exploiting the role of such coupling parameters we are able to control certain interaction effects, namely beating, breathing, bouncing, attraction, jumping, etc., without affecting other soliton parameters. Particularly, the results of the interactions between the bound state dark-bright vector solitons reveal oscillations in their amplitudes under certain parametric choices. A similar kind of effect was also observed experimentally in the BECs. We have also characterized the solutions with complicated structure and nonobvious wrinkle to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation. It is interesting to identify that the polarization vector of the dark-bright one-soliton evolves on a spherical surface instead of a hyperboloid surface as in the bright-bright case of the mixed coupled nonlinear Schrödinger equations.
D'Aguanno, Giuseppe; Menyuk, Curtis R.
2017-03-01
Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have dispersions of opposite sign in spectral regions that would otherwise be characterized by either positive (normal) or negative (anomalous) dispersion. In this paper, we study, both analytically and computationally, the general properties of nonlinear frequency comb generation at an avoided crossing using the coupled Lugiato-Lefever equation. In particular, we find that bright solitons and broadband frequency combs can be excited when both branches are pumped for a suitable choice of the pump powers and the detuning parameters. A deterministic path for soliton generation is found. Contribution to the Topical Issue "Theory and applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Lorin, E.; Lytova, M.; Memarian, A.; Bandrauk, A. D.
2015-03-01
This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser-molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3-9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects.
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 coupling between cortical oscillations and muscle activity during isotonic wrist flexion
Yang, Y.; Solis Escalante, T.; van de Ruit, M.L.; van der Helm, F.C.T.; Schouten, A.C.
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been
A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations
Zhang, Guoyu; Huang, Chengming; Li, Meng
2018-04-01
We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.
Directory of Open Access Journals (Sweden)
Xujian Shu
2018-03-01
Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.
International Nuclear Information System (INIS)
Holland, C.; Kim, E.J.; Champeaux, S.; Gurcan, O.; Rosenbluth, M.N.; Diamond, P.H.; Tynan, G.R.; Nevins, W.; Candy, J.
2003-01-01
Understanding the physics of shear flow and structure formation in plasmas is a central problem for the advancement of magnetic fusion because of the roles such flows are believed to play in regulating turbulence and transport levels. In this paper, we report on integrated experimental, computational, and theoretical studies of sheared zonal flows and radially extended convective cells, with the aim of assessing the results of theory experiment and theory-simulation comparisons. In particular, simulations are used as test beds for verifying analytical predictions and demonstrating the suitability of techniques such as bispectral analysis for isolating nonlinear couplings in data. Based on intriguing initial results suggesting increased levels of nonlinear coupling occur during L-H transitions, we have undertaken a comprehensive study of bispectral quantities in fluid and gyrokinetic simulations, and compared these results with theoretical expectations. Topics of study include locality and directionality of energy transfer, amplitude scaling, and parameter dependences. Techniques for inferring nonlinear coupling coefficients from data are discussed, and initial results from experimental data are presented. Future experimental studies are motivated. We also present work investigating the role of structures in transport. Analysis of simulation data indicates that the turbulent heat flux can be represented as an ensemble of 'heat pulses' of varying sizes, with a power law distribution. The slope of the power law is shown to determine global transport scaling (i.e. Bohm or gyro-Bohm). Theoretical work studying the dynamics of the largest cells (termed 'streamers') is presented, as well as results from ongoing analysis studying connections between heat pulse distribution and bispectral quantities. (author)
Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power
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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.
Comments on Nonlinear Sigma Models Coupled to Supergravity arXiv
Ferrara, Sergio
2017-12-10
N=1 , D=4 nonlinear sigma models, parametrized by chiral superfields, usually describe Kählerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kähler when local supersymmetry becomes nonlinearly realized through the nilpotency of the supergravity auxiliary fields. In some cases the nonlinear realization eliminates one scalar propagating degree of freedom. This happens when the sigma model conformal-frame metric has co-rank 2. In the geometry of the inflaton, this effect eliminates its scalar superpartner. We show that the sigma model metric remains semidefinite positive in all cases, due the to positivity properties of the conformal-frame sigma model metric.
International Nuclear Information System (INIS)
Mehdian, H.; Mohammadzahery, Z.; Hasanbeigi, A.
2014-01-01
In this work, we study the defect mode and bistability behavior of 1-D photonic band gap structure with magnetized plasma and coupled nonlinear defects. The transfer matrix method has been employed to investigate the magnetic field effect on defect mode frequency and bistability threshold. The obtained results show that the frequency of defect mode and bistability threshold can be altered, without changing the structure of the photonic multilayer. Therefore, the bistability behavior of the subjected structure in the presence of magnetized plasma can be utilized in manufacturing wide frequency range devices
Luo, Zhaochu; Xiong, Chengyue; Zhang, Xu; Guo, Zhen-Gang; Cai, Jianwang; Zhang, Xiaozhong
2016-04-13
The anomalous Hall effect of a magnetic material is coupled to the nonlinear transport effect of a semiconductor material in a simple structure to achieve a large geometric magnetoresistance (MR) based on a diode-assisted mechanism. An extremely large MR (>10(4) %) at low magnetic fields (1 mT) is observed at room temperature. This MR device shows potential for use as a logic gate for the four basic Boolean logic operations. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Directory of Open Access Journals (Sweden)
Adrian Petruşel
2015-01-01
Full Text Available We will discuss discrete dynamics generated by single-valued and multivalued operators in spaces endowed with a generalized metric structure. More precisely, the behavior of the sequence (fn(xn∈N of successive approximations in complete generalized gauge spaces is discussed. In the same setting, the case of multivalued operators is also considered. The coupled fixed points for mappings t1:X1×X2→X1 and t2:X1×X2→X2 are discussed and an application to a system of nonlinear integral equations is given.
Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman
2015-04-01
The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.
Wu, Rongxing; Wang, Ji; Du, Jianke; Huang, Dejin; Yan, Wei; Hu, Yuantai
2012-01-01
We investigated the nonlinear vibrations of the coupled thickness-shear and flexural modes of quartz crystal plates with the nonlinear Mindlin plate equations, taking into consideration the kinematic and material nonlinearities. The nonlinear Mindlin plate equations for strongly coupled thickness- shear and flexural modes have been established by following Mindlin with the nonlinear constitutive relations and approximation procedures. Based on the long thickness-shear wave approximation and aided by corresponding linear solutions, the nonlinear equation of thickness-shear vibrations of quartz crystal plate has been solved by the combination of the Galerkin and homotopy analysis methods. The amplitude frequency relation we obtained showed that the nonlinear frequency of thickness-shear vibrations depends on the vibration amplitude, thickness, and length of plate, which is significantly different from the linear case. Numerical results from this study also indicated that neither kinematic nor material nonlinearities are the main factors in frequency shifts and performance fluctuation of the quartz crystal resonators we have observed. These efforts will result in applicable solution techniques for further studies of nonlinear effects of quartz plates under bias fields for the precise analysis and design of quartz crystal resonators. © 2012 IEEE
Painlevйe analysis and integrability of two-coupled non-linear ...
Indian Academy of Sciences (India)
For non-linear systems integrating the equations of motion completely, obtaining analytical solutions and finding acceptable constants of motions seem to be rare. From a qualitative point of view, integrability can be considered as a mathemat- ical property that can be successfully used to obtain more predictive power and.
Directory of Open Access Journals (Sweden)
Lixiang Wang
2013-01-01
Full Text Available This study reports the GPU parallelization of complex three-dimensional software for nonlinear analysis of concrete structures. It focuses on coupled thermomechanical analysis of complex structures. A coupled FEM/DEM approach (CDEM is given from a fundamental theoretical viewpoint. As the modeling of a large structure by means of FEM/DEM may lead to prohibitive computation times, a parallelization strategy is required. With the substantial development of computer science, a GPU-based parallel procedure is implemented. A comparative study between the GPU and CPU computation results is presented, and the runtimes and speedups are analyzed. The results show that dramatic performance improvements are gained from GPU parallelization.
Mode competition in a system of two parametrically driven pendulums with nonlinear coupling
Banning, E.J.; Banning, E.J.; van der Weele, 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
Liu, Tianyang; Chan, Hiu Ning; Grimshaw, Roger; Chow, Kwok Wing
2017-11-01
The spatial structure of small disturbances in stratified flows without background shear, usually named the `Taylor-Goldstein equation', is studied by employing the Boussinesq approximation (variation in density ignored except in the buoyancy). Analytical solutions are derived for special wavenumbers when the Brunt-Väisälä frequency is quadratic in hyperbolic secant, by comparison with coupled systems of nonlinear Schrödinger equations intensively studied in the literature. Cases of coupled Schrödinger equations with four, five and six components are utilized as concrete examples. Dispersion curves for arbitrary wavenumbers are obtained numerically. The computations of the group velocity, second harmonic, induced mean flow, and the second derivative of the angular frequency can all be facilitated by these exact linear eigenfunctions of the Taylor-Goldstein equation in terms of hyperbolic function, leading to a cubic Schrödinger equation for the evolution of a wavepacket. The occurrence of internal rogue waves can be predicted if the dispersion and cubic nonlinearity terms of the Schrödinger equations are of the same sign. Partial financial support has been provided by the Research Grants Council contract HKU 17200815.
Zañartu, Matías; Mehta, Daryush D; Ho, Julio C; Wodicka, George R; Hillman, Robert E
2011-01-01
Different source-related factors can lead to vocal fold instabilities and bifurcations referred to as voice breaks. Nonlinear coupling in phonation suggests that changes in acoustic loading can also be responsible for this unstable behavior. However, no in vivo visualization of tissue motion during these acoustically induced instabilities has been reported. Simultaneous recordings of laryngeal high-speed videoendoscopy, acoustics, aerodynamics, electroglottography, and neck skin acceleration are obtained from a participant consistently exhibiting voice breaks during pitch glide maneuvers. Results suggest that acoustically induced and source-induced instabilities can be distinguished at the tissue level. Differences in vibratory patterns are described through kymography and phonovibrography; measures of glottal area, open/speed quotient, and amplitude/phase asymmetry; and empirical orthogonal function decomposition. Acoustically induced tissue instabilities appear abruptly and exhibit irregular vocal fold motion after the bifurcation point, whereas source-induced ones show a smoother transition. These observations are also reflected in the acoustic and acceleration signals. Added aperiodicity is observed after the acoustically induced break, and harmonic changes appear prior to the bifurcation for the source-induced break. Both types of breaks appear to be subcritical bifurcations due to the presence of hysteresis and amplitude changes after the frequency jumps. These results are consistent with previous studies and the nonlinear source-filter coupling theory.
Zañartu, Matías; Mehta, Daryush D.; Ho, Julio C.; Wodicka, George R.; Hillman, Robert E.
2011-01-01
Different source-related factors can lead to vocal fold instabilities and bifurcations referred to as voice breaks. Nonlinear coupling in phonation suggests that changes in acoustic loading can also be responsible for this unstable behavior. However, no in vivo visualization of tissue motion during these acoustically induced instabilities has been reported. Simultaneous recordings of laryngeal high-speed videoendoscopy, acoustics, aerodynamics, electroglottography, and neck skin acceleration are obtained from a participant consistently exhibiting voice breaks during pitch glide maneuvers. Results suggest that acoustically induced and source-induced instabilities can be distinguished at the tissue level. Differences in vibratory patterns are described through kymography and phonovibrography; measures of glottal area, open∕speed quotient, and amplitude∕phase asymmetry; and empirical orthogonal function decomposition. Acoustically induced tissue instabilities appear abruptly and exhibit irregular vocal fold motion after the bifurcation point, whereas source-induced ones show a smoother transition. These observations are also reflected in the acoustic and acceleration signals. Added aperiodicity is observed after the acoustically induced break, and harmonic changes appear prior to the bifurcation for the source-induced break. Both types of breaks appear to be subcritical bifurcations due to the presence of hysteresis and amplitude changes after the frequency jumps. These results are consistent with previous studies and the nonlinear source-filter coupling theory. PMID:21303014
Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study
Directory of Open Access Journals (Sweden)
H. F. Abundis-Fong
2018-01-01
Full Text Available This paper presents the optimal design of a passive autoparametric cantilever beam vibration absorber for a linear mass-spring-damper system subject to harmonic external force. The design of the autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response function, computed via the multiple scales method. Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters (mass and length of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; then, a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, thus enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. Finally, some simulations and experimental results are included to validate and illustrate the dynamic performance of the overall system.
Non-Linear Coupling Among Cardiovascular Variability Signals in Neuromediate Syncope
National Research Council Canada - National Science Library
Censi, F
2001-01-01
Aim of this study is to evaluate the degree of coupling among the cardiovascular variability series and the respiration in subjects susceptible to neurally mediated syncope, in comparison to normal subjects...
Solitons in coupled nonlinear Schrödinger models: A survey of recent developments
Directory of Open Access Journals (Sweden)
P.G. Kevrekidis
2016-11-01
Full Text Available In this review we try to capture some of the recent excitement induced by experimental developments, but also by a large volume of theoretical and computational studies addressing multi-component nonlinear Schrödinger models and the localized structures that they support. We focus on some prototypical structures, namely the dark-bright and dark-dark solitons. Although our focus will be on one-dimensional, two-component Hamiltonian models, we also discuss variants, including three (or more-component models, higher-dimensional states, as well as dissipative settings. We also offer an outlook on interesting possibilities for future work on this theme.
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
Gromov, Evgeny; Malomed, Boris
2017-11-01
New two-component soliton solutions of the coupled high-frequency (HF)—low-frequency (LF) system, based on Schrödinger-Korteweg-de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode. In addition to the above-mentioned results for LF-dominated two-component solitons, which always run in one (positive) velocities, we produce HF
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.
Morelli, Maria Sole; Valenza, Gaetano; Greco, Alberto; Giannoni, Alberto; Passino, Claudio; Emdin, Michele; Scilingo, Enzo Pasquale; Vanello, Nicola
2016-08-01
Brain activations underlying control of breathing are not completely known. Furthermore, the coupling between neural and respiratory dynamics is usually estimated through linear correlation measures, thus totally disregarding possible underlying nonlinear interactions. To overcome these limitations, in this preliminary study we propose a nonlinear coupling analysis of simultaneous recordings of electroencephalographic (EEG) and respiratory signals at rest and after variation of carbon dioxide (CO2) level. Specifically, a CO2 increase was induced by a voluntary breath hold task. EEG global field power (GFP) in different frequency bands and end-tidal CO2 (PETCO2) were estimated in both conditions. The maximum information coefficient (MIC) and MIC-ρ2 (where ρ represents the Pearson's correlation coefficient) between the two signals were calculated to identify generic associations (i.e. linear and nonlinear correlations) and nonlinear correlations, respectively. With respect to a free breathing state, our results suggest that a breath hold state is characterized by an increased coupling between respiration activity and specific EEG oscillations, mainly involving linear and nonlinear interactions in the delta band (1-4 Hz), and prevalent nonlinear interactions in the alpha band (8-13 Hz).
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.
Czech Academy of Sciences Publication Activity Database
Klika, Václav; Grmela, M.
2013-01-01
Roč. 87, č. 1 (2013), s. 1-9 ISSN 1539-3755 Institutional support: RVO:61388998 Keywords : gemneric * non-equilibrium thermodynamics * coupling Subject RIV: BJ - Thermodynamics Impact factor: 2.326, year: 2013 http://link.aps.org/doi/10.1103/PhysRevE.87.012141
On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2014-01-01
). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications......The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second...
Grigorev, Valery A; Katsnelson, Boris G; Lynch, James F
2016-11-01
Analyses of fluctuations of low frequency signals (300 ± 30 Hz) propagating in shallow water in the presence of nonlinear internal waves (NIWs) in the Shallow Water 2006 experiment are carried out. Signals were received by a vertical line array at a distance of ∼20 km from the source. A NIW train was moving totally inside of the acoustic track, and the angle between the wave front of the NIW and the acoustic track in the horizontal plane was ∼10°. It is shown that the spectrum of the sound intensity fluctuations contains peaks corresponding to the coupling of pairs of propagating modes. Analysis of spectra at different hydrophone depths, and also summed over depth allows the authors to estimate attenuation in the bottom sediments.
Directory of Open Access Journals (Sweden)
Pothanna N.
2017-12-01
Full Text Available In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.
Aguero, M.; Frantzeskakis, D. J.; Kevrekidis, P. G.
2006-06-01
We consider a system of two coupled (2 + 1)-dimensional nonlinear Schrödinger equations, describing two-component disc-shaped Bose-Einstein condensates. We present three different asymptotic reductions of this system. In particular, we derive the Mel'nikov system, the Yajima-Oikawa system as well as the Davey-Stewartson system (the latter is found as a special case of the Djordjevic-Redekopp system). Conditions for integrability of the reduced systems, their soliton solutions and the asymptotic relevance of such solutions to the original system are also discussed. Numerical results pertaining to the reduction to the Davey-Stewartson system are found to be in good agreement with the analytical predictions.
International Nuclear Information System (INIS)
Song Yongli; Tadé, Moses O; Zhang Tonghua
2009-01-01
In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained
Pandey, Vinay Kumar; Kar, Indrani; Mahanta, Chitralekha
2017-07-01
In this paper, an adaptive control method using multiple models with second level adaptation is proposed for a class of nonlinear multi-input multi-output (MIMO) coupled systems. Multiple estimation models are used to tune the unknown parameters at the first level. The second level adaptation provides a single parameter vector for the controller. A feedback linearization technique is used to design a state feedback control. The efficacy of the designed controller is validated by conducting real time experiment on a laboratory setup of twin rotor MIMO system (TRMS). The TRMS setup is discussed in detail and the experiments were performed for regulation and tracking problem for pitch and yaw control using different reference signals. An Extended Kalman Filter (EKF) has been used to observe the unavailable states of the TRMS. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Harker, K. J.
1972-01-01
Two basic high-frequency ionospheric instabilities are discussed - i.e., the three-wave parametric interaction, and the oscillating two-stream instability. In the parametric instability, the ion-acoustic wave has a complex frequency, whereas in the oscillating two-stream instability the ion-acoustic frequency is purely imaginary. The parametric instability is shown to be the only one whose threshold depends on the ion collision frequency. A coupled-mode theory is proposed which permits study and classification of high-frequency instabilities on a unified basis.
A strongly coupled open system with a non-linear bath: fluctuation-dissipation and Langevin dynamics
Bhadra, Chitrak
2018-03-01
The study of Langevin dynamics and fluctuation-dissipation relation (FDR) for a generic probe system (represented by a mass M ), bilinearly coupled to a bath of harmonic oscillators, has been a standard paradigm for the microscopic theory of stochastic processes for several decades. The question that we probe in this paper is, how robust the structure of the classical FDR is, when one replaces the harmonic bath by an anharmonic one in the limit of strong system-bath coupling? Such a picture carries the signature of the probe system in the zeroth order through a nonlocal time kernel. We observe that the two-time noise correlations hold a rich structure from which the usual FDR emerges only in the leading order of perturbation. Beyond this order, multiple time scales and nontrivial dependence on the temperature starts to manifest. These new aspects conspire to break the time-translational invariance of the noise-correlations. Several other interesting features show up and we discuss them methodically through rigorous calculations order-by-order in perturbation. This formalistic derivation along with a specific example of non-linearity can be easily applied to a huge range of processes and statistical observables that fall under the purview of a system-reservoir theory.
Markowich, Peter
2010-06-01
We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty with respect to previous papers in the literature lies in the presence of nonlinear porous-medium-like diffusion in the equation for the density n of the bacteria, motivated by a finite size effect. We prove that, under the constraint m ε (3/2, 2] for the adiabatic exponent, such system features global in time solutions in two space dimensions for large data. Moreover, in the case m = 2 we prove that solutions converge to constant states in the large-time limit. The proofs rely on standard energy methods and on a basic entropy estimate which cannot be achieved in the case m = 1. The case m = 2 is very special as we can provide a Lyapounov functional. We generalize our results to the three-dimensional case and obtain a smaller range of exponents m ε (m*, 2] with m* > 3/2, due to the use of classical Sobolev inequalities.
Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations
Bajars, J.; Frank, J. E.; Leimkuhler, B. J.
2013-07-01
Thermal bath coupling mechanisms as utilized in molecular dynamics are applied to partial differential equation models. Working from a semi-discrete (Fourier mode) formulation for the Burgers-Hopf or Korteweg-de Vries equation, we introduce auxiliary variables and stochastic perturbations in order to drive the system to sample a target ensemble which may be a Gibbs state or, more generally, any smooth distribution defined on a constraint manifold. We examine the ergodicity of approaches based on coupling of the heat bath to the high wave numbers, with the goal of controlling the ensemble through the fast modes. We also examine different thermostat methods in the extent to which dynamical properties are corrupted in order to accurately compute the average of a desired observable with respect to the invariant distribution. The principal observation of this paper is that convergence to the invariant distribution can be achieved by thermostatting just the highest wave number, while the evolution of the slowest modes is little affected by such a thermostat.
3D nonlinear modeling of the coupling and phase locking of magnetic Islands in tokamaks
Jardin, Stephen; Ferraro, Nathaniel; Chen, Jin; Pfefferle, David
2017-10-01
Many tokamak discharges develop multiple tearing modes possessing different mode numbers. These modes are observed to phase lock to one another, resulting in a flattening of the core toroidal plasma rotation profile, which can have deleterious effects on transport and MHD stability. In order to study these phenomena with minimum assumptions, we use the M3D-C1 3D nonlinear MHD code to perform initial value simulations of the evolution of equilibria unstable to both the 2/1 and 3/2 modes, but having sheared toroidal rotation. Initial attempts to perform these simulations led to numerical instabilities developing once the islands got to a certain size. In order to study the cause of this instability, we developed a small model code that solves a pure convection equation in 1D. We find that an implicit Crank-Nicholson method in time and Hermite Cubic finite elements (as are used in the toroidal direction in the M3D-C1 code) is not a convergent algorithm. Adding a small second order diffusion term, proportional to the velocity, improves the numerical stability properties but is not convergent in the first-derivative of the solution. Instead, adding a much smaller forth-order spatial derivative term proportional to the velocity leads to an algorithm in which both the solution and the first derivative converge as 1/N2,. Adding similar toroidal forth derivative terms to the M3D-C1 code eliminated the numerical instability. This work was supported by US DOE Contract DE-AC02-09-CH11466.
Directory of Open Access Journals (Sweden)
Irwin Yousept
2010-07-01
Full Text Available An optimal control problem arising in the context of 3D electromagnetic induction heating is investigated. The state equation is given by a quasilinear stationary heat equation coupled with a semilinear time harmonic eddy current equation. The temperature-dependent electrical conductivity and the presence of pointwise inequality state-constraints represent the main challenge of the paper. In the first part of the paper, the existence and regularity of the state are addressed. The second part of the paper deals with the analysis of the corresponding linearized equation. Some suffcient conditions are presented which guarantee thesolvability of the linearized system. The final part of the paper is concerned with the optimal control. The aim of the optimization is to find the optimal voltage such that a desired temperature can be achieved optimally. The corresponding first-order necessary optimality condition is presented.
Duxbury, N. S.; Romanovsky, V. E.; Romanovskii, N. N.; Garagulya, L. S.; Brouchkov, A. V.; Komarov, I. A.; Roman, L. T.; Tipenko, G. S.; Buldovich, S. N.; Maximova, L. N.
2012-12-01
We have developed coupled permafrost - carbon physical and numerical models, where carbon is in the form of methane clathrate hydrate ( CH4*6H2O ) in a porous subsurface environment. The driving force for the subsurface temperature field dynamics is climate variations on the Earth's surface. This is an upper boundary condition for the nonlinear evolutionary system of partial differential equations (PDEs) describing subsurface heat transfer (parabolic PDEs) in a generalized Stefan formulation. The developed numerical model is a valuable computational tool to quantitatively study nonlinear dynamical thermal processes with phase transitions in terrestrial and Martian subsurfaces. Our model is multifrontal and therefore allows one to perform computations for a problem with any number of emerging/vanishing phase transition interfaces (both in methane gas hydrate deposits and in permafrost), since the model treats these fronts implicitly in an enthalpy formulation and in corresponding finite-difference scheme. This model takes into account the pressure (and therefore the depth) dependence of the phase transition temperature for methane clathrate hydrate. We have performed model computations using the thermophysical characteristics (heat capacity, density/porosity, thermal conductivity) for the Siberian subsurface. It can be used as a terrestrial analog for the Martian subsurface (e.g., Duxbury et al., 2001). Also, thermophysical coefficients from laboratory experiments for methane clathrate hydrate were used in our model. In addition, our model takes into account the dependence of subsurface thermophysical characteristics on temperature and spatial coordinates. The results of our computations and their interpretation will be presented. References. N. S. Duxbury, I. A. Zotikov, K. H. Nealson, V. E. Romanovsky, F. D. Carsey (2001). A numerical model for an alternative origin of Lake Vostok and its exobiological implications for Mars, Journal of Geophysical Research
International Nuclear Information System (INIS)
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
Bulgakov, Evgeny; Sadreev, Almas
2011-08-10
Using coupled mode theory we consider transmission in a T-shaped waveguide coupled with two identical symmetrically positioned nonlinear micro-cavities with mirror symmetry. For input power injected into the central waveguide we show the existence of a symmetry breaking solution which is a result of mixing of the symmetrical input wave with an antisymmetric standing wave in the Fabry-Pérot interferometer. With growth of the input power, a feature in the form of loops arises in the solution which originates from bistability in the transmission in the output left/right waveguide coupled with the first/second nonlinear cavity. The domains of stability of the solution are found. The breaking of mirror symmetry gives rise to nonsymmetrical left and right outputs. We demonstrate that this phenomenon can be explored for all-optical switching of light transmission from the left output waveguide to the right one by application of input pulses.
Capillary transit time heterogeneity and flow-metabolism coupling after traumatic brain injury
Østergaard, Leif; Engedal, Thorbjørn S; Aamand, Rasmus; Mikkelsen, Ronni; Iversen, Nina K; Anzabi, Maryam; Næss-Schmidt, Erhard T; Drasbek, Kim R; Bay, Vibeke; Blicher, Jakob U; Tietze, Anna; Mikkelsen, Irene K; Hansen, Brian; Jespersen, Sune N; Juul, Niels; Sørensen, Jens CH; Rasmussen, Mads
2014-01-01
Most patients who die after traumatic brain injury (TBI) show evidence of ischemic brain damage. Nevertheless, it has proven difficult to demonstrate cerebral ischemia in TBI patients. After TBI, both global and localized changes in cerebral blood flow (CBF) are observed, depending on the extent of diffuse brain swelling and the size and location of contusions and hematoma. These changes vary considerably over time, with most TBI patients showing reduced CBF during the first 12 hours after injury, then hyperperfusion, and in some patients vasospasms before CBF eventually normalizes. This apparent neurovascular uncoupling has been ascribed to mitochondrial dysfunction, hindered oxygen diffusion into tissue, or microthrombosis. Capillary compression by astrocytic endfeet swelling is observed in biopsies acquired from TBI patients. In animal models, elevated intracranial pressure compresses capillaries, causing redistribution of capillary flows into patterns argued to cause functional shunting of oxygenated blood through the capillary bed. We used a biophysical model of oxygen transport in tissue to examine how capillary flow disturbances may contribute to the profound changes in CBF after TBI. The analysis suggests that elevated capillary transit time heterogeneity can cause critical reductions in oxygen availability in the absence of ‘classic' ischemia. We discuss diagnostic and therapeutic consequences of these predictions. PMID:25052556
Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu
2018-04-01
In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.
Mohammed, K. Elboree
2015-10-01
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.
International Nuclear Information System (INIS)
Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin
2014-01-01
This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
2018-01-01
This paper addresses the coupled nonlinear Schrödinger equation (CNLSE) in monomode step-index in optical fibers which describes the nonlinear modulations of two monochromatic waves, whose group velocities are almost equal. A class of dark, bright, dark-bright and dark-singular optical solitary wave solutions of the model are constructed using the complex envelope function ansatz. Singular solitary waves are also retrieved as bye products of the in integration scheme. This naturally lead to some constraint conditions placed on the solitary wave parameters which must hold for the solitary waves to exist. The modulation instability (MI) analysis of the model is studied based on the standard linear-stability analysis. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CNLSE.
Directory of Open Access Journals (Sweden)
G. Wollenberg
2004-01-01
Full Text Available An interconnection system whose loads protected by a voltage suppressor and a low-pass filter against overvoltages caused by coupling pulse-shaped electromagnetic waves is analyzed. The external wave influencing the system is assumed as a plane wave with HPM form. The computation is provided by a full-wave PEEC model for the interconnection structure incorporated in the SPICE code. Thus, nonlinear elements of the protection circuit can be included in the calculation. The analysis shows intermodulation distortions and penetrations of low frequency interferences caused by intermodulations through the protection circuits. The example examined shows the necessity of using full-wave models for interconnections together with non-linear circuit solvers for simulation of noise immunity in systems protected by nonlinear devices.
Asadi, Reza; Ouyang, Zhengbiao; Yu, Quanqiang; Ruan, Shuangchen
2014-06-16
We realize all-optical sensitive phase shifting based on nonlinear out-of-plane coupling to a slab waveguide through Fano resonance of a slab 1-D photonic crystal (PhC). We use a graphene layer as the nonlinear material and change its refractive index by the input light intensity through Kerr nonlinear effect to obtain a shift in the Fano resonance frequency. The Fano resonance and self-focusing effect lead to light-intensity enhancement on the graphene in the PhC, reinforcing the nonlinear effect of refractive index in the graphene. Through finite-difference time-domain simulation, we demonstrate that the phase changing sensitivity obtained can be 4 orders higher than that by a single graphene under the same input light intensity. Moreover the threshold pump intensity for all-optical sensitive phase shifting in the coupled light to the waveguide is as low as ~4 MW per square centimeter. The results are applicable in micro optical integrated circuits for phase shifters, phase modulators, power limiters, and phase logic elements for optical computation, digital phase shift keying in communication systems, and non-contact sensitive signal detectors.
Directory of Open Access Journals (Sweden)
M. L. Santos
2007-04-01
in a non cylindrical domain of $\\mathbb{R}^{n+1}$ $(n\\ge1$ under suitable hypothesis on the scalar functions $M$, $h$, $g_1$ and $g_2$, and where $\\alpha$ is a positive constant. We show that such dissipation is strong enough to produce uniform rate of decay. Besides, the coupling is nonlinear which brings up some additional difficulties, which plays the problem interesting. We establish existence and uniqueness of regular solutions for any $n\\ge 1$.
Dai, Chao-Qing; Fan, Yan; Wang, Yue-Yue; Zheng, Jun
2018-02-01
The (3 + 1)-dimensional generalized coupled nonlinear Schrödinger equation with electric and magnetic nonlinearities of Kerr type and self-steepening effects is studied, and bright and dark soliton solutions are derived. Based on these analytical solutions, dynamical behaviors of bright and dark solitons are discussed. The amplitudes, widths and velocities of bright and dark solitons are all constants determined by the self-steepening effect parameters SE, SH. The phase chirp of a bright soliton diminishes in the pulse front of y-direction, however, it increases in the pulse back edge of y-direction. On the contrary, the phase chirp of a dark soliton increases in the pulse front of y-direction, however, it diminishes in the pulse back edge of y-direction. The phase chirps of a bright and dark soliton both shift along positive y -axis as time goes on. Moreover, the stability of the solutions is discussed.
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav; Růžička, František; Zloshchastiev, K. G.
2017-01-01
Roč. 9, č. 8 (2017), č. článku 165. ISSN 2073-8994 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : PT symmetry * nonlinear Schrodinger equations * logarithmic nonlinearities Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.457, year: 2016
Directory of Open Access Journals (Sweden)
Maxim Goryachev
2018-04-01
Full Text Available A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10 18 Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.
Zhang, Jian-Song; Zeng, Wei; Chen, Ai-Xi
2017-06-01
We study the influence of cross-Kerr (CK) coupling and optical parametric amplifier (OPA) on the effective frequency, damping, normal mode splitting, ground state cooling, and steady state entanglement of an optomechanical system formed by one fixed mirror and one movable mirror. The CK coupling could increase the damping of the movable mirror. The normal mode splitting of the output field is observed due to the CK coupling. The combination of the CK coupling and OPA decreases the minimum attainable phonon number and the effective temperature of the movable mirror. The amount of stationary entanglement between the mechanical and cavity modes can be enhanced by the weak CK coupling. In particular, we find the stationary entanglement becomes more robust against thermal fluctuations of the movable mirror in the presence of the weak CK coupling.
Mann, Nishan; Hughes, Stephen
2018-02-01
We present the analytical and numerical details behind our recently published article [Phys. Rev. Lett. 118, 253901 (2017), 10.1103/PhysRevLett.118.253901], describing the impact of disorder-induced multiple scattering on counterpropagating solitons in photonic crystal waveguides. Unlike current nonlinear approaches using the coupled mode formalism, we account for the effects of intraunit cell multiple scattering. To solve the resulting system of coupled semilinear partial differential equations, we introduce a modified Crank-Nicolson-type norm-preserving implicit finite difference scheme inspired by the transfer matrix method. We provide estimates of the numerical dispersion characteristics of our scheme so that optimal step sizes can be chosen to either minimize numerical dispersion or to mimic the exact dispersion. We then show numerical results of a fundamental soliton propagating in the presence of multiple scattering to demonstrate that choosing a subunit cell spatial step size is critical in accurately capturing the effects of multiple scattering, and illustrate the stochastic nature of disorder by simulating soliton propagation in various instances of disordered photonic crystal waveguides. Our approach is easily extended to include a wide range of optical nonlinearities and is applicable to various photonic nanostructures where power propagation is bidirectional, either by choice, or as a result of multiple scattering.
Simon, J. S.; Valavani, L.
1991-01-01
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
International Nuclear Information System (INIS)
Zhou, Hao-Miao; Qu, Shao-Xing; Ou, Xiao-Wei; Xiao, Ying; Wu, Hua-Ping
2013-01-01
Based on the equivalent circuit method, this paper adopts the nonlinear magnetostrictive constitutive relations to establish an analytical nonlinear magnetoelectric coefficient model for magnetostrictive/piezoelectric/magnetostrictive laminated magnetoelectric composites. When the pre-stress is set to zero in the model, the predicted results of the magnetoelectric coefficient coincide well with the available experimental results both qualitatively and quantitatively. Using the model, we can qualitatively predict the influence of the pre-stress, magnetic bias fields and the volume fraction of the magnetostrictive material on the magnetoelectric coefficient. The predicted results show that the influences of the pre-stress on the magnetoelectric coefficient, which varies with the magnetic bias field, before and after reaching the magnetoelectric coefficient maximum, are opposite. That is, the influence of the pre-stress on curves of the magnetoelectric coefficient reverses when the magnetoelectric coefficient reaches its maximum. Therefore, the correct setting of the pre-stress can lower the applied magnetic bias field and improve the magnetoelectric coefficient. The established nonlinear magnetoelectric effect model can provide a theoretical basis for regulating the magnetoelectric coefficient by the pre-stress and magnetic bias field and make it possible to design high-precision miniature magnetoelectric devices. (paper)
Directory of Open Access Journals (Sweden)
D. Béal
2010-02-01
Full Text Available In biogeochemical models coupled to ocean circulation models, vertical mixing is an important physical process which governs the nutrient supply and the plankton residence in the euphotic layer. However, vertical mixing is often poorly represented in numerical simulations because of approximate parameterizations of sub-grid scale turbulence, wind forcing errors and other mis-represented processes such as restratification by mesoscale eddies. Getting a sufficient knowledge of the nature and structure of these errors is necessary to implement appropriate data assimilation methods and to evaluate if they can be controlled by a given observation system.
In this paper, Monte Carlo simulations are conducted to study mixing errors induced by approximate wind forcings in a three-dimensional coupled physical-biogeochemical model of the North Atlantic with a 1/4° horizontal resolution. An ensemble forecast involving 200 members is performed during the 1998 spring bloom, by prescribing perturbations of the wind forcing to generate mixing errors. The biogeochemical response is shown to be rather complex because of nonlinearities and threshold effects in the coupled model. The response of the surface phytoplankton depends on the region of interest and is particularly sensitive to the local stratification. In addition, the statistical relationships computed between the various physical and biogeochemical variables reflect the signature of the non-Gaussian behaviour of the system. It is shown that significant information on the ecosystem can be retrieved from observations of chlorophyll concentration or sea surface temperature if a simple nonlinear change of variables (anamorphosis is performed by mapping separately and locally the ensemble percentiles of the distributions of each state variable on the Gaussian percentiles. The results of idealized observational updates (performed with perfect observations and neglecting horizontal correlations
Chakraborty, Sushmita; Nandy, Sudipta; Barthakur, Abhijit
2015-02-01
We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.
Zhu, Shengyang; Cai, Chengbiao; Spanos, Pol D.
2015-01-01
A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads. It is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems. The vehicle is treated as a multi-body system with 10 degrees of freedom, and the slab track is represented by a three layer Bernoulli-Euler beam model. The model for the rail pads is one dimensional, and the force-displacement relation is based on a superposition of elastic, friction, and FDV forces. This model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the CVST system by means of an explicit integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail harmonic irregularities is carried out, pointing out the stiffness and damping dependence on the excitation frequency and the displacement amplitude. The analysis indicates that the dynamic stiffness and damping of the rail pads increase with the excitation frequency while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under excitations of welded rail joint irregularities and of random track irregularities, are conducted in the time domain as well as in the frequency domain. The proposed model is shown to possess several modeling advantages over the ordinary Kelvin element which overestimates both the stiffness and damping features at high frequencies.
DEFF Research Database (Denmark)
Santos, Ilmar; Saracho, C.M.; Smith, J.T.
2004-01-01
, it is possible to highlight some dynamic effects and experimentally simulate the structural behavior of a windmill in two dimensions (2D-model). Only lateral displacement of the rotor in the horizontal direction is taken into account. Gyroscopic effect due to rotor angular vibrations is eliminated in the test......This work gives a theoretical and experimental contribution to the problem of rotor-blades dynamic interaction. A validation procedure of mathematical models is carried out with help of a simple test rig, built by a mass-spring system attached to four flexible rotating blades. With this test rig...... linear, non-linear and time-depending terms in a very transparent way. Although neither gyroscopic effect due to rotor angular vibrations nor higher blade mode shapes are considered in the analysis, the equations of motion of the rotor-blades system are still general enough for the purpose of the work...
International Nuclear Information System (INIS)
Lu, LingFeng
2016-01-01
Ion Cyclotron Resonant Heating (ICRH) by waves in 30-80 MHz range is currently used in magnetic fusion plasmas. Excited by phased arrays of current straps at the plasma periphery, these waves exist under two polarizations. The Fast Wave tunnels through the tenuous plasma edge and propagates to its center where it is absorbed. The parasitically emitted Slow Wave only exists close to the launchers. How much power can be coupled to the center with 1 A current on the straps? How do the emitted radiofrequency (RF) near and far fields interact parasitically with the edge plasma via RF sheath rectification at plasma-wall interfaces? To address these two issues simultaneously, in realistic geometry over the size of ICRH antennas, this thesis upgraded and tested the Self-consistent Sheaths and Waves for ICH (SSWICH) code. SSWICH couples self-consistently RF wave propagation and Direct Current (DC) plasma biasing via non-linear RF and DC sheath boundary conditions (SBCs) at plasma/wall interfaces. Its upgrade is full wave and was implemented in two dimensions (toroidal/radial). New SBCs coupling the two polarizations were derived and implemented along shaped walls tilted with respect to the confinement magnetic field. Using this new tool in the absence of SBCs, we studied the impact of a density decaying continuously inside the antenna box and across the Lower Hybrid (LH) resonance. Up to the memory limits of our workstation, the RF fields below the LH resonance changed with the grid size. However the coupled power spectrum hardly evolved and was only weakly affected by the density inside the box. In presence of SBCs, SSWICH-FW simulations have identified the role of the fast wave on RF sheath excitation and reproduced some key experimental observations. SSWICH-FW was finally adapted to conduct the first electromagnetic and RF-sheath 2D simulations of the cylindrical magnetized plasma device ALINE. (author) [fr
International Nuclear Information System (INIS)
Souto, W A; Oliveira, J C T; Rodrigues, H; Duarte, S B; Chiapparini, M
2015-01-01
In this work we determine the equation of state and the population of baryons and leptons and discuss the effects of the hyperon-meson coupling constants to the formation of delta resonances in the stellar medium. We also discuss the structure of the protoneutron stars including the delta matter in their composition, and compared the results of a cooled neutron star, after escape of neutrinos. For protoneutron stars structure and composition, the neutrinos are considered trapped. (paper)
Carranza, Coleen; van der Ploeg, Martine
2017-04-01
Accurate estimates of water content in the soil profile are essential for environmental and climate modeling studies. Current trends for estimating profile soil moisture incorporate remote sensing methods for mapping soil moisture at greater spatial coverage but is limited to the upper soil layers (e.g. 5cm for radar satellites). Data assimilation methods offer promising computational techniques to translate mapped surface soil moisture to estimates of profile soil moisture, in conjunction with physical models. However, a variety of factors, such as differences in the drying rates, can lead to "decoupling" (Capehart and Carlson, 1997) of surface and subsurface soil moisture. In other words, surface soil moisture conditions no longer reflect or represent subsurface conditions. In this study, we investigated the relation and observed decoupling between surface and subsurface soil moisture from 15-minute interval time series datasets in four selected Dutch agricultural fields (SM_05, SM_09, SM_13, SM_20) from the soil moisture network in Twente region. The idea is that surface soil moisture conditions will be reflected in the subsurface after a certain time lag because of its movement or flow from the surface. These lagged associations were analysed using distributed lag non-linear model (DLNM). This statistical technique provides a framework to simultaneously represent non-linear exposure-response dependencies and delayed effects. DNLM was applied to elucidate which surface soil moisture conditions resulted in a high association to subsurface values, indicating good correlation between the two zones. For example, initial results for this ongoing study from SM_13 show an overall low but increasing association from dry to intermediate soil moisture values (0 to 25%). At this range of values, we say that the two zones are decoupled. Above these values towards near saturated conditions ( 40%), associations between the two zones remain high. For predictor
Song, Yongli; Makarov, Valeri A; Velarde, Manuel G
2009-08-01
A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.
Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo
2017-03-01
The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2013-01-01
. To study the non-linear behaviour of the coupled problem analytically, the classical multiple scale method is applied. The response at each mode in resonant as well as in sub-harmonic excitation conditions is analysed in the cases of internal resonance and internal parametric resonance....
Cardiac PET Imaging of Blood Flow, Metabolism, and Function in Normal and Infarcted Rats
Lecomte, R.; Croteau, E.; Gauthier, M.-E.; Archambault, M.; Aliaga, A.; Rousseau, J.; Cadorette, J.; Leroux, J.-D.; Lepage, M. D.; Benard, F.; Bentourkia, M.
2004-06-01
The rat heart is an excellent model for the investigation of cardiac physiology and metabolism. It has been used extensively for ex vivo studies of the normal heart as well as for the study of various heart diseases. With the advent of dedicated high-resolution small animal PET scanners, it is now possible to transpose many of the cardiac studies routinely used in humans to the rat. These include the in vivo measurement of myocardial blood flow, metabolism, and function. Because these techniques are noninvasive, the same animal can be imaged repetitively, thus allowing for follow-up studies of disease progression and for the assessment of new therapeutic methods. In this work, we report on cardiac studies performed in normal and diseased rats using the Sherbrooke avalanche photodiode PET scanner, a small animal PET imaging device achieving 14 /spl mu/l volumetric spatial resolution with excellent image signal-to-noise ratio. The system also features flexible list-mode data acquisition, which allows dynamic studies to be resampled as desired for kinetic modeling. These cardiac PET imaging methods were used for the follow-up of infarcted rats submitted to experimental intramyocardial revascularization therapy.
Klöppel, Thomas; Wall, Wolfgang A
2011-07-01
A novel finite element approach is presented to simulate the mechanical behavior of human red blood cells (RBC, erythrocytes). As the RBC membrane comprises a phospholipid bilayer with an intervening protein network, we propose to model the membrane with two distinct layers. The fairly complex characteristics of the very thin lipid bilayer are represented by special incompressible solid shell elements and an anisotropic viscoelastic constitutive model. Properties of the protein network are modeled with an isotropic hyperelastic third-order material. The elastic behavior of the model is validated with existing optical tweezers studies with quasi-static deformations. Employing material parameters consistent with literature, simulation results are in excellent agreement with experimental data. Available models in literature neglect either the surface area conservation of the RBC membrane or realistic loading conditions of the optical tweezers experiments. The importance of these modeling assumptions, that are both included in this study, are discussed and their influence quantified. For the simulation of the dynamic motion of RBC, the model is extended to incorporate the cytoplasm. This is realized with a monolithic fully coupled fluid-structure interaction simulation, where the fluid is described by the incompressible Navier-Stokes equations in an arbitrary Lagrangian Eulerian framework. It is shown that both membrane viscosity and cytoplasm viscosity have significant influence on simulation results. Characteristic recovery times and energy dissipation for varying strain rates in dynamic laser trap experiments are calculated for the first time and are found to be comparable with experimental data.
International Nuclear Information System (INIS)
Chang-Jian, C.-W.; Chen, C.-K.
2008-01-01
This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze couple stress fluid film journal bearings with non-linear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor-bearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincare maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios, the non-dimensional parameter l* and the permeability. The modeling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided
Liu, Lei; Tian, Bo; Xie, Xi-Yang; Guan, Yue-Yang
2017-01-01
Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively. Especially, from the interaction between a Type-I soliton and a Type-II soliton, we see that the Type-II soliton exhibits the oscillation periodically before such an interaction and becomes the double-hump soliton after the interaction, which is different from the previously reported.
International Nuclear Information System (INIS)
Weinberg, Nevin N.; Arras, Phil; Burkart, Joshua
2013-01-01
A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω a excites a pair of secondary waves of frequency ω b + ω c ≅ ω a . Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ω b + ω c >> ω a . We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f gw ≳ 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δφ ≳ 1 radian) that accumulate primarily at low frequencies (f gw ≲ 50 Hz) and (2) heat the neutron star core to a temperature of T ∼ 10 10 K. Since there are at least ∼100 unstable p-g daughter pairs, Δφ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously
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......NL to demonstrate a significant soliton selffrequency shift of a fundamental soliton, and we show that nonlinear matching can take precedence over linear mode matching. The nonlinear coupling coefficient depends on both the dispersion (β2) and nonlinearity (γ), as well as on the power coupling efficiency η. Being...
Energy Technology Data Exchange (ETDEWEB)
Sigrist, J.F
2004-11-15
The present work deals with the numerical simulation of a coupled fluid/structure problem with fluid free surface. A generic coupled fluid/structure system is defined, on which a linear problem (modal analysis) and a non-linear problem (temporal analysis) are stated. In the linear case, a strong coupled method is used. It is based on a finite element approach of the structure problem and a finite or a boundary element approach of the fluid problem. The coupled problem is formulated in terms of pressure and displacement, leading to a non-symmetric problem which is solved with an appropriate algorithm. In the non-linear case, the structure problem is described with non-linear equations of motion, whereas the fluid problem is modeled with the Stokes equations. The numerical resolution of the coupled problem is based on a weak coupling procedure. The fluid problem is solved with a finite volume technique, using a moving mesh technique to adjust the structure motion, a VOF method for the description of the free surface and the PISO algorithm for the time integration. The structure problem is solved with a finite element technique, using an explicit/implicit time integration algorithm. A procedure is developed in order to handle the coupling in space (fluid forces and structure displacement exchanges between fluid and structure mesh, fluid re-meshing) and in time (staggered explicit algorithm, dynamic filtering of numerical oscillations). The non linear coupled problem is solved using a CFD code, whose use for FSI problem is validated with a benchmark presented in this work. A comparison is proposed between numerical results and analytical solution for two elementary fluid problems. The validation process can be applied for any CFD numerical code. A numerical study is then proposed on the generic coupled case in order to describe the fluid/structure interaction phenomenon (added mass, displaced mass, mode coupling, influence of structural non-linearity). An industrial
Directory of Open Access Journals (Sweden)
Grégory Antoni
2016-01-01
Full Text Available This study concerns the development of a straightforward numerical technique associated with Classical Newton’s Method for providing a more accurate approximate solution of scalar nonlinear equations. The proposed procedure is based on some practical geometric rules and requires the knowledge of the local slope of the curve representing the considered nonlinear function. Therefore, this new technique uses, only as input data, the first-order derivative of the nonlinear equation in question. The relevance of this numerical procedure is tested, evaluated, and discussed through some examples.
FRF decoupling of nonlinear systems
Kalaycıoğlu, Taner; Özgüven, H. Nevzat
2018-03-01
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
Digital Repository Service at National Institute of Oceanography (India)
Mandal, S.
.C., Yasuda, T., 2002. Analysis of freak wave measurements in the sea of Japan. Ocean Engineering 29, 1399–1414. Sand, S.E., Hansen, Neo, Klingting, P., Gudmestad, O.T., Sterndorff, M.J., 1990. Freak waves kinematics. Proc. NATO advanced research workshop... 31 (2004) 791–793 www.elsevier.com/locate/oceaneng Letter to the editor “Nonlinear coupled dynamic response of offshore spar platforms under regular sea waves” By Agarwal, AK and Jain, AK. Ocean Engineering, 2003, 30, 517-555 The authors have shown...
International Nuclear Information System (INIS)
Vlahostergios, Z.; Yakinthos, K.; Goulas, A.
2009-01-01
We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
International Nuclear Information System (INIS)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2010-01-01
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have been derived, which are capable of determining the various
Chamberlain Chedjou, Jean; Kyamakya, Kyandoghere
2010-10-01
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have been derived, which are capable of determining the various
Nonlinear matching of Solitons - Continued redshift between silica and soft-glass fibers
DEFF Research Database (Denmark)
Agger, Christian; Sørensen, Simon Toft; Thomsen, Carsten
2012-01-01
We present an analysis of nonlinear coupling between fibers. We introduce the nonlinear coupling coefficient and investigate solitons coupling from one fiber into another. We will also present simulated supercontinuum from concatenated fiber systems.......We present an analysis of nonlinear coupling between fibers. We introduce the nonlinear coupling coefficient and investigate solitons coupling from one fiber into another. We will also present simulated supercontinuum from concatenated fiber systems....
Nonlinear evolution of drift instabilities
International Nuclear Information System (INIS)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
International Nuclear Information System (INIS)
Dorning, J.J.
1993-05-01
All the objectives originally scheduled for the first year of this grant have been achieved. Furthermore, the project is ahead of schedule, in that a substantial amount of work has been completed on two significant objectives originally planned for the second year. This interim report is divided into five parts, summarizing the mathematical development, analysis and results of the project goals -- goals originally planned for the first year and completed, and those on which substantial progress has been made ahead of schedule. Effects of unheated riser sections and the downcomer recirculation loop on the stability characteristics of advanced boiling water reactor designs that incorporate risers or unheated channel extensions are summarized in Part A. Such extensions are incorporated above the heated reactor core channels to enhance buoyancy-driven natural thermal convection both during normal at-power operation and during emergency shutdown. The effects of both, the inclusion of unheated riser sections in the designs (one of the goals substantially completed ahead of schedule), and the inclusion of the recirculation loop in the models (first year goal) were generally found to be destabilizing. In general, as riser lengths were increased equilibria that previously were stable became unstable, and the systems with the taller risers evolved to density-wave limit cycle oscillations. As a building block of the second year goal -- to extend the one dimensional dynamical analysis of reactor thermal-hydraulics/neutron-kinetics to two and three dimensions -- we have carried out, ahead of schedule, the nonlinear dynamical analysis of two-phase flow in multiple parallel heated channels. Some basic aspects of bifurcation phenomena in two-phase flow and the related nonlinear dynamics of single and multiple parallel, uniformly and nonuniformly heated channels are studied
National Research Council Canada - National Science Library
Rassias, Themistocles M
1987-01-01
... known that nonlinear partial differential equations can not be treated in the same systematic way as linear ones and this volume provides, among other things, proofs of existence and uniqueness theorems for nonlinear differential equations of a global nature. However, the basic techniques which have proven to be efficient in dealing with li...
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
DEFF Research Database (Denmark)
Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus
2004-01-01
We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Directory of Open Access Journals (Sweden)
Henry J. P.
2006-11-01
Full Text Available Nous présentons dans ce travail une étude numérique basée sur la méthode des éléments finis, du comportement thermoporoélastique de certaines roches. Les trois effets de couplage : déformabilité de la roche, pression interstitielle et température sont pris en compte simultanément dans la résolution numérique. Une application simple sur un puits pétrolier en conditions axisymétriques est finalement présentée afin de dégager en particulier l'influence du terme de couplage convectif non linéaire, obtenu dans l'équation de diffusivité thermique, sur l'évolution de la température et de la pression interstitielle autour du forage. This article describes a finite-element method for solving the problem of nonlinear coupling between interstitial pressure and temperature during stress on a poroelastic rock. Such coupling phenomena occur during massive injection of cold water into a petroleum borehole for example. The implementation of such a numerical solution, used here with the assumption of small deformations, first requires a review of the behavior law of the material (Eq. 2. 2 and of the equations for hydraulic diffusivity (Eq. 2. 3 and thermal diffusivity (Eq. 2. 4. This last equation (2. 4 is the one containing the nonlinear coupling terms in Grad P Grad P and Grad T. Grad P. During simulation of flow at a high flow rate, these products can no longer be neglected as shown by the results in Fig. 2. The variational formulation of the problem is then determined in relation to the three equations for equilibrium, thermal diffusivity and hydraulic diffusivity. After geometric and temporal discretizations, this formulation leads to a finite-element calculating scheme resulting in the simultaneous solving of all three equations. This solution, based on the inversion of the system of equations (2. 15, requires the updating of the rigidity matrix at each time step to take nonlinear coupling into consideration. Calculations with an
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-08
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....
Energy Technology Data Exchange (ETDEWEB)
Theiler, J. [Los Alamos National Lab., NM (United States)]|[Santa Fe Inst., NM (United States); Nichols, S. [Georgia Inst. of Tech., Atlanta, GA (United States). School of Physics
1993-09-01
The sensitivity to noise of the coherent (or in-phase) attractor for a set of N globally coupled maps is studied; these discrete-time maps are associated with the continuous-time equations of motion for a series array of Josephson junction oscillators. We investigate both geometrical properties of the basin of attraction in the large N limit, and the implications of this geometry on the average time for the system to ``escape`` from the coherently oscillating mode. Our main results are that the attractor basin maintains a box-shaped ``core`` of finite radius even as N {yields} {infinity}, and that the in-phase attractor of a large N array is much less vulnerable to noise than are the out-of-phase attractors.
Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2017-12-01
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (rδrδL>0.5 for k ≲1 h /Mpc ) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21 cm intensity mapping initiatives.
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
2016-07-01
architectures , practical nonlinearities, nonlinear dynamics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 8. NUMBER OF PAGES...performers from Mesodynamic Architectures (MESO) and uPNT all to include devices in these runs. This cost-sharing was planned, and is necessary for...contributions to the performance of MEMS gyroscopes. In particular, we have demonstrated for the first time that Parametric Amplification can improve the
Kerr nonlinear coupler and entanglement
International Nuclear Information System (INIS)
Leonski, Wieslaw; Miranowicz, Adam
2004-01-01
We discuss a model comprising two coupled nonlinear oscillators (Kerr-like nonlinear coupler) with one of them pumped by an external coherent excitation. Applying the method of nonlinear quantum scissors we show that the quantum evolution of the coupler can be closed within a finite set of n-photon Fock states. Moreover, we show that the system is able to generate Bell-like states and, as a consequence, the coupler discussed behaves as a two-qubit system. We also analyse the effects of dissipation on entanglement of formation parametrized by concurrence
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Energy Technology Data Exchange (ETDEWEB)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere, E-mail: kyandoghere.kyamakya@uni-klu.ac.a, E-mail: jean.chedjou@uni-klu.ac.a [Transportation Informatics Group, Institute of Smart Systems Technologies, University of Klagenfurt (Austria)
2010-10-15
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Nonlinear simulation of meander evolution
Chen, D.; Zhang, Y.; Ottevanger, W.; Blanckaert, K.; Leilei, G.
2012-01-01
Evolution of meanders, a complex morpho-dynamic process, has been the focus of research challenging river engineers for decades. The study replicates the natural evolution of meandering processes by coupling the Bank Erosion and Retreat Model (BERM, by Chen and Duan) with a nonlinear flow model (by
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....
Analytic treatment of nonlinear evolution equations using first ...
Indian Academy of Sciences (India)
power of this manageable method is confirmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations. Keywords. Exact solutions; first integral method; combined KdV–mKdV equation; Pochhammer–. Chree equation; coupled nonlinear ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have ... The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
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...
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
of the major milestones (and a principal thrust of recent activity) regarding the physical/ experimental realizability of the corresponding Hamiltonians stemmed from progress in optics both at the theoretical [2,3] and experimental [4,5] levels. In particular, the real- ization that in optics, the ubiquitous loss can be counteracted ...
Nonlinearly coupled thermo-visco-elasticity
Czech Academy of Sciences Publication Activity Database
Roubíček, Tomáš
2013-01-01
Roč. 20, č. 3 (2013), s. 1243-1275 ISSN 1021-9722 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:61388998 Keywords : kelvin-voigt rheology * small strains * nonsimple materials Subject RIV: BA - General Mathematics Impact factor: 0.971, year: 2013 http://link.springer.com/article/10.1007%2Fs00030-012-0207-9
Coupled diffusion systems with localized nonlinear reactions
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit - Î´ui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Î© Ã— (0, T) with boundary conditions ui = 0 on âˆ‚Î© Ã— [0, T). We show that the solution has a global blowup. The exact rate of t...
Counter operation in nonlinear micro-electro-mechanical resonators
International Nuclear Information System (INIS)
Yao, Atsushi; Hikihara, Takashi
2013-01-01
This Letter discusses a logical operation of multi-memories that consist of coupled nonlinear micro-electro-mechanical systems (MEMS) resonators. A MEMS resonator shows two coexisting stable states when nonlinear responses appear. Previous studies addressed that a micro- or nano-electrical-mechanical resonator can be utilized as a mechanical 1-bit memory or mechanical logic gates. The next phase is the development of logic system with coupled multi-resonators. From the viewpoint of application of nonlinear dynamics in coupled MEMS resonators, we show the first experimental success of the controlling nonlinear behavior as a 2-bit binary counter.
Nonlinear optics principles and applications
Rottwitt, Karsten
2014-01-01
IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...
MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet
Directory of Open Access Journals (Sweden)
B.C. Prasannakumara
2017-01-01
Full Text Available The problem of heat and mass transfer of Siskonanofluid flow over a nonlinear stretching sheet under the influence of nonlinear thermal radiation and chemical reaction is considered. suitable set of similarity transformations are implemented to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. An efficient Runge–Kutta–Fehlberg fourth–fifth order method along with shooting technique is employed to solve the reduced equations. The influence of several emerging physical parameters on velocity, temperature and concentration profiles for both linear and nonlinear stretching sheet in the presence of linear and nonlinear thermal radiation has been studied and analyzed through plotted graphs and tables in detail. It is found that the Nusselt and Sherwood number are high in case of nonlinear stretching sheet than linear. Further, it is observed that the nonlinear thermal radiation has more influence on temperature profiles than linear.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah
2016-10-04
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
DEFF Research Database (Denmark)
Chen, X.; Cui, W.; Jensen, Jørgen Juncher
2003-01-01
The theory and typical numerical results of a second order nonlinear hydroelastic analysis of floating bodies are presented in a series of papers in which only nonlinearity in fluids is considered. Under the assumption of linear fluid, the hydroelastic analysis methods of nonlinear structure...... are introduced in this paper. With the examples of the motion and displacement reponses of a floating plate undergoing large vertical deflections in multidirectional waves, the analysis method of the couple action between the vertical deflections in multidirectional waves, the analysis method of the couple...
Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.
2018-04-01
The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Statistical approach of weakly nonlinear ablative Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Garnier, J.; Masse, L.
2005-01-01
A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1λ for long wavelengths, but higher for short instable wavelengths in the ablative regime
Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis, Phase I
National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...
Control methods for localization of nonlinear waves.
Porubov, Alexey; Andrievsky, Boris
2017-03-06
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).
Nonlinear single-spin spectrum analyzer.
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2013-03-15
Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.
Coherent Nonlinear Longitudinal Phenomena in Unbunched Synchrotron Beams
Energy Technology Data Exchange (ETDEWEB)
Spentzouris, Linda Klamp [Northwestern U.
1996-12-01
Coherent nonlinear longitudinal phenomena are studied in proton and antiproton synchrotron beams. Theoretical development done in the eld of plasma physics for resonant wave-wave coupling is applied to the case of a particle beam. Results are given from experiments done to investigate the nature of the weakly nonlinear three-wave coupling processes known as parametric coupling and echoes. Storage ring impedances are shown to amplify the parametric coupling process, underlining the possibility that machine impedances might be extracted from coupling events instigated by external excitation. Echo amplitudes are demonstrated to be sensitive to diusion processes, such as intrabeam scattering, which degrade a beam. The result of a fast diusion rate measurement using echo amplitudes is presented. In addition to the wave-wave interactions, observations of moderately nonlinear waveparticle interactions are also included. The manifestations of these interactions that are documented include nonlinear Landau damping, higher harmonic generation, and signs of the possible formation of solitons.
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
All-optical signal processing in quadratic nonlinear materials
DEFF Research Database (Denmark)
Johansen, Steffen Kjær
2002-01-01
and the SH. Via quasi-phase-matching (QPM) the phase mismatch and hence the nonlinearity is eÙectively brought under control through periodic sign reversal of the nonlinearity. On theaverage QPM changes the quadratic nonlinearity and induces new cubic nonlinearities in the system. The engineering...... of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...
Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane
Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.
2018-01-01
We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that
Nonlinear spectral correlation for fatigue crack detection under noisy environments
Liu, Peipei; Sohn, Hoon; Jeon, Ikgeun
2017-07-01
When ultrasonic waves at two distinct frequencies are applied to a structure with a fatigue crack, crack-induced nonlinearity creates nonlinear ultrasonic modulations at the sum and difference of the two input frequencies. The amplitude of the nonlinear modulation components is typically one or two orders of magnitude smaller than that of the primary linear components. Therefore, the modulation components can be easily buried under noise levels and it becomes difficult to extract the nonlinear modulation components under noisy environments using a conventional spectral density function. In this study, nonlinear spectral correlation, which calculates the spectral correlation between nonlinear modulation components, is proposed to isolate the nonlinear modulation components from noisy environments and used for fatigue crack detection. The proposed nonlinear spectral correlation offers the following benefits: (1) Stationary noises have little effect on nonlinear spectral correlation; (2) By using a wideband high-frequency input and a single low-frequency input, the contrast of nonlinear spectral correlation between damage and intact conditions can be enhanced; and (3) The test efficiency can be also improved via reducing the data collection time. Validation tests are performed on aluminum plates and scaled steel shafts with real fatigue cracks. The experimental results demonstrate that the proposed nonlinear spectral correlation owns a higher sensitivity to fatigue crack than the classical nonlinear coefficient estimated from the spectral density function, and the usage of nonlinear spectral correlation allows the detection of fatigue crack even using noncontact air-coupled transducers with a low signal-to-noise ratio.
Nonlinear Dynamics of Nanomechanical Resonators
Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym
2007-03-01
Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).
Event–Related Synchronization/Desynchronization in Coupled ...
Indian Academy of Sciences (India)
V. K. Chandrasekar
ERS ERD/ERS in an array of coupled Stuart-Landau oscill. Aim . Aim . . To present a general coupled nonlinear oscillator model for event-related synchronization/desynchronization (ESR/ERD). To explain relevant experiment in brain dynamics.
Coupled transfers; Transferts couples
Energy Technology Data Exchange (ETDEWEB)
Nicolas, X.; Lauriat, G.; Jimenez-Rondan, J. [Universite de Marne-la-Vallee, Lab. d' Etudes des Transferts d' Energie et de Matiere (LETEM), 77 (France); Bouali, H.; Mezrhab, A. [Faculte des Sciences, Dept. de Physique, Lab. de Mecanique et Energetique, Oujda (Morocco); Abid, C. [Ecole Polytechnique Universitaire de Marseille, IUSTI UMR 6595, 13 Marseille (France); Stoian, M.; Rebay, M.; Lachi, M.; Padet, J. [Faculte des Sciences, Lab. de Thermomecanique, UTAP, 51 - Reims (France); Mladin, E.C. [Universitaire Polytechnique Bucarest, Faculte de Genie Mecanique, Bucarest (Romania); Mezrhab, A. [Faculte des Sciences, Lab. de Mecanique et Energetique, Dept. de Physique, Oujda (Morocco); Abid, C.; Papini, F. [Ecole Polytechnique, IUSTI, 13 - Marseille (France); Lorrette, C.; Goyheneche, J.M.; Boechat, C.; Pailler, R. [Laboratoire des Composites ThermoStructuraux, UMR 5801, 33 - Pessac (France); Ben Salah, M.; Askri, F.; Jemni, A.; Ben Nasrallah, S. [Ecole Nationale d' Ingenieurs de Monastir, Lab. d' Etudes des Systemes Thermiques et Energetiques (Tunisia); Grine, A.; Desmons, J.Y.; Harmand, S. [Laboratoire de Mecanique et d' Energetique, 59 - Valenciennes (France); Radenac, E.; Gressier, J.; Millan, P. [ONERA, 31 - Toulouse (France); Giovannini, A. [Institut de Mecanique des Fluides de Toulouse, 31 (France)
2005-07-01
This session about coupled transfers gathers 30 articles dealing with: numerical study of coupled heat transfers inside an alveolar wall; natural convection/radiant heat transfer coupling inside a plugged and ventilated chimney; finite-volume modeling of the convection-conduction coupling in non-stationary regime; numerical study of the natural convection/radiant heat transfer coupling inside a partitioned cavity; modeling of the thermal conductivity of textile reinforced composites: finite element homogenization on a full periodical pattern; application of the control volume method based on non-structured finite elements to the problems of axisymmetrical radiant heat transfers in any geometries; modeling of convective transfers in transient regime on a flat plate; a conservative method for the non-stationary coupling of aero-thermal engineering codes; measurement of coupled heat transfers (forced convection/radiant transfer) inside an horizontal duct; numerical simulation of the combustion of a water-oil emulsion droplet; numerical simulation study of heat and mass transfers inside a reactor for nano-powders synthesis; reduction of a combustion and heat transfer model of a direct injection diesel engine; modeling of heat transfers inside a knocking operated spark ignition engine; heat loss inside an internal combustion engine, thermodynamical and flamelet model, composition effects of CH{sub 4}H{sub 2} mixtures; experimental study and modeling of the evolution of a flame on a solid fuel; heat transfer for laminar subsonic jet of oxygen plasma impacting an obstacle; hydrogen transport through a A-Si:H layer submitted to an hydrogen plasma: temperature effects; thermal modeling of the CO{sub 2} laser welding of a magnesium alloy; radiant heat transfer inside a 3-D environment: application of the finite volume method in association with the CK model; optimization of the infrared baking of two types of powder paints; optimization of the emission power of an infrared
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Matter couplings in supergravity theories
International Nuclear Information System (INIS)
Bagger, J.A.
1983-01-01
The N = 1 supersymmetric nonlinear sigma model is coupled to supergravity. The results are expressed in the language of Kahler geometry. Topological considerations constrain the scalar fields to lie on a Kahler manifold of restricted type, or a Hodge manifold. For topologically nontrivial manifolds, this leads to the quantization of Newton's constant in terms of the scalar self-coupling. The isometries of the N = 1 model are gauged. This gives a geometrical picture of what might be called the gauge invariant supersymmetric nonlinear sigma model. It also provides a new interpretation of the Fayet-Iliopoulos D-term. The gauge invariant supersymmetric nonlinear sigma model is coupled to N = 1 supergravity. This leads to a deeper understanding of the connections between supergravity, R-invariance and the Fayet-Iliopoulos D-term. It also provides a foundation for phenomenological studies of supergravity theories. Finally, the N = 2 supersymmetric nonlinear sigma model is coupled to supergravity. The scalar fields are found to lie on a negatively curved quaternionic manifold. This implies that matter self-couplings that are allowed in N = 2 supersymmetry are forbidden in N = 2 supergravity, and vice versa
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and
Analytic treatment of nonlinear evolution equations using ﬁrst ...
Indian Academy of Sciences (India)
https://www.ias.ac.in/article/fulltext/pram/079/01/0003-0017 ... Exact solutions; ﬁrst integral method; combined KdV–mKdV equation; Pochhammer–Chree equation; coupled nonlinear evolution equations. ... The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... Abstract. In this article, a variety of solitary wave solutions are found for some nonlinear equations. In math- ematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
Abstract. The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
Analytic treatment of nonlinear evolution equations using first ...
Indian Academy of Sciences (India)
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be ...
Nonlinear elliptic differential equations with multivalued nonlinearities
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Nonlinear elliptic differential equations with multivalued ... has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth .... A is upper semicontinuous (as a set-valued map) from every finite dimensional subspace of X into ...
Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials
International Nuclear Information System (INIS)
Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan
2007-01-01
A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models
Modelling nonlinearity in piezoceramic transducers: From equations to nonlinear equivalent circuits.
Parenthoine, D; Tran-Huu-Hue, L-P; Haumesser, L; Vander Meulen, F; Lematre, M; Lethiecq, M
2011-02-01
Quadratic nonlinear equations of a piezoelectric element under the assumptions of 1D vibration and weak nonlinearity are derived by the perturbation theory. It is shown that the nonlinear response can be represented by controlled sources that are added to the classical hexapole used to model piezoelectric ultrasonic transducers. As a consequence, equivalent electrical circuits can be used to predict the nonlinear response of a transducer taking into account the acoustic loads on the rear and front faces. A generalisation of nonlinear equivalent electrical circuits to cases including passive layers and propagation media is then proposed. Experimental results, in terms of second harmonic generation, on a coupled resonator are compared to theoretical calculations from the proposed model. Copyright © 2010 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Directory of Open Access Journals (Sweden)
Ilić Dejan
2010-01-01
Full Text Available We introduce the concept of a -compatible mapping to obtain a coupled coincidence point and a coupled point of coincidence for nonlinear contractive mappings in partially ordered metric spaces equipped with -distances. Related coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend, and unify several well-known comparable results in the literature.
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-06-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
International Nuclear Information System (INIS)
Romeo, Francesco; Rega, Giuseppe
2006-01-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Nonlinear Krylov acceleration of reacting flow codes
Energy Technology Data Exchange (ETDEWEB)
Kumar, S.; Rawat, R.; Smith, P.; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz nonlinear...
Nonlinear Microwave Optomechanics
Shevchuk, O.
2017-01-01
The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Got, J. L.; Carrier, A.; Marsan, D.; Amitrano, D.; Jouanne, F.; Hreinsdottir, S.; Vogfjord, K. S.; Villemin, T.; Peltier, A.; Ferrazzini, V.
2016-12-01
Continuous monitoring of seismicity and surface displacement on active volcanoes reveals important features of the eruptive cycle. In this work we analyzed high-quality GPS and earthquake data recorded at Grimsvötn volcano by the Icelandic Meteorological Office during its 2004-2011 inter-eruptive period. GPS data show a characteristic pattern with an initial 2 year-long exponential decay followed by a 3 year-long constant inflation rate surface displacement. We proposed a model with one magma reservoir in a non-linear elastic damaging edifice, with incompressible magma and a constant pressure at the base of the magma conduit. We first modelled seismicity rate and damage as a function of time, and derived simple analytical expressions for the magma reservoir overpressure and the surface displacement as a function of time. We got a very good fit of the seismicity and surface displacement data, by adjusting only three phenomenological parameters. Characteristic time and power strain exhibit maxima from which we infer reference times that split the inter-eruptive period into five phases. After the pressurization phases, damage occurs in a third phase, inducing weakly non-linear variations controlled by the feeding system. During the fourth phase damage dominates the dynamics of the inter-eruptive process and variations becomes more strongly non-linear; reservoir overpressure decreases and magma flow increases. It lasts until the power strain reaches its second maxima, where instability is generalized. This maximum is a physical limit, after which the elasticity laws are no longer valid, earthquakes cluster, cumulative number of earthquakes departs from the model. This fifth phase corresponds to strain localization and plasticity-controlled limit equilibrium ; It ends with rupture and eruption. This mechanical characterization supports mean-term eruption prediction. Comparison with results got from Piton de la Fournaise will be discussed.
Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.
1996-01-01
Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Study of nonlinear resonance effect in Paul trap.
Zhou, Xiaoyu; Xiong, Caiqiao; Zhang, Shuo; Zhang, Ning; Nie, Zongxiu
2013-05-01
In this article, we investigated the nonlinear resonance effect in the Paul trap with a superimposed hexapole field, which was assumed as a perturbation to the quadrupole field. On the basis of the Poincare-Lighthill-Kuo (PLK) perturbation method, ion motional equation, known as nonlinear Mathieu equation (NME) was expressed as the addition of approximation equations in terms of perturbation order. We discussed the frequency characteristics of ion axial-radial (z-r) coupled motion in the nonlinear field, derived the expressions of ion trajectories and nonlinear resonance conditions, and found that the mechanism of nonlinear resonance is similar to the normal resonance. The frequency spectrum of ion motion in nonlinear field includes not only the natural frequency series but also nonlinear introduced frequency series, which provide the driving force for the nonlinear resonance. The nonlinear field and the nonlinear effects are inevitable in practical ion trap experiments. Our method provides better understanding of these nonlinear effects and would be helpful for the instrumentation for ion trap mass spectrometers.
Nonlinear effects in modulated quantum optomechanics
Yin, Tai-Shuang; Lü, Xin-You; Zheng, Li-Li; Wang, Mei; Li, Sha; Wu, Ying
2017-05-01
The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplification. Moreover, the amplified phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir, which ultimately leads to the realization of photon blockade in a weakly coupled OMS. The reached nonlinear quantum regime also allows us to engineer the nonclassical states (e.g., Schrödinger cat states) of the cavity field, which are robust against the phonon noise. This work offers an alternative approach to enhance the quantum nonlinearity of an OMS, which should expand the applications of cavity optomechanics in the quantum realm.
Homogenized description and retrieval method of nonlinear metasurfaces
Liu, Xiaojun; Larouche, Stéphane; Smith, David R.
2018-03-01
A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry
Synchronization of indirectly coupled Lorenz oscillators: An ...
Indian Academy of Sciences (India)
Partial synchronization occurs in a population of chemical oscillators coupled through the concentration of chemical in the surrounding solutions [19]. Two nonlinear chaotic systems coupled indirectly through a common dynamic environment synchronize to in-phase or anti-phase state [20]. The early stages of Alzheimer's ...
Topological horseshoes in travelling waves of discretized nonlinear wave equations
International Nuclear Information System (INIS)
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-01-01
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes
Nonlinear acoustic techniques for landmine detection
Korman, Murray S.; Sabatier, James M.
2004-12-01
Measurements of the top surface vibration of a buried (inert) VS 2.2 anti-tank plastic landmine reveal significant resonances in the frequency range between 80 and 650 Hz. Resonances from measurements of the normal component of the acoustically induced soil surface particle velocity (due to sufficient acoustic-to-seismic coupling) have been used in detection schemes. Since the interface between the top plate and the soil responds nonlinearly to pressure fluctuations, characteristics of landmines, the soil, and the interface are rich in nonlinear physics and allow for a method of buried landmine detection not previously exploited. Tuning curve experiments (revealing ``softening'' and a back-bone curve linear in particle velocity amplitude versus frequency) help characterize the nonlinear resonant behavior of the soil-landmine oscillator. The results appear to exhibit the characteristics of nonlinear mesoscopic elastic behavior, which is explored. When two primary waves f1 and f2 drive the soil over the mine near resonance, a rich spectrum of nonlinearly generated tones is measured with a geophone on the surface over the buried landmine in agreement with Donskoy [SPIE Proc. 3392, 221-217 (1998); 3710, 239-246 (1999)]. In profiling, particular nonlinear tonals can improve the contrast ratio compared to using either primary tone in the spectrum. .
Synchronization Phenomena in Coupled Colpitts Circuits
Directory of Open Access Journals (Sweden)
Ch. K. Volos
2014-11-01
Full Text Available In this work, the case of coupling (bidirectional and unidirectional between two identical nonlinear chaotic circuits via a linear resistor, is studied. The produced dynamical systems have different structure, in regard to other similar works, due to the choice of coupling nodes. As a circuit, a modification of the most well-known nonlinear circuit that can operate in a wide range of radiofrequencies, the Colpitts oscillator, is chosen. The simulation and the experimental results show a variety of dynamical phenomena, such as periodic, quasi-periodic and chaotic behaviors, as well as anti-phase and complete synchronization phenomena, depending on the value of the coupling coefficient.
Ooi, Kelvin J. A.; Tan, Dawn T. H.
2017-10-01
The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Stationary nonlinear Airy beams
International Nuclear Information System (INIS)
Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.
2011-01-01
We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear optics at interfaces
International Nuclear Information System (INIS)
Chen, C.K.
1980-12-01
Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory
International Nuclear Information System (INIS)
Zelenyj, L.M.; Kuznetsova, M.M.
1989-01-01
Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed
Quantum Nonlinear Optics in Optomechanical Nanoscale Waveguides.
Zoubi, Hashem; Hammerer, Klemens
2017-09-22
We show that strong nonlinearities at the few photon level can be achieved in optomechanical nanoscale waveguides. We consider the propagation of photons in cm-scale one-dimensional nanophotonic structures where stimulated Brillouin scattering (SBS) is strongly enhanced by radiation pressure coupling. We introduce a configuration that allows slowing down photons by several orders of magnitude via SBS from sound waves using two pump fields. Slowly propagating photons can then experience strong nonlinear interactions through virtual off-resonant exchange of dispersionless phonons. As a benchmark we identify requirements for achieving a large cross-phase modulation among two counterpropagating photons applicable for photonic quantum gates. Our results indicate that strongly nonlinear quantum optics is possible in continuum optomechanical systems realized in nanophotonic structures.
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Nonlinear Optics and Applications
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Stochastic resonance in biological nonlinear evolution models
Dunkel, Jörn; Hilbert, Stefan; Schimansky-Geier, Lutz; Hänggi, Peter
2004-05-01
We investigate stochastic resonance in the nonlinear, one-dimensional Fisher-Eigen model (FEM), which represents an archetypal model for biological evolution based on a global coupling scheme. In doing so we consider different periodically driven fitness functions which govern the evolution of a biological phenotype population. For the case of a simple harmonic fitness function we are able to derive the exact analytic solution for the asymptotic probability density. A distinct feature of this solution is a phase lag between the driving signal and the linear response of the system. Furthermore, for more complex systems a general perturbation theory (linear response approximation) is put forward. Using the latter approach, we investigate stochastic resonance in terms of the spectral amplification measure for a quadratic, a quartic single-peaked, and for a bistable fitness function. Our analytical results are also compared with those of detailed numerical simulations. Our findings vindicate that stochastic resonance does occur in these nonlinear, globally coupled biological systems.
Nonlinear wave interactions of kinetic sound waves
Directory of Open Access Journals (Sweden)
G. Brodin
2015-08-01
Full Text Available We reconsider the nonlinear resonant interaction between three electrostatic waves in a magnetized plasma. The general coupling coefficients derived from kinetic theory are reduced here to the low-frequency limit. The main contribution to the coupling coefficient we find in this way agrees with the coefficient recently presented in Annales Geophysicae. But we also deduce another contribution which sometimes can be important, and which qualitatively agrees with that of an even more recent paper. We have thus demonstrated how results derived from fluid theory can be improved and generalized by means of kinetic theory. Possible extensions of our results are outlined.
Depression of nonlinearity in decaying isotropic turbulence
International Nuclear Information System (INIS)
Kraichnan, R.H.; Panda, R.
1988-01-01
Simulations of decaying isotropic Navier--Stokes turbulence exhibit depression of the normalized mean-square nonlinear term to 57% of the value for a Gaussianly distributed velocity field with the same instantaneous velocity spectrum. Similar depression is found for dynamical models with random coupling coefficients (modified Betchov models). This suggests that the depression is dynamically generic rather than specifically driven by alignment of velocity and vorticity
Chaotic synchronization of three coupled oscillators with ring connection
Kyprianidis, I M
2003-01-01
We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).
Delay or anticipatory synchronization in one-way coupled systems ...
Indian Academy of Sciences (India)
Abstract. We present a mechanism for the synchronization of one-way coupled nonlinear systems in which the coupling uses a variable delay, that is reset at finite intervals. Here the delay varies in the same way as the system in time and so the coupling function remains constant for the reset interval at the end of which it is ...
Nonlinear Dynamical Analysis for a Plain Bearing
Directory of Open Access Journals (Sweden)
Ali Belhamra
2014-03-01
Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.
International Nuclear Information System (INIS)
Khoroshun, L.P.
1995-01-01
The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero
Probabilistic graphs using coupled random variables
Nelson, Kenric P.; Barbu, Madalina; Scannell, Brian J.
2014-05-01
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic reasoning, but the restrictions reduce the expressive capability of each node making network designs complex. The ability to model coupled random variables using the calculus of nonextensive statistical mechanics provides a neural node design incorporating nonlinear coupling between input states while maintaining the rigor of probabilistic reasoning. A generalization of Bayes rule using the coupled product enables a single node to model correlation between hundreds of random variables. A coupled Markov random field is designed for the inferencing and classification of UCI's MLR `Multiple Features Data Set' such that thousands of linear correlation parameters can be replaced with a single coupling parameter with just a (3%, 4%) reduction in (classification, inference) performance.
Hagedorn, Peter
1982-01-01
Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Propagation of nonlinear reactive contaminants in porous media
Serrano, Sergio E.
2003-08-01
A study on the effect of nonlinear reactions on the space and time distribution of contaminant plumes governed by the advective-dispersive equation in porous media was conducted. Several models of nonlinear reactions were considered: the irreversible nonlinear first-order kinetic sorption model, the nonlinear Freundlich sorption isotherm model, the nonlinear Langmuir sorption isotherm model, and the reversible nonlinear kinetic sorption model. Each of these models was coupled with the advective-dispersive equation with dimensionless concentration and an approximate analytical series solutions was obtained. Comparison between linear and nonlinear plumes indicated that nonlinear reactions may have a significant effect on the shape and spatial distribution of a contaminant at a given time and in certain cases may explain quantitatively the occurrence of scaled (e.g., concentration change while preserving shape), retarded, and nonsymmetric plumes as well as the presence of back tails and sharp front ends usually observed in the field. By adopting a nonlinear model of contaminant migration a more realistic representation of contaminant propagation is possible than that obtained with a linear model.
Modulational instability of coupled waves
International Nuclear Information System (INIS)
McKinstrie, C.J.; Bingham, R.
1989-01-01
The collinear propagation of an arbitrary number of finite-amplitude waves is modeled by a system of coupled nonlinear Schroedinger equations; one equation for each complex wave amplitude. In general, the waves are modulationally unstable with a maximal growth rate larger than the modulational growth rate of any wave alone. Moreover, waves that are modulationally stable by themselves can be driven unstable by the nonlinear coupling. The general theory is then applied to the relativistic modulational instability of two laser beams in a beat-wave accelerator. For parameters typical of a proposed beat-wave accelerator, this instability can seriously distort the incident laser pulse shapes on the particle-acceleration time scale, with detrimental consequences for particle acceleration
Hadron–Quark Combustion as a Nonlinear, Dynamical System
Directory of Open Access Journals (Sweden)
Amir Ouyed
2018-03-01
Full Text Available The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.
Hadron–Quark Combustion as a Nonlinear, Dynamical System
Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth
2018-03-01
The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.
Probing nonlinear electrodynamics in slowly rotating spacetimes through neutrino astrophysics
Cuesta, Herman J. Mosquera; Lambiase, Gaetano; Pereira, Jonas P.
2017-01-01
Huge electromagnetic fields are known to be present during the late stages of the dynamics of supernovae. Thus, when dealing with electrodynamics in this context, the possibility may arise to probe nonlinear theories (generalizations of the Maxwellian electromagnetism). We firstly solve Einstein field equations minimally coupled to an arbitrary (current-free) nonlinear Lagrangian of electrodynamics (NLED) in the slow rotation regime $a\\ll M$ (black hole's mass), up to first order in $a/M$. We...
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
parametric nonlinear quasivariational inequalities
Directory of Open Access Journals (Sweden)
Zeqing Liu
2005-01-01
uniqueness results and sensitivity analysis of solutions are also established for the system of generalized nonlinear parametric quasivariational inequalities and some convergence results of iterative sequence generated by the algorithm with errors are proved.
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE...... of a proposed NSE system with high dynamic performance. The goal of the work is to achieve a state-of-the art transient time of 10 µs. In order to produce the arbitrary nonlinear curve, the exponential function of a typical diode is used, but the diode can be replaced by other nonlinear curve reference...... simulation of nonlinear source systems with higher output power. In this work, a module will consist of two fundamental units: an isolated power supply and an NSE. The isolated power supply has to possess a very low circuit input-to-output capacitance (very low Cio) in order to reduce the effect...
2013-01-01
filter, Bayesian decision theory, Generalized Likelihood Ratio Test (GLRT), and constant false alarm rate ( CFAR ) processing (31). Once the...Abbreviations, and Acronyms CFAR constant false alarm rate CNR cognitive nonlinear radar EM electromagnetic FCC Federal Communications Comission
Nonlinear Optical Terahertz Technology
National Aeronautics and Space Administration — We develop a new approach to generation of THz radiation. Our method relies on mixing two optical frequency beams in a nonlinear crystalline Whispering Gallery Mode...
Nonlinear differential equations
Struble, Raimond A
2017-01-01
Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.
Nonlinear ambipolar diffusion waves
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T.; Rowlands, G.
1985-07-01
The evolution of a plasma perturbation in a neutral gas is considered using the ambipolar diffusion approximation. A nonlinear diffusion equation is derived and, in the one-dimensional case, exact solutions of shock type are obtained.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Crossing a Nonlinear Resonance
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Crossing a Nonlinear Resonance: Adiabatic Invariants and the Melnikov-Arnold Integral. Sudhir R Jain. General Article Volume 19 Issue 9 September 2014 pp 797-813 ...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...
Time History Forced Response in Nonlinear Mechanical Systems
Directory of Open Access Journals (Sweden)
Magnevall M.
2012-07-01
Full Text Available A formulation of a digital filter method for computing the forced response of a linear MDOF mechanical system is proposed. It is shown how aliasing error effects can be avoided at the expense of a bias error. The bias error is however completely known and it is system independent, as it only depends on the sampling frequency used. The mechanical system is described by its modal parameters, poles and residues. The method is extended to include non-linear elements. A toolbox in MATLAB has been created where nonlinear elements with and without memory can be treated, as well as system described by coupled non-linear equations.
Symbolic computation of nonlinear wave interactions on MACSYMA
International Nuclear Information System (INIS)
Bers, A.; Kulp, J.L.; Karney, C.F.F.
1976-01-01
In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Asadi, Reza; Ouyang, Zhengbiao
2018-03-01
A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.
Fundamentals of nonlinear optical materials
Indian Academy of Sciences (India)
Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.
Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.
Kourakis, I; Shukla, P K
2005-07-01
We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.
Nguyen, Nhan; Ting, Eric
2018-01-01
This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
NONLINEAR TIDES IN CLOSE BINARY SYSTEMS
International Nuclear Information System (INIS)
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-01-01
; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.
International Nuclear Information System (INIS)
Shen Yuanrang
2011-01-01
This article presents a brief introduction to the birth and early investigations of nonlinear optics, such as second harmonic generation,sum and difference frequency generation, stimulated Raman scattering,and self-action of light etc. Several important research achievements and applications of nonlinear optics are presented as well, including nonlinear optical spectroscopy, phase conjugation and adaptive optics, coherent nonlinear optics, and high-order harmonic generation. In the end, current and future research topics in nonlinear optics are summarized. (authors)
Artificial muscle using nonlinear elastomers
Ratna, Banahalli
2002-03-01
Anisotropic freestanding films or fibers of nematic elastomers from laterally attached side-chain polymers show muscle-like mechanical properties. The orientational order of the liquid crystal side groups imposes a conformational anisotropy in the polymer backbone. When a large change in the order parameter occurs, as at the nematic-isotropic phase transition, there is a concomitant loss of order in the backbone which results in a contraction of the film in the direction of the director orientation. The crosslinked network imposes a symmetry-breaking field on the nematic and drives the nematic-isotropic transition towards a critical point with the application of external stress. Isostrain studies on these nonlinear elastomers, show that there are large deviations from ideal classical rubber elasticity and the contributions from total internal energy to the elastic restoring force cannot be ignored. The liquid crystal elastomers exhibiting anisoptopic contraction/extension coupled with a graded strain response to an applied external stimulus provide an excellent framework for mimicking muscular action. Liquid crystal elastomers by their very chemical nature have a number of ‘handles’ such as the liquid crystalline phase range, density of crosslinking, flexibility of the backbone, coupling between the backbone and the mesogen and the coupling between the mesogen and the external stimulus, that can be tuned to optimize the mechanical properties. We have demonstrated actuation in nematic elastomers under thermal and optical stimuli. We have been able to dope the elastomers with dyes to make them optically active. We have also doped them with carbon nanotubes in order to increase the thermal and electrical conductivity of the elastomer.
Coupled DM Heating in SCDEW Cosmologies
Directory of Open Access Journals (Sweden)
Silvio Bonometto
2017-08-01
Full Text Available Strongly-Coupled Dark Energy plus Warm dark matter (SCDEW cosmologies admit the stationary presence of ∼1% of coupled-DM and DE, since inflationary reheating. Coupled-DM fluctuations therefore grow up to non-linearity even in the early radiative expansion. Such early non-linear stages are modelized here through the evolution of a top-hat density enhancement, reaching an early virial balance when the coupled-DM density contrast is just 25–26, and the DM density enhancement is ∼10 % of the total density. During the time needed to settle in virial equilibrium, the virial balance conditions, however, continue to modify, so that “virialized” lumps undergo a complete evaporation. Here, we outline that DM particles processed by overdensities preserve a fraction of their virial momentum. Although fully non-relativistic, the resulting velocities (moderately affect the fluctuation dynamics over greater scales, entering the horizon later on.
Nonlinear self-duality and supergravity
International Nuclear Information System (INIS)
Kuzenko, Sergei M.; McCarthy, Shane A.
2003-01-01
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N=1 supergravity, for both the old minimal and the new minimal versions of N=1 supergravity. We derive the self-duality equation, which has to be satisfied by the action functional of any U(1) duality invariant model of a massless vector multiplet, and construct a family of self-dual nonlinear models. This family includes a curved superspace extension of the N=1 super Born-Infeld action. The supercurrent and supertrace in such models are proved to be duality invariant. The most interesting and unexpected result is that the requirement of nonlinear self-duality yields nontrivial couplings of the vector multiplet to Kaehler sigma models. We explicitly derive the couplings to general Kaehler sigma models in the case when the matter chiral multiplets are inert under the duality rotations, and more specifically to the dilaton-axion chiral multiplet when the group of duality rotations is enhanced to SL(2,R). (author)
Nonlinear optical response in narrow graphene nanoribbons
Karimi, Farhad; Knezevic, Irena
We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...... discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term...
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304...
Nonclassical statistics of intracavity coupled chi((2)) waveguides: The quantum optical dimer
DEFF Research Database (Denmark)
Bache, Morten; Gaididei, Yuri Borisovich; Christiansen, Peter Leth
2003-01-01
A model is proposed where two chi((2)) nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives...
Single-photon all-optical switching using coupled microring resonators
Indian Academy of Sciences (India)
Abstract. We study the nonlinear phase response of a microring resonator coupled to a bus waveguide and the use of this nonlinear phase shift to store information in the microring resonator and enhance the switching characteristics of a Mach–Zehnder interferometer (MZI). By introducing coupling between adjacent ...
Mohamadou, A.; Tatsing, P. H.; Latchio Tiofack, C. G.; Tabi, C. B.; Kofane, T. C.
2014-11-01
We are motivated by recent studies in medium formed by two tunnel-coupled waveguides. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. We present an investigation of the gain spectrum permitting modulation instability in the nonlinear optical coupler with a negative-index metamaterial channel whose non-linear response includes third- and fifth-order terms. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective cubic-quintic nonlinearity. We emphasize the influence of higher order nonlinear terms, over the MI phenomena, and the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near-zero dispersion regime where higher order linear dispersive effects emerge. Our results show that the MI gain spectra consist of multiple spectral region which are symmetric to the zero point. Moreover, some spectra have a high cut-off frequency but a narrow spectral width, which is obviously beneficial to the generation of high-repetition-rate pulse trains.
Kernel Method for Nonlinear Granger Causality
Marinazzo, Daniele; Pellicoro, Mario; Stramaglia, Sebastiano
2008-04-01
Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.
Minimum Dissipation Principle in Nonlinear Transport
Directory of Open Access Journals (Sweden)
Giorgio Sonnino
2015-10-01
Full Text Available We extend Onsager’s minimum dissipation principle to stationary states that are only subject to local equilibrium constraints, even when the transport coefficients depend on the thermodynamic forces. Crucial to this generalization is a decomposition of the thermodynamic forces into those that are held fixed by the boundary conditions and the subspace that is orthogonal with respect to the metric defined by the transport coefficients. We are then able to apply Onsager and Machlup’s proof to the second set of forces. As an example, we consider two-dimensional nonlinear diffusion coupled to two reservoirs at different temperatures. Our extension differs from that of Bertini et al. in that we assume microscopic irreversibility, and we allow a nonlinear dependence of the fluxes on the forces.
Nonlinear continuum mechanics and large inelastic deformations
Dimitrienko, Yuriy I
2010-01-01
This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...
Non-linear realization of the Virasoro-Kac-Moody algebra and the anomalies
International Nuclear Information System (INIS)
Aoyama, S.
1988-01-01
The non-linear realization of the Virasoro algebra x Kac-Moody algebra will be studied. We will calculate the Ricci tensor of the relevant Kaehler manifold to show a new vacuum structure for this coupled algebra. (orig.)
Dovgiy, A. A.
2014-12-01
The modulation instability is analytically investigated in a zigzag array of tunnel-coupled optical waveguides with alternating refractive indices and Kerr nonlinearity. Particular solutions to a system of coupled nonlinear equations are found. They describe the propagation of electromagnetic waves that are uniform along the waveguide and their instability is studied. It is shown that the coupling coefficient between the waveguides, which are non-nearest neighbours, has a significant effect on the instability of the waves in question. When the coupling coefficient exceeds a certain threshold, the modulation instability disappears regardless of the radiation power. The influence of the ratio of the wave amplitudes in adjacent waveguides to the instability of the particular solutions is studied. Different variants of the nonlinear response in waveguides are considered. The studies performed present a new unusual type of the modulation instability in nonlinear periodic systems.
Dispersion Effects in Nonlinear Light Propagation in 1-D Fiber Gratings
National Research Council Canada - National Science Library
Martel, Carlos
2003-01-01
...: The contractor will investigate the use of the so-called nonlinear coupled mode equations (NLCME) to obtain approximate solutions of Maxwells equations for light propagation in periodic optical fiber structures...
Energy Technology Data Exchange (ETDEWEB)
Dovgiy, A A [National Research Nuclear University ' ' MEPhI' ' (Russian Federation)
2014-12-31
The modulation instability is analytically investigated in a zigzag array of tunnel-coupled optical waveguides with alternating refractive indices and Kerr nonlinearity. Particular solutions to a system of coupled nonlinear equations are found. They describe the propagation of electromagnetic waves that are uniform along the waveguide and their instability is studied. It is shown that the coupling coefficient between the waveguides, which are non-nearest neighbours, has a significant effect on the instability of the waves in question. When the coupling coefficient exceeds a certain threshold, the modulation instability disappears regardless of the radiation power. The influence of the ratio of the wave amplitudes in adjacent waveguides to the instability of the particular solutions is studied. Different variants of the nonlinear response in waveguides are considered. The studies performed present a new unusual type of the modulation instability in nonlinear periodic systems. (metamaterials)
Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R.
2016-01-01
We apply the pseudospectral discretization approach to nonlinear delay models described by delay differential equations, renewal equations, or systems of coupled renewal equations and delay differential equations. The aim is to derive ordinary differential equations and to investigate the stability
E Heebner, John; Boyd, Robert W; Park, Q-Han
2002-03-01
We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which can be described by a generalized nonlinear Schrodinger equation.
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
Electrical characteristics for capacitively coupled radio frequency ...
Indian Academy of Sciences (India)
MURAT TANISLI
2017-08-16
Aug 16, 2017 ... cally parallel. Here, the RF voltage is usually applied to one of the two electrodes and the other electrode is used for grounding. The plasma sheath and bulk plasma ... Nonlinear plasma series resonance (PSR) effect ... Equivalent circuit for the capacitively coupled RF discharge of the homogenous model.
Kundt spacetimes minimally coupled to scalar field
Energy Technology Data Exchange (ETDEWEB)
Tahamtan, T. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic); Astronomical Institute, Czech Academy of Sciences, Prague (Czech Republic); Svitek, O. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic)
2017-06-15
We derive an exact solution belonging to the Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations. (orig.)
Theory and simulation of laser plasma coupling
International Nuclear Information System (INIS)
Kruer, W.L.
1979-01-01
The theory and simulation of these coupling processes are considered. Particular emphasis is given to their nonlinear evolution. First a brief introduction to computer simulation of plasmas using particle codes is given. Then the absorption of light via the generation of plasma waves is considered, followed by a discussion of stimulated scattering of intense light. Finally these calculations are compared with experimental results
Synchronization of coupled nonidentical multidelay feedback systems
International Nuclear Information System (INIS)
Hoang, Thang Manh; Nakagawa, Masahiro
2007-01-01
We present the lag synchronization of coupled nonidentical multidelay feedback systems, in which the synchronization signal is the sum of nonlinearly transformed components of delayed state variable. The sufficient condition for synchronization is considered by the Krasovskii-Lyapunov theory. The specific examples will demonstrate and verify the effectiveness of the proposed model
Gorban, A. N.; Karlin, I. V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
Abstract. We define a nonlinear model for fractional relaxation phenomena. We use ε-expansion method to analyse this model. By studying the fundamental solutions of this model we find that when t → 0 the model exhibits a fast decay rate and when t → ∞ the model exhibits a power-law decay. By analysing the frequency ...
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Directory of Open Access Journals (Sweden)
Jaydeep Jesur
2000-01-01
and features are added such a way that it can be also used for design of nonlinear control systems to achieve desired performance. It is very simple to learn this tool. One can easily use it with preliminary knowledge of DF and PPT methods.
Nonlinear collisionless magnetic reconnection
Ottaviani, M.; Porcelli, F.
1993-12-01
Collisionless magnetic reconnection in regimes where the mode structure is characterized by global convection cells is found to exhibit a quasiexplosive time behavior in the early nonlinear stage where the fluid displacement is smaller than the equilibrium scale length. This process is accompanied by the formation of a current density sublayer narrower than the skin depth. This sublayer keeps shrinking with time.
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Nonlinear modes of the tensor Dirac equation and CPT violation
Reifler, Frank J.; Morris, Randall D.
1993-01-01
Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.
Iterative analysis of concrete gravity dam-nonlinear foundation ...
African Journals Online (AJOL)
This paper deals with finite element analysis of the soil–structure systems considering the coupled effect of elastic structure and materially nonlinear soil. The equations of motion of both soil and structure have been expressed in terms of displacement variable. The structure and the soil domain are treated as two separate ...
Flexible Aircraft Gust Load Alleviation with Incremental Nonlinear Dynamic Inversion
Wang, X.; van Kampen, E.; Chu, Q.; De Breuker, R.
2018-01-01
In this paper, an Incremental Nonlinear Dynamic Inversion (INDI) controller is
developed for the flexible aircraft gust load alleviation (GLA) problem. First, a flexible aircraft model captures both inertia and aerodynamic coupling effects between flight dynamics and structural vibration
Viscosity solutions of fully nonlinear functional parabolic PDE
Directory of Open Access Journals (Sweden)
Liu Wei-an
2005-01-01
Full Text Available By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of ...
Is DNA a nonlinear dynamical system where solitary conformational ...
Indian Academy of Sciences (India)
Unknown
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the ..... nucleotides; K is the coupling constant along each strand;. R0 is the radius of DNA; a is .... Let us note that the system of equations (12)–(17) can be divided into two independent ...
Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium.
Lee, Wonjung; Kovačič, Gregor; Cai, David
2013-02-26
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave-like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig-Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber-frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves.
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua
2016-11-14
In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
Proceedings of the workshop on nonlinear MHD and extended MHD
International Nuclear Information System (INIS)
1998-01-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database
Electrodynamics: a consequence of nonlinear realizations of the Lorentz group
International Nuclear Information System (INIS)
Dalton, B.
1981-01-01
Extensions from the representations of the Lorentz group to include local nonlinear diagonal transformations is sufficient to generate, via the covariant derivative, the interaction of minimal coupling. These diagonal realizations are characterized by six functions phisub(i) which must satisfy a system of transformation equations. Inequivalent categories of solutions for the phisub(i) give rise to different electromagnetic fields. The Dirac monopole and Coulomb potentials follow directly from two different categories of these nonlinear realizations. Within this theory, charge becomes simply the nonlinear counterpart of intrinsic spin for a particular nonlinear realization of the Lorentz group. Charge is thus placed on equal footing with intrinsic spin in the sense that both phenomena can be described as consequences of our space-time symmetry. Other solutions for the six phisub(i) exist, including a spinor. The possibility that with these other solutions, these realizations could represent some other basic properties of elementary particles is discussed. (author)
Proceedings of the workshop on nonlinear MHD and extended MHD
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
Linear and non-linear optics of condensed matter
International Nuclear Information System (INIS)
McLean, T.P.
1977-01-01
Part I - Linear optics: 1. General introduction. 2. Frequency dependence of epsilon(ω, k vector). 3. Wave-vector dependence of epsilon(ω, k vector). 4. Tensor character of epsilon(ω, k vector). Part II - Non-linear optics: 5. Introduction. 6. A classical theory of non-linear response in one dimension. 7. The generalization to three dimensions. 8. General properties of the polarizability tensors. 9. The phase-matching condition. 10. Propagation in a non-linear dielectric. 11. Second harmonic generation. 12. Coupling of three waves. 13. Materials and their non-linearities. 14. Processes involving energy exchange with the medium. 15. Two-photon absorption. 16. Stimulated Raman effect. 17. Electro-optic effects. 18. Limitations of the approach presented here. (author)
Weak nonlinear coupling between epicyclic modes in slender tori
Czech Academy of Sciences Publication Activity Database
Horák, Jiří
2008-01-01
Roč. 486, č. 1 (2008), s. 1-8 ISSN 0004-6361 R&D Projects: GA ČR GP205/06/P415; GA MŠk(CZ) LC06014 Institutional research plan: CEZ:AV0Z10030501 Keywords : accretion-disks * black hole physics * solar system formation Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 4.153, year: 2008
Solitons and periodic solutions to a couple of fractional nonlinear ...
Indian Academy of Sciences (India)
in engineering science and theoretical physics with fractional evolution. They are foam drainage equation and Klein–Gordon equation, the latter of which is considered in (2+1) dimensions. Foam drainage is the flow of liquid through foam when the effects of capillarity and gravity are taken into consideration. The physics of ...
Solitons and periodic solutions to a couple of fractional nonlinear ...
Indian Academy of Sciences (India)
2014-02-26
Feb 26, 2014 ... Home; Journals; Pramana – Journal of Physics; Volume 82; Issue 3 ... First integral method; solitons; foam drainage equation; Klein–Gordon equation. ... East of Guilan, University of Guilan, Rudsar, Iran; Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran ...
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
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 ...
UV Nano-Lights: Nonlinear Quantum Dot-Plasmon Coupling
2014-08-01
RESPONSIBLE PERSON Kenneth Caster , Ph.D. a. REPORT U b. ABSTRACT U c. THIS PAGE U 19b. TELEPHONE NUMBER (Include area code) +81-42-511-2000...INVESTIGATOR Associate Professor Eric Waclawik, e.waclawik@qut.edu.au, +61-7-3138-2579 GOVERNMENT PROGRAM MANAGER Dr Kenneth Caster , kenneth.caster
Experiments with Geometric Non-Linear Coupling for Analytical Validation
2010-03-01
qualification tests are applied to the joined-wing models. 31 Figure 3.28: Material Dogbone For all the FE models, several versions of Nastran were...used interchangeably: MD Nastran V2007.0, MD Nastran V2008.0, and NX Nastran V5.0. MD Nastran V2007.0 was the primary solver for most analyses. For all...linear solution would only converge to a 15 lb load; all solution attempts above this load failed. Nastran had trouble solving this FE model because of
UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
intense electric fields generated by the localised surface plasmon absorption at the Au nanoparticle interface. it was found that a significant improvement...ZnO nanocrystal growth at their surfaces. These small Au nanoparticle seeds thereby behaved as crystallisation ‘catalysts’. Large Au seeds (~9 nm...intense electric fields generated by the localised surface plasmon absorption at the Au nanoparticle interface. When measured, it was found that a
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
Author Affiliations. Li Zhang1 Shutang Liu2 Chenglong Yu3. Business School, Shandong University of Political Science and Law, Jinan 250014, China; College of Control Science and Engineering, Shandong University, Jinan 250061, China; Department of Mathematics, Statistics and Computer Science, University of Illinois ...
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
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.
Solitons and periodic solutions to a couple of fractional nonlinear ...
Indian Academy of Sciences (India)
KGE), on the other hand, is a relativistic field equation for scalar particles (spin-0). KGE is a relativistic generalization of the well-known. Schrödinger's equation. While there are other relativistic wave equations, KGE has been the most frequently ...
On nonlinear Fourier transform: towards the nonlinear superposition
Saksida, Pavle
2017-01-01
In the paper we consider the nonlinear Fourier transform associated to the AKNSZS systems. In particular, we discuss the construction of the nonlinear Fourier modes of this transform by means of a perturbation scheme. The linearization of the AKNS-ZS nonlinear Fourier transform is the usual, linear Fourier transform and the linearization of a nonlinear Fourier mode of frequency d is the linear Fourier mode of the same frequency. We show that the first non-trivial term in the perturbation expression of any nonlinear Fourier mode is given by the dilogarithm function.
Enhancement of optical nonlinearities with stationary light
DEFF Research Database (Denmark)
Iakoupov, Ivan
Stationary light arises in atomic ensembles with certain energy level configurations, when two counter-propagating classical drives (lasers) are applied. Probe light coupled to a different energy level transition than the classical drives can be completely stopped, while still retaining its light...... character. We will be interested in the regime of stationary light, where the probe light still propagates through the atomic ensemble, but extremely slowly. In other words, probe field has a very low group velocity, which increases its interaction time with any optical nonlinearity. The enhancement...
Asymmetrical transverse structures in nonlinear interferometers
Romanov, O G
2003-01-01
The work presents a novel type of optical instability, which leads to the spontaneous formation of a stationary or pulsating asymmetrical structure in the problem of interaction between two counterpropagating waves in a ring cavity with Kerr-like nonlinearity. Linear stability analysis of interferometer transmission stationary states enabled: (1) to mark out typical bifurcations for this system: self- and cross-modulational instabilities, (2) to determine the range of parameters for which the symmetry breaking of transverse structures and complex temporal behaviour of the light field could be observed. The predictions of linear stability analysis have been verified with numerical modelling of coupled-modes equations.
Nonlinearity, Conservation Law and Shocks
Indian Academy of Sciences (India)
Nonlinearity, Conservation Law and Shocks. Part I : Genuine Nonlinearity and Discontinuous Solutions. Phoolan Prasad is with the. Department of. Mathematics, Indian. Institute of Science and has been working in the area of nonlinear waves and hyperbolic partial differential equations. He is deeply interested in.
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...... breathing of a single-cycle THz pulse in a semiconductor....
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based o...
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
The Optimal Income Taxation of Couples
DEFF Research Database (Denmark)
Kleven, Henrik Jacobsen; Kreiner, Claus Thustrup; Saez, Emmanuel
2009-01-01
This paper analyzes the general nonlinear optimal income tax for couples, a multidimensional screening problem. Each couple consists of a primary earner who always participates in the labor market, but makes an hours-of-work choice, and a secondary earner who chooses whether or not to work....... If second-earner participation is a signal of the couple being better (worse) off, we prove that optimal tax schemes display a positive tax (subsidy) on secondary earnings and that the tax (subsidy) on secondary earnings decreases with primary earnings and converges to zero asymptotically. We present...
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
Here we introduce a model of parametrically coupled logistic maps on a one- dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled.
Synchronization of two coupled fractional-order chaotic oscillators
International Nuclear Information System (INIS)
Gao Xin; Yu, Juebang
2005-01-01
The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, the synchronization of two coupled nonlinear fractional order chaotic oscillators is numerically demonstrated using the master-slave synchronization scheme. It is shown that fractional-order chaotic oscillators can be synchronized with appropriate coupling strength
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear terahertz superconducting plasmonics
Energy Technology Data Exchange (ETDEWEB)
Wu, Jingbo; Liang, Lanju; Jin, Biaobing, E-mail: bbjin@nju.edu.cn, E-mail: tonouchi@ile.osaka-u.ac.jp, E-mail: phwu@nju.edu.cn; Kang, Lin; Xu, Weiwei; Chen, Jian; Wu, Peiheng, E-mail: bbjin@nju.edu.cn, E-mail: tonouchi@ile.osaka-u.ac.jp, E-mail: phwu@nju.edu.cn [Research Institute of Superconductor Electronics (RISE), School of Electronic Science and Engineering, Nanjing University, Nanjing 210093 (China); Zhang, Caihong; Kawayama, Iwao; Murakami, Hironaru; Tonouchi, Masayoshi, E-mail: bbjin@nju.edu.cn, E-mail: tonouchi@ile.osaka-u.ac.jp, E-mail: phwu@nju.edu.cn [Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka 565-0871 (Japan); Wang, Huabing [Research Institute of Superconductor Electronics (RISE), School of Electronic Science and Engineering, Nanjing University, Nanjing 210093 (China); National Institute for Materials Science, Tsukuba 305-0047 (Japan)
2014-10-20
Nonlinear terahertz (THz) transmission through subwavelength hole array in superconducting niobium nitride (NbN) film is experimentally investigated using intense THz pulses. The good agreement between the measurement and numerical simulations indicates that the field strength dependent transmission mainly arises from the nonlinear properties of the superconducting film. Under weak THz pulses, the transmission peak can be tuned over a frequency range of 145 GHz which is attributed to the high kinetic inductance of 50 nm-thick NbN film. Utilizing the THz pump-THz probe spectroscopy, we study the dynamic process of transmission spectra and demonstrate that the transition time of such superconducting plasmonic device is within 5 ps.
Essentials of nonlinear optics
Murti, Y V G S
2014-01-01
Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.
Van Leeuwen, Peter Jan; Reich, Sebastian
2015-01-01
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Nonlinear (Anharmonic Casimir Oscillator
Directory of Open Access Journals (Sweden)
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
Nonlinear chiral transport phenomena
Chen, Jiunn-Wei; Ishii, Takeaki; Pu, Shi; Yamamoto, Naoki
2016-06-01
We study the nonlinear responses of relativistic chiral matter to the external fields such as the electric field E , gradients of temperature and chemical potential, ∇T and ∇μ . Using the kinetic theory with Berry curvature corrections under the relaxation time approximation, we compute the transport coefficients of possible new electric currents that are forbidden in usual chirally symmetric matter but are allowed in chirally asymmetric matter by parity. In particular, we find a new type of electric current proportional to ∇μ ×E due to the interplay between the effects of the Berry curvature and collisions. We also derive an analog of the "Wiedemann-Franz" law specific for anomalous nonlinear transport in relativistic chiral matter.
The forced nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
Nonlinear gyrokinetic tokamak physics
International Nuclear Information System (INIS)
Brizard, A.J.
1990-01-01
The gyrokinetic reduced description of low-frequency and small-perpendicular-wavelength nonlinear tokamak dynamics is presented in three different versions: the reduced dynamical description of test particles moving in electromagnetic fields; the reduced gyrokinetic description of the self-consistent interaction of particles and fields through the Maxwell-Vlasov equations; and the reduced description of nonlinear fluid motion. The unperturbed tokamak plasma is described in terms of a noncanonical Hamiltonian guiding-center theory. The unperturbed guiding-center tokamak plasma is then perturbed by gyrokinetic electromagnetic fields and consequently the perturbed guiding-center dynamical system acquires new gyrophase dependence. The perturbation analysis that follows makes extensive use of Lie-transform perturbation techniques. Because the electromagnetic perturbations affect both the Hamiltonian and the Poisson-bracket structure, the Phase-space Lagrangian Lie perturbation method is used. The description of the reduced test-particle dynamics is given in terms of a non-canonical Hamiltonian gyrocenter theory. The description of the reduced kinetic dynamics is concerned with the self consistent response of the guiding-center plasma and is described in terms of the nonlinear gyrokinetic Maxwell-Vlasov equations. It is also shown that the gyrokinetic Maxwell-Vlasov system possesses a gyrokinetic energy adiabatic invariant and that, in both the linear and nonlinear (quadratic) approximations, the corresponding energy invariants are exact. The description of the reduced fluid dynamics is concerned with the derivation of a closed set of reduced fluid equations. Three generations of reduced fluid models are presented: the reduced MHD equations; the reduced FLR-MHD equations; and the gyrofluid equations
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
99.8 % of the power from the fundamental mode to a specific HOM in the custom designed fiber. Furthermore, it is demonstrated that stable propagation in the considered fiber is possible, without deterioration from mode coupling. Finally, modulation instability and multiple FWM signal and idler lines......The nonlinear process of four-wave mixing (FWM) enables coupling of energy between wavelengths. This is useful for both optical amplification and wavelength conversion. A crucial prerequisite for the process is phase matching. This PhD project investigates how higher order modes (HOMs) in fibers...... can be used as an additional degree of freedom to fulfill this phase matching requirement. The design of a specialty few moded fiber is discussed. This fiber allows for FWM between a pump in the Ytterbium gain region with a signal at telecommunication wavelengths, hereby generating a new wavelength...
Nonlinear energy loss of highly charged heavy ions
International Nuclear Information System (INIS)
Zwicknagel, G.Guenter.
2000-01-01
For slow, highly charged heavy ions strong coupling effects in the energy transfer from the projectile-ion to an electron target plasma become important. A theoretical description of this nonlinear ion stopping has to go beyond the standard approaches like the dielectric linear response or the binary collision model which are strictly valid only at weak ion-target coupling. Here we outline an improved treatment which is based on a suitable combination of binary collision and linear response contributions. As has been verified for isotropic, nonmagnetized electron plasmas by comparison with simulations, this approach well reproduces the essential features of nonlinear stopping up to moderate coupling strength. Its extension to anisotropic, magnetized electron plasmas basically involves the fully numerical determination of the momentum and energy transfer in binary ion-electron collisions in the presence of a magnetic field. First results of such calculations are presented and discussed
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Finite-temperature Casimir effect in the presence of nonlinear dielectrics
DEFF Research Database (Denmark)
Kheirandish, Fardin; Amooghorban, Ehsan; Soltani, Morteza
2011-01-01
Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupl......Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations...
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening....../softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples...
Nonlinear flow response of soft hair beds
Alvarado, José
2017-11-01
We are hairy inside: beds of passive fibers anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. Such hairs are soft enough to deform in response to stresses from fluid flows. Fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem which is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear- driven Stokes flows. We characterize this system with a theoretical model which accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers toward the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter which controls nonlinear behavior. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps. J.A. acknowledges support the U. S. Army Research Office under Grant Number W911NF-14-1-0396.
Nonlinear dynamics of two-phase flow
International Nuclear Information System (INIS)
Rizwan-uddin
1986-01-01
Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques
Measurement of nonlinear refractive index and ionization rates in air using a wavefront sensor.
Schwarz, Jens; Rambo, Patrick; Kimmel, Mark; Atherton, Briggs
2012-04-09
A wavefront sensor has been used to measure the Kerr nonlinear focal shift of a high intensity ultrashort pulse beam in a focusing beam geometry while accounting for the effects of plasma-defocusing. It is shown that plasma-defocusing plays a major role in the nonlinear focusing dynamics and that measurements of Kerr nonlinearity and ionization are coupled. Furthermore, this coupled effect leads to a novel way that measures the laser ionization rates in air under atmospheric conditions as well as Kerr nonlinearity. The measured nonlinear index n₂ compares well with values found in the literature and the measured ionization rates could be successfully benchmarked to the model developed by Perelomov, Popov, and Terentev (PPT model) [Sov. Phys. JETP 50, 1393 (1966)].