Energy Technology Data Exchange (ETDEWEB)
Chandra, J; Scott, A C
1983-01-01
Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.
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
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Lie Algebras for Constructing Nonlinear Integrable Couplings
International Nuclear Information System (INIS)
Zhang Yufeng
2011-01-01
Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ) hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their Hamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations. (general)
Nonlinear coupled Alfven and gravitational waves
International Nuclear Information System (INIS)
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
Nonlinear coupling of kink modes in Tokamaks
International Nuclear Information System (INIS)
Dagazian, R.Y.
1975-07-01
The m = 2, n = 1 kink mode is shown to be capable of destabilizing the m = 1, n = 1 internal kink. A nonlinear Lagrangian theory is developed for the coupling of modes of different pitch, and it is applied to the interaction of these modes. The coupling to the m = 2 mode provides sufficient additional destabilization to the internal mode to permit it to account even quantitatively (where it had failed when considered by itself) for many of the features of the disruptive instability. (U.S.)
Radiation from nonlinear coupling of plasma waves
International Nuclear Information System (INIS)
Fung, S.F.
1986-01-01
The author examines the generation of electromagnetic radiation by nonlinear resonant interactions of plasma waves in a cold, uniformly magnetized plasma. In particular, he considers the up-conversion of two electrostatic wave packets colliding to produce high frequency electromagnetic radiation. Efficient conversion of electrostatic to electromagnetic wave energy occurs when the pump amplitudes approach and exceed the pump depletion threshold. Results from the inverse scattering transform analysis of the three-wave interaction equations are applied. When the wave packets are initially separated, the fully nonlinear set of coupling equations, which describe the evolution of the wave packets, can be reduced to three separate eigenvalue problems; each can be considered as a scattering problem, analogous to eh Schroedinger equation. In the scattering space, the wave packet profiles act as the scattering potentials. When the wavepacket areas approach (or exceed) π/2, the wave functions are localized (bound states) and the scattering potentials are said to contain solitons. Exchange of solitons occurs during the interaction. The transfer of solitons from the pump waves to the electromagnetic wave leads to pump depletion and the production of strong radiation. The emission of radio waves is considered by the coupling of two upper-hybrid branch wave packets, and an upper-hybrid and a lower hybrid branch wave packet
Nonlinear wave coupling in a warm plasma in the fluid
International Nuclear Information System (INIS)
Malara, F.; Veltri, P.
1984-01-01
The general expression for nonlinear coupling between plasma modes is obtained. The nonlinear conductivity tensor is then calculated by means of the two-fluid plasma description taking into account the thermal pressure effects
Directory of Open Access Journals (Sweden)
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
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.
Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
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
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
We provide a systematic analysis of a prototypical nonlinear oscillator ... recently, a number of nonlinear variants have been explored, like split-ring resonator chain .... Note that these solutions are valid for any value of ǫ (and hence δ) including ǫ ..... [16] M Abramowitz and I A Stegun, Handbook of mathematical functions ...
Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems
International Nuclear Information System (INIS)
Zhou Jin; Lu Junan; Wu Xiaoqun
2007-01-01
To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems
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.
The nonlinear dynamics of a coupled fission system
International Nuclear Information System (INIS)
Bilanovic, Z.; Harms, A.A.
1993-01-01
The dynamic properties of a nonlinear and in situ vibrationally perturbed nuclear-to-thermal coupled neutron multiplying medium are examined. Some unique self-organizational temporal patterns appear in such fission systems and suggest a complex underlying dynamic. (Author)
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.; Jenkins, Eleanor W.; Sun, Shuyu
2011-01-01
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
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Nonlinear spin wave coupling in adjacent magnonic crystals
International Nuclear Information System (INIS)
Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.
2016-01-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Exact solutions of some coupled nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...
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.
International Nuclear Information System (INIS)
Kosevich, Y A; Manevitch, L I; Savin, A V
2007-01-01
We consider, both analytically and numerically, the dynamics of stationary and slowly-moving breathers (localized short-wavelength excitations) in two weakly coupled nonlinear oscillator chains (nonlinear phononic waveguides). We show that there are two qualitatively different dynamical regimes of the coupled breathers: the oscillatory exchange of the low-amplitude breather between the phononic waveguides (wandering breather), and one-waveguide-localization (nonlinear self-trapping) of the high-amplitude breather. We also show that phase-coherent dynamics of the coupled breathers in two weakly linked nonlinear phononic waveguides has a profound analogy, and is described by a similar pair of equations, to the tunnelling quantum dynamics of two weakly linked Bose-Einstein condensates in a symmetric double-well potential (single bosonic Josephson junction). The exchange of phonon energy and excitations between the coupled phononic waveguides takes on the role which the exchange of atoms via quantum tunnelling plays in the case of the coupled condensates. On the basis of this analogy, we predict a new tunnelling mode of the coupled Bose-Einstein condensates in a single bosonic Josephson junction in which their relative phase oscillates around π/2. The dynamics of relative phase of two weakly linked Bose-Einstein condensates can be studied by means of interference, while the dynamics of the exchange of lattice excitations in coupled nonlinear phononic waveguides can be observed by means of light scattering
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.
Space and time evolution of two nonlinearly coupled variables
International Nuclear Information System (INIS)
Obayashi, H.; Totsuji, H.; Wilhelmsson, H.
1976-12-01
The system of two coupled linear differential equations are studied assuming that the coupling terms are proportional to the product of the dependent variables, representing e.g. intensities or populations. It is furthermore assumed that these variables experience different linear dissipation or growth. The derivations account for space as well as time dependence of the variables. It is found that certain particular solutions can be obtained to this system, whereas a full solution in space and time as an initial value problem is outside the scope of the present paper. The system has a nonlinear equilibrium solution for which the nonlinear coupling terms balance the terms of linear dissipation. The case of space and time evolution of a small perturbation of the nonlinear equilibrium state, given the initial one-dimensional spatial distribution of the perturbation, is also considered in some detail. (auth.)
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.
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.
Some remarks on coherent nonlinear coupling of waves in plasmas
International Nuclear Information System (INIS)
Wilhelmsson, H.
1976-01-01
The analysis of nonlinear processes in plasma physics has given rise to a basic set of coupled equations. These equations describe the coherent nonlinear evolution of plasma waves. In this paper various possibilities of analysing these equations are discussed and inherent difficulties in the description of nonlinear interactions between different types of waves are pointed out. Specific examples of stimulated excitation of waves are considered. These are the parametric excitation of hybrid resonances in hot magnetized multi-ion component plasma and laser-plasma interactions. (B.D.)
Nonlinear steady-state coupling of LH waves
International Nuclear Information System (INIS)
Ko, K.; Krapchev, V.B.
1981-02-01
The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Spatiotemporal light-beam compression from nonlinear mode coupling
Krupa, Katarzyna; Tonello, Alessandro; Couderc, Vincent; Barthélémy, Alain; Millot, Guy; Modotto, Daniele; Wabnitz, Stefan
2018-04-01
We experimentally demonstrate simultaneous spatial and temporal compression in the propagation of light pulses in multimode nonlinear optical fibers. We reveal that the spatial beam self-cleaning recently discovered in graded-index multimode fibers is accompanied by significant temporal reshaping and up to fourfold shortening of the injected subnanosecond laser pulses. Since the nonlinear coupling among the modes strongly depends on the instantaneous power, we explore the entire range of the nonlinear dynamics with a single optical pulse, where the optical power is continuously varied across the pulse profile.
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 charge reduction effect in strongly coupled plasmas
International Nuclear Information System (INIS)
Sarmah, D; Tessarotto, M; Salimullah, M
2006-01-01
The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occurring in strongly coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor (f c ) which determines the Debye-Hueckel potential generated by a charged test particle. Its relevant parametric dependencies are analysed and shown to predict a strong charge reduction effect in strongly coupled plasmas
On the recovering of a coupled nonlinear Schroedinger potential
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx
2000-04-28
We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)
Nonlinear 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...
The coupled nonlinear dynamics of a lift system
Energy Technology Data Exchange (ETDEWEB)
Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
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
Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes
International Nuclear Information System (INIS)
Liu Tao; Zhao Jun; Hill, David J.
2009-01-01
In this paper, we study the global synchronization of nonlinearly coupled complex delayed dynamical networks with both directed and undirected graphs. Via Lyapunov-Krasovskii stability theory and the network topology, we investigate the global synchronization of such networks. Under the assumption that coupling coefficients are known, a family of delay-independent decentralized nonlinear feedback controllers are designed to globally synchronize the networks. When coupling coefficients are unavailable, an adaptive mechanism is introduced to synthesize a family of delay-independent decentralized adaptive controllers which guarantee the global synchronization of the uncertain networks. Two numerical examples of directed and undirected delayed dynamical network are given, respectively, using the Lorenz system as the nodes of the networks, which demonstrate the effectiveness of proposed results.
Nonlinear coupling of flow harmonics: Hexagonal flow and beyond
Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves
2018-05-01
Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.
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.
Nonlinearly coupled dynamics of irregularities in the equatorial electrojet
Energy Technology Data Exchange (ETDEWEB)
Atul, J.K., E-mail: jkatulphysics@gmail.com [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India); Sarkar, S. [FCIPT, Institute for Plasma Research, Gandhinagar 382428 (India); Singh, S.K. [Department of Physics, College of Commerce under Magadh University, Patna 800020 (India)
2016-04-01
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.
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.
Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures
International Nuclear Information System (INIS)
Zhao, Y.
1996-01-01
Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed
Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks
Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming
2018-04-01
Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.
Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua
2009-01-01
The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.
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.
Rotating Dilaton Black Strings Coupled to Exponential Nonlinear Electrodynamics
Directory of Open Access Journals (Sweden)
Ahmad Sheykhi
2014-01-01
Full Text Available We construct a new class of charged rotating black string solutions coupled to dilaton and exponential nonlinear electrodynamic fields with cylindrical or toroidal horizons in the presence of a Liouville-type potential for the dilaton field. Due to the presence of the dilaton field, the asymptotic behaviors of these solutions are neither flat nor (AdS. We analyze the physical properties of the solutions in detail. We compute the conserved and thermodynamic quantities of the solutions and verify the first law of thermodynamics on the black string horizon. When the nonlinear parameter β2 goes to infinity, our results reduce to those of black string solutions in Einstein-Maxwell-dilaton gravity.
Neutron stars in non-linear coupling models
International Nuclear Information System (INIS)
Taurines, Andre R.; Vasconcellos, Cesar A.Z.; Malheiro, Manuel; Chiapparini, Marcelo
2001-01-01
We present a class of relativistic models for nuclear matter and neutron stars which exhibits a parameterization, through mathematical constants, of the non-linear meson-baryon couplings. For appropriate choices of the parameters, it recovers current QHD models found in the literature: Walecka, ZM and ZM3 models. We have found that the ZM3 model predicts a very small maximum neutron star mass, ∼ 0.72M s un. A strong similarity between the results of ZM-like models and those with exponential couplings is noted. Finally, we discuss the very intense scalar condensates found in the interior of neutron stars which may lead to negative effective masses. (author)
Neutron stars in non-linear coupling models
Energy Technology Data Exchange (ETDEWEB)
Taurines, Andre R.; Vasconcellos, Cesar A.Z. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil); Malheiro, Manuel [Universidade Federal Fluminense, Niteroi, RJ (Brazil); Chiapparini, Marcelo [Universidade do Estado, Rio de Janeiro, RJ (Brazil)
2001-07-01
We present a class of relativistic models for nuclear matter and neutron stars which exhibits a parameterization, through mathematical constants, of the non-linear meson-baryon couplings. For appropriate choices of the parameters, it recovers current QHD models found in the literature: Walecka, ZM and ZM3 models. We have found that the ZM3 model predicts a very small maximum neutron star mass, {approx} 0.72M{sub s}un. A strong similarity between the results of ZM-like models and those with exponential couplings is noted. Finally, we discuss the very intense scalar condensates found in the interior of neutron stars which may lead to negative effective masses. (author)
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
The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid
Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John
1988-01-01
The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.
Color image encryption based on Coupled Nonlinear Chaotic Map
International Nuclear Information System (INIS)
Mazloom, Sahar; Eftekhari-Moghadam, Amir Masud
2009-01-01
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
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.
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......-nonlinearities. Therefore, we use the system of generalized coupled nonlinear Schrödinger equations (GCNLSE) to describe the signal propagation. We analytically show that the presence of linear mode coupling may cause increasing of the nonlinear signal distortions. For the detailed study we solve GCNLSE numerically...... for the standard step index fiber at the wavelength of 850 nm in the basis of spatial modes with helical phase front (vortex modes) and for a special kind of few-mode fiber with enlarged core, providing propagation of five spatial modes at 1550 nm. Simulation results confirm that the linear mode coupling may lead...
Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.
2018-05-01
Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.
Geng, Qi; Zhu, Ka-Di
2016-07-10
We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.
Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model
Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.
2009-01-01
Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.
On the nucleon-nucleon potential obtained from non-linear coupling
International Nuclear Information System (INIS)
El Ghabaty, S.S.
1975-07-01
The static limit of a pseudoscalar symmetric meson theory of nuclear forces is examined. The Born-Oppenheimer potential is determined for the case of two very heavy nucleons exchanging pseudoscalar isovector pions with non-linear coupling. It is found that the non-linear terms induced by the γ 5 coupling are cancelled by the additional pion-nucleon coupling of the non-linear sigma model. The nucleon-nucleon potential thus obtained is the same as the Yukava potential except for strength at different separations between the two nucleons
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.
Coordination of the Walking Stick Insect Using a System of Nonlinear Coupled Oscillators
National Research Council Canada - National Science Library
Marvin, Daryl J
1992-01-01
The area of walking machines is investigated. A design for a central pattern generator composed of nonlinear coupled oscillators which generates the characteristic gaits of the walking stick insect is presented...
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.
Periodic wavetrains for systems of coupled nonlinear Schrödinger ...
Indian Academy of Sciences (India)
Systems of coupled nonlinear Schrödinger equations (cNLS) have received tremendous ..... The propagation of optical solitons along fibers has played an important role ... To increase the information carrying capacity, it will be desirable and ...
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
Nonlinear Excitations in Strongly-Coupled Fermi-Dirac Plasmas
Akbari-Moghanjoughi, M.
2012-01-01
In this paper we use the conventional quantum hydrodynamics (QHD) model in combination with the Sagdeev pseudopotential method to explore the effects of Thomas-Fermi nonuniform electron distribution, Coulomb interactions, electron exchange and ion correlation on the large-amplitude nonlinear soliton dynamics in Fermi-Dirac plasmas. It is found that in the presence of strong interactions significant differences in nonlinear wave dynamics of Fermi-Dirac plasmas in the two distinct regimes of no...
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
Matsuda, Nobuyuki; Kato, Takumi; Harada, Ken-Ichi; Takesue, Hiroki; Kuramochi, Eiichi; Taniyama, Hideaki; Notomi, Masaya
2011-10-10
We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
oscillators. We analyze the behavior of coupled systems with respect to the coupling switching frequency using ..... are of potential utility in appropriate design strategies and/or understanding of complex systems with dynamic interaction ...
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.
A nonlinear magnetoelectric model for magnetoelectric layered composite with coupling stress
International Nuclear Information System (INIS)
Shi, Yang; Gao, Yuanwen
2014-01-01
Based on a linear piezoelectric relation and a nonlinear magnetostrictive constitutive relation, A nonlinear magnetoelectric (ME) effect model for flexural layered ME composites is established in in-plane magnetic field. In the proposed model, the true coupling stress and the equivalent piezomagnetic coefficient are taken into account and obtained through an iterative approach. Some calculations on nonlinear ME coefficient are conducted and discussed. Our results show that for both the flexural bilayer and trilayer composites, the true coupling stress in the composites first increase and then approach to a constant value with the increase of applied magnetic fields, affecting the nonlinear ME effect significantly. With consideration of the true coupling stress, the ME effect is smaller than that without consideration of the true coupling stress. Moreover, the proposed theoretical model predicts that the ME coefficient of the trilayer composite (does not generate the bending deflection) is much larger than that of bilayer composite (generates the bending deflection), which is in well agreement with the previous works. The influences of the applied magnetic field on the true coupling stress and fraction ratio corresponding to the extreme ME coefficients of layered structures are also investigated. - Highlights: • This paper develops a nonlinear model for layered ME composite. • The true coupling stress is obtained through an iterative approach. • The influences of coupling stress and flexural deformation are discussed. • The dependence of ME coefficient on magnetic field is studied
International Nuclear Information System (INIS)
Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2011-01-01
In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)
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
Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions
International Nuclear Information System (INIS)
Geng Xianguo; Su Ting
2007-01-01
A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived
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
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.
Non-linear coupling of drift modes in a quadrupole
International Nuclear Information System (INIS)
Elliott, J.A.; Sandeman, J.C.; Tessema, G.Y.
1990-01-01
We report continuing experimental studies of non-linear interactions of drift waves, with direct evidence of a growth saturation mechanism by transfer of energy to lower frequency modes. Wave launching experiments show that the decay rate of drift waves can be strongly amplitude dependent. (author) 9 refs., 5 figs
Breathers and rogue waves: Demonstration with coupled nonlinear ...
Indian Academy of Sciences (India)
It has been found that the rational solution of nonlinear Schrödinger (NLS) ..... Figures 3a and 3b illustrate the behaviour of this solution, which is periodic both ... peaks increases or decreases and if the direction gets changed or not when the ...
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
chaos in four-dimensional space by the generalized definitions of spatial ... according to nonlinear noise in the real physical world, f(φ(x),ψ(x)) and g(φ(x) ... tion in ecological system, where φm,n(s) is the host density in generations s and s + 1,.
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.
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
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......, 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...
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.
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)
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.
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 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
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.
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.
Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun
2018-01-01
In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.
International Nuclear Information System (INIS)
Kobayashi, Akira; Ohnishi, Yuzo
1986-01-01
The nonlinearity of material properties used in the coupled mechanical-hydraulic-thermal analysis is investigated from the past literatures. Some nonlinearity that is respectively effective for the system is introduced into our computer code for analysis such a coupling problem by using finite element method. And the effects of nonlinearity of each material property on the coupled behavior in rock mass are examined for simple model and Stripa project model with the computer code. (author)
Coupled bending and torsional vibration of a rotor system with nonlinear friction
International Nuclear Information System (INIS)
Hua, Chunli; Cao, Guohua; Zhu, Zhencai; Rao, Zhushi; Ta, Na
2017-01-01
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
Stevanović Hedrih, K.
2008-02-01
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
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.
Nonlinear thermoelectric properties of molecular junctions with vibrational coupling
DEFF Research Database (Denmark)
Leijnse, Martin Christian; Wegewijs, M. R.; Flensberg, Karsten
2010-01-01
exchange with both electrodes, investigating how these contribute to the heat and charge transports. We calculate the efficiency and power output of the device operated as a heat to electric power converter in the regime of weak tunnel coupling and phonon exchange rate and identify the optimal operating...
Study on Nonlinear Vibration and Crack Fault of Rotor-bearing-seal Coupling System
Directory of Open Access Journals (Sweden)
Yuegang LUO
2014-02-01
Full Text Available The nonlinear dynamic model of rotor-bearing-seal system with crack in shaft is set up based on the coupling model of nonlinear oil-film force and Muszyska’s nonlinear seal fluid force. The dynamic vibration characteristics of the rotor-bearing-seal system and the effects of physical and structural parameters of labyrinth seal and crack fault on movement character of the rotor were analyzed. The increases of seal length, seal pressure differential, seal radius and axial velocity are in favor of the stability of the system, and it of seal gap and crack depth are not in favor of the stability of the system.
Localized excitations in a nonlinearly coupled magnetic drift wave-zonal flow system
International Nuclear Information System (INIS)
Shukla, Nitin; Shukla, P.K.
2010-01-01
We consider the amplitude modulation of the magnetic drift wave (MDW) by zonal flows (ZFs) in a nonuniform magnetoplasma. For this purpose, we use the two-fluid model to derive a nonlinear Schroedinger equation for the amplitude modulated MDWs in the presence of the ZF potential, and an evolution equation for the ZF potential which is reinforced by the nonlinear Lorentz force of the MDWs. Our nonlinearly coupled MDW-ZFs system of equations admits stationary solutions in the form of a localized MDW envelope and a shock-like ZF potential profile.
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
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
Exploiting nonlinear dynamics in a coupled-core fluxgate magnetometer
International Nuclear Information System (INIS)
Bulsara, Adi R; In, Visarath; Kho, Andy; Longhini, Patrick; Neff, Joe; Anderson, Gregory; Obra, Christopher; Palacios, Antonio; Baglio, Salvatore; Ando, Bruno
2008-01-01
Unforced bistable dynamical systems having dynamics of the general form τ F x-dot (t)=-∇ x U(x) cannot oscillate (i.e. switch between their stable attractors). However, a number of such systems subject to carefully crafted coupling schemes have been shown to exhibit oscillatory behavior under carefully chosen operating conditions. This behavior, in turn, affords a new mechanism for the detection and quantification of target signals having magnitude far smaller than the energy barrier height in the potential energy function U(x) for a single (uncoupled) element. The coupling-induced oscillations are a feature that appears to be universal in systems described by bi- or multi-stable potential energy functions U(x), and are being exploited in a new class of dynamical sensors being developed by us. In this work we describe one of these devices, a coupled-core fluxgate magnetometer (CCFM), whose operation is underpinned by this dynamic behavior. We provide an overview of the underlying dynamics and, also, quantify the performance of our test device; in particular, we provide a quantitative performance comparison to a conventional (single-core) fluxgate magnetometer via a 'resolution' parameter that embodies the device sensitivity (the slope of its input–output transfer characteristic) as well as the noise floor
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.
Effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh–Rose neurons
Energy Technology Data Exchange (ETDEWEB)
Li, Chun-Hsien, E-mail: chli@nknucc.nknu.edu.tw [Department of Mathematics, National Kaohsiung Normal University, Yanchao District, Kaohsiung City 82444, Taiwan (China); Yang, Suh-Yuh, E-mail: syyang@math.ncu.edu.tw [Department of Mathematics, National Central University, Jhongli District, Taoyuan City 32001, Taiwan (China)
2015-10-23
This work is devoted to investigate the effects of network structure on the synchronizability of nonlinearly coupled dynamical network of Hindmarsh–Rose neurons with a sigmoidal coupling function. We mainly focus on the networks that exhibit the small-world character or scale-free property. By checking the first nonzero eigenvalue of the outer-coupling matrix, which is closely related to the synchronization threshold, the synchronizabilities of three specific network ensembles with prescribed network structures are compared. Interestingly, we find that networks with more connections will not necessarily result in better synchronizability. - Highlights: • We investigate the effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh–Rose neurons. • We mainly consider the networks that exhibit the small-world character or scale-free property. • The synchronizability of three specific network ensembles with prescribed network structures are compared. • Networks with more connections will not necessarily result in better synchronizability.
Effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh–Rose neurons
International Nuclear Information System (INIS)
Li, Chun-Hsien; Yang, Suh-Yuh
2015-01-01
This work is devoted to investigate the effects of network structure on the synchronizability of nonlinearly coupled dynamical network of Hindmarsh–Rose neurons with a sigmoidal coupling function. We mainly focus on the networks that exhibit the small-world character or scale-free property. By checking the first nonzero eigenvalue of the outer-coupling matrix, which is closely related to the synchronization threshold, the synchronizabilities of three specific network ensembles with prescribed network structures are compared. Interestingly, we find that networks with more connections will not necessarily result in better synchronizability. - Highlights: • We investigate the effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh–Rose neurons. • We mainly consider the networks that exhibit the small-world character or scale-free property. • The synchronizability of three specific network ensembles with prescribed network structures are compared. • Networks with more connections will not necessarily result in better synchronizability
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.
Energy Technology Data Exchange (ETDEWEB)
Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
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.
Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation
Energy Technology Data Exchange (ETDEWEB)
Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com [Department of Physics, Anna University, Madurai Region, Ramanathapuram (India); Mahalingam, A. [Department of Physics, Anna University, Chennai - 600 025 (India); Uthayakumar, A. [Department of Physics, Presidency College, Chennai - 600 005 (India)
2014-07-15
We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.
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.
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; Arcak, Murat; Salama, Khaled N.
2010-01-01
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.
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...
Fitting and forecasting coupled dark energy in the non-linear regime
Energy Technology Data Exchange (ETDEWEB)
Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, Heidelberg, 69120 Germany (Germany); Baldi, Marco, E-mail: casas@thphys.uni-heidelberg.de, E-mail: l.amendola@thphys.uni-heidelberg.de, E-mail: mail@marcobaldi.it, E-mail: v.pettorino@thphys.uni-heidelberg.de, E-mail: vollmer@thphys.uni-heidelberg.de [Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Università di Bologna, viale Berti Pichat, 6/2, Bologna, I-40127 Italy (Italy)
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{sup 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.
Painlevйe analysis and integrability of two-coupled non-linear ...
Indian Academy of Sciences (India)
the Painlevйe property. In this case the system is expected to be integrable. In recent years more attention is paid to the study of coupled non-linear oscilla- ... Painlevйe analysis. To be self-contained, in §2 we briefly outline the salient features.
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
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 ...
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)
Singular solitons and other solutions to a couple of nonlinear wave equations
International Nuclear Information System (INIS)
Inc Mustafa; Ulutaş Esma; Biswas Anjan
2013-01-01
This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method
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
Energy Technology Data Exchange (ETDEWEB)
Taverniers, Søren; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu
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.
International Nuclear Information System (INIS)
Zheng Song
2012-01-01
In this paper, the exponential synchronization between two nonlinearly coupled complex networks with non-delayed and delayed coupling is investigated with Lyapunov-Krasovskii-type functionals. Based on the stability analysis of the impulsive differential equation and the linear matrix inequality, sufficient delay-dependent conditions for exponential synchronization are derived, and a linear impulsive controller and simple updated laws are also designed. Furthermore, the coupling matrices need not be symmetric or irreducible. Numerical examples are presented to verify the effectiveness and correctness of the synchronization criteria obtained.
Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F
2014-11-21
Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.
Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars
International Nuclear Information System (INIS)
Schenk, A.K.; Arras, P.; Flanagan, E.E.; Teukolsky, S.A.; Wasserman, I.
2002-01-01
We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars, assuming that the mode amplitudes are only mildly nonlinear. The formalism is simpler than previous treatments of mode-mode interactions for spherical stars, and simplifies and corrects previous treatments for rotating stars. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings, which suffices for moderate amplitude modal excitations; the formalism is easy to extend to higher order couplings. We describe a new, efficient way to compute the modal coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. The formalism is general enough to allow computation of the initial trends in the evolution of the spin frequency and differential rotation of the background star. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. First, we clarify some aspects of the expansion in stellar rotation frequency Ω that is often used to compute approximate mode functions. We show that, in zero-buoyancy stars, the rotational modes (those modes whose frequencies vanish as Ω→0) are orthogonal to zeroth order in Ω. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r modes to other rotational modes are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in Ω or in compressibility. In particular, in zero-buoyancy stars, the coupling of three r modes is forbidden
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.
Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma
International Nuclear Information System (INIS)
Wang Yunliang; Shukla, P. K.; Eliasson, B.
2013-01-01
We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.
International Nuclear Information System (INIS)
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
2009-01-01
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system
International Nuclear Information System (INIS)
Zeng, Zaiping; Garoufalis, Christos S.; Baskoutas, Sotirios
2014-01-01
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system have been theoretically studied. In general, we find that the structure parameters of the coupled system significantly affect the optical susceptibilities. The enhancement of the coupling effects between the dot and ring is found to increase considerably the optical susceptibilities and redshift drastically the transition energies. Comparing to the linear susceptibility, the nonlinear optical susceptibility is found to be more sensitive to the variation of the structure parameters. A comprehensive analysis of the electron probability density movement with respect to the modification of the structure parameters is provided, which offers a unique perspective of the ground-state localization. - Highlights: • Optical susceptibilities in a quantum-dot–quantum-ring system are studied. • The structure parameters significantly affect the optical susceptibilities. • The enhancement of the coupling effects increases the optical susceptibilities. • The nonlinear susceptibility is more sensitive to the change in structure parameters. • A comprehensive analysis of the electron probability density movement is provided
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.
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...
Holland, Christopher George
Studies of nonlinear couplings and dynamics in plasma turbulence are presented. Particular areas of focus are analytic studies of coherent structure formation in electron temperature gradient turbulence, measurement of nonlinear energy transfer in simulations of plasma turbulence, and bispectral analysis of experimental and computational data. The motivation for these works has been to develop and expand the existing theories of plasma transport, and verify the nonlinear predictions of those theories in simulation and experiment. In Chapter II, we study electromagnetic secondary instabilities of electron temperature gradient turbulence. The growth rate for zonal flow generation via modulational instability of electromagnetic ETG turbulence is calculated, as well as that for zonal (magnetic) field generation. In Chapter III, the stability and saturation of streamers in ETG turbulence is considered, and shown to depend sensitively upon geometry and the damping rates of the Kelvin-Helmholtz mode. Requirements for a credible theory of streamer transport are presented. In addition, a self-consistent model for interactions between ETG and ITG (ion temperature gradient) turbulence is presented. In Chapter IV, the nonlinear transfer of kinetic and internal energy is measured in simulations of plasma turbulence. The regulation of turbulence by radial decorrelation due to zonal flows and generation of zonal flows via the Reynolds stress are explicitly demonstrated, and shown to be symmetric facets of a single nonlinear process. Novel nonlinear saturation mechanisms for zonal flows are discussed. In Chapter V, measurements of fluctuation bicoherence in the edge of the DIII-D tokamak are presented. It is shown that the bicoherence increases transiently before a L-H transition, and decays to its initial value after the barrier has formed. The increase in bicoherence is localized to the region where the transport barrier forms, and shows strong coupling between well
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)
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.
Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.
Shah, Kamal; Khan, Rahmat Ali
2016-01-01
In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.
(2,0)-Super-Yang-Mills coupled to non-linear {sigma}-model
Energy Technology Data Exchange (ETDEWEB)
Goes-Negrao, M.S.; Penna-Firme, A.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Negrao, M.R. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
1999-07-01
Considering a class of (2,0)-super yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter to non-linear {sigma}-models in (2,0)-superspace. The dynamics and the coupling of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials once light-cone coordinates are chosen. (author)
(2,0)-Super-Yang-Mills coupled to non-linear σ-model
International Nuclear Information System (INIS)
Goes-Negrao, M.S.; Penna-Firme, A.B.; Negrao, M.R.
1999-07-01
Considering a class of (2,0)-super yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter to non-linear σ-models in (2,0)-superspace. The dynamics and the coupling of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials once light-cone coordinates are chosen. (author)
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
International Nuclear Information System (INIS)
Mokhtari, R.; Toodar, A. Samadi; Chegini, N. G.
2011-01-01
We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrödinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge—Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out. (general)
Photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling
Zhang, X. Y.; Zhou, Y. H.; Guo, Y. Q.; Yi, X. X.
2018-03-01
We explore the photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling, i.e. H_int˜\\hat{a}\\dagger2\\hat{a}^2(\\hat{b}_1^\\dagger+\\hat{b}_1) . We find that the Kerr-type nonlinear coupling can enhance the photon blockade greatly. We evaluate the equal-time second-order correlation function of the cavity photons and find that the optimal photon blockade does not happen at the single photon resonance. By working within the few-photon subspace, we get an approximate analytical expression for the correlation function and the condition for the optimal photon blockade. We also find that the photon blockade effect is not always enhanced as the Kerr-type nonlinear coupling strength g 2 increases. At some values of g 2, the photon blockade is even weakened. For the system we considered here, the second-order correlation function can be smaller than 1 even in the unresolved sideband regime. By numerically simulating the master equation of the system, we also find that the thermal noise of the mechanical environment can enhance the photon blockade. We give out an explanation for this counter-intuitive phenomenon qualitatively.
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-03-12
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.
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.
Finding structure in the dark: Coupled dark energy, weak lensing, and the mildly nonlinear regime
Miranda, Vinicius; González, Mariana Carrillo; Krause, Elisabeth; Trodden, Mark
2018-03-01
We reexamine interactions between the dark sectors of cosmology, with a focus on robust constraints that can be obtained using only mildly nonlinear scales. While it is well known that couplings between dark matter and dark energy can be constrained to the percent level when including the full range of scales probed by future optical surveys, calibrating matter power spectrum emulators to all possible choices of potentials and couplings requires many computationally expensive n-body simulations. Here we show that lensing and clustering of galaxies in combination with the cosmic microwave background (CMB) are capable of probing the dark sector coupling to the few percent level for a given class of models, using only linear and quasilinear Fourier modes. These scales can, in principle, be described by semianalytical techniques such as the effective field theory of large-scale structure.
International Nuclear Information System (INIS)
An Xinlei; Yu Jianning; Chu Yandong; Zhang Jiangang; Zhang Li
2009-01-01
In this paper, we discussed the fixed points and their linear stability of a new nonlinear autonomous system that introduced by J.C. Sprott. Based on Lyapunov stabilization theorem, a global chaos synchronization scheme of three coupled identical systems is investigated. By choosing proper coupling parameters, the states of all the three systems can be synchronized. Then this method was applied to secure communication through chaotic masking, used three coupled identical systems, propose a novel method of chaos encryption, after encrypting in the previous two transmitters, information signal can be recovered exactly at the receiver end. Simulation results show that the method can realize monotonous synchronization. Further more, the information signal can be recovered undistorted when applying this method to secure communication.
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.
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).
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.
Nonlinear saturation of the trapped-ion mode by mode coupling in two dimensions
International Nuclear Information System (INIS)
Cohen, B.I.; Tang, W.M.
1977-01-01
A study of the nonlinear saturation by mode coupling of the dissipative trapped-ion mode is presented in which both radial and poloidal variations are considered. The saturation mechanism consists of the nonlinear coupling via E x B convection of energy from linearly unstable modes to stable modes. Stabilization is provided at short poloidal wavelengths by Landau damping from trapped and circulating ions, at short radial wavelengths by effects associated with the finite ion banana excursions and at long wavelengths by ion collisions. A one-dimensional, nonlinear partial differential equation for the electrostatic potential derived in earlier work is extended to two dimensions and to third order in amplitude. Included systematically are kinetic effects, e.g., Landau damping and its spatial dependence due to magnetic shear. The stability and accessibility of equilibria are considered in detail for cases far from as well as close to marginal stability. In the first case three-wave interactions are found to be important when the spectrum of unstable modes is sufficiently narrow. In the latter case, it is found that for a single unstable mode, a four-wave interaction can provide the dominant saturation mechanism. Cross-field transport is calculated, and the scaling of results is considered for tokamak parameters
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.
Zhang, Jinggui
2018-06-01
In this paper, we investigate the dynamical behaviors of the modulation instability (MI) of copropagating optical beams in fractional coupled nonlinear Schrödinger equations (NLSE) with the aim of revealing some novel properties different from those in the conventional coupled NLSE. By applying the standard linear stability method, we first derive an expression for the gain resulting from the instability induced by cross-phase modulation (CPM) in the presence of the Lévy indexes related to fractional effects. It is found that the modulation instability of copropagating optical beams still occurs even in the fractional NLSE with self-defocusing nonlinearity. Then, the analysis of our results further reveals that such Lévy indexes increase the fastest growth frequency and the bandwidth of conventional instability not only for the self-focusing case but also for the self-defocusing case, but do not influence the corresponding maximum gain. Numerical simulations are performed to confirm theoretical predictions. These findings suggest that the novel fractional physical settings may open up new possibilities for the manipulation of MI and nonlinear waves.
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
Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators
International Nuclear Information System (INIS)
Eriksson, A M; Midtvedt, D; Croy, A; Isacsson, A
2013-01-01
We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings. (paper)
Geometry effect on energy transfer rate in a coupled-quantum-well structure: nonlinear regime
International Nuclear Information System (INIS)
Salavati-fard, T; Vazifehshenas, T
2014-01-01
We study theoretically the effect of geometry on the energy transfer rate at nonlinear regime in a coupled-quantum-well system using the balance equation approach. To investigate comparatively the effect of both symmetric and asymmetric geometry, different structures are considered. The random phase approximation dynamic dielectric function is employed to include the contributions from both quasiparticle and plasmon excitations. Also, the short-range exchange interaction is taken into account through the Hubbard approximation. Our numerical results show that the energy transfer rate increases by increasing the well thicknesses in symmetric structures. Furthermore, by increasing spatial asymmetry, the energy transfer rate decreases for the electron temperature range of interest. From numerical calculations, it is obtained that the nonlinear energy transfer rate is proportional to the square of electron drift velocity in all structures and also, found that the influence of Hubbard local field correction on the energy transfer rate gets weaker by increasing the strength of applied electric field. (paper)
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.
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.
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.
Masood, W.; Mirza, Arshad M.
2010-11-01
Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.
International Nuclear Information System (INIS)
Masood, W.; Mirza, Arshad M.
2010-01-01
Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.
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......) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved...
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
Yerrapragada, Karthik; Ansari, M. H.; Karami, M. Amin
2017-09-01
We propose utilization of the nonlinear coupling between the roll and pitch motions of wave energy harvesting vessels to increase their power generation by orders of magnitude. Unlike linear vessels that exhibit unidirectional motion, our vessel undergoes both pitch and roll motions in response to frontal waves. This significantly magnifies the motion of the vessel and thus improves the power production by several orders of magnitude. The ocean waves result in roll and pitch motions of the vessel, which in turn causes rotation of an onboard pendulum. The pendulum is connected to an electric generator to produce power. The coupled electro-mechanical system is modeled using energy methods. This paper investigates the power generation of the vessel when the ratio between pitch and roll natural frequencies is about 2 to 1. In that case, a nonlinear energy transfer occurs between the roll and pitch motions, causing the vessel to perform coupled pitch and roll motion even though it is only excited in the pitch direction. It is shown that co-existence of pitch and roll motions significantly enhances the pendulum rotation and power generation. A method for tuning the natural frequencies of the vessel is proposed to make the energy generator robust to variations of the frequency of the incident waves. It is shown that the proposed method enhances the power output of the floating wave power generators by multiple orders of magnitude. A small-scale prototype is developed for the proof of concept. The nonlinear energy transfer and the full rotation of the pendulum in the prototype are observed in the experimental tests.
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.
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)
Simple and complex chimera states in a nonlinearly coupled oscillatory medium
Bolotov, Maxim; Smirnov, Lev; Osipov, Grigory; Pikovsky, Arkady
2018-04-01
We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. In terms of a local coarse-grained complex order parameter, the problem of finding stationary rotating nonhomogeneous solutions reduces to a third-order ordinary differential equation. This allows finding chimera-type and other inhomogeneous states as periodic orbits of this equation. Stability calculations reveal that only some of these states are stable. We demonstrate that an oscillatory instability leads to a breathing chimera, for which the synchronous domain splits into subdomains with different mean frequencies. Further development of instability leads to turbulent chimeras.
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Lennart; García-Morales, Vladimir [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching (Germany); Schönleber, Konrad; Krischer, Katharina, E-mail: krischer@tum.de [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)
2014-03-15
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars
International Nuclear Information System (INIS)
Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.
2004-01-01
We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars
Nonlinear coupling of lower-hybrid waves at the edge of tokamak plasmas
International Nuclear Information System (INIS)
Krapchev, V.B.; Theilhaber, K.S.; Ko, K.C.; Bers, A.
1981-01-01
We solve the steady-state coupling problem of lower-hybrid waves excited by a waveguide array. The theory takes into account the ponderomotive density modulation to all orders in the electric field amplitude but assumes that the nonlinear effects are important only along the magnetic field lines. The important new feature is the appearance of a resonant term in the transverse refractive index, which is due to the finite size of the excitation structure. A calculation for two waveguides, linear density profile, and constant temperature is presented
MOOSE: A parallel computational framework for coupled systems of nonlinear equations
International Nuclear Information System (INIS)
Gaston, Derek; Newman, Chris; Hansen, Glen; Lebrun-Grandie, Damien
2009-01-01
Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton-Krylov (JFNK). Utilizing the mathematical structure present in JFNK, physics expressions are modularized into 'Kernels,' allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics-based preconditioning, which provides great flexibility even with large variance in time scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.
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.
Malvestio, Irene; Kreuz, Thomas; Andrzejak, Ralph G.
2017-08-01
The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons. One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L . Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes. We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data.
Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators
International Nuclear Information System (INIS)
Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito
2008-01-01
This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions
International Nuclear Information System (INIS)
Passamonti, Andrea; Stergioulas, Nikolaos; Nagar, Alessandro
2007-01-01
The postbounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wideband resonant detectors
Non-linear coupling of the lower hybrid grill in ASDEX
International Nuclear Information System (INIS)
Petrzilka, V.A.
1991-01-01
Computations of the reflection coefficient based on a non-linear lower hybrid (LH) coupling theory are presented and compared with the measurements of the reflection coefficient of the ASDEX tokamak LH grill, where powers up to 4 kW/cm 2 have been launched. This high LH power density modifies the electron density in front of the grill because of ponderomotive forces. Thus, the coupling and the power reflection coefficient change. To explain the observed saturation of the growth of the reflection coefficient with power, it is necessary to take into account some heating of the plasma in front of the grill by the transmitted LH power, which also leads to a poloidally inhomogeneous edge electron density. (author). Letter-to-the-editor. 14 refs, 13 figs
Non-linear coupling of the lower hybrid grill in ASDEX
Energy Technology Data Exchange (ETDEWEB)
Petrzilka, V A [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu; Leuterer, F; Soeldner, F X; Giannone, L.; Schubert, R [Association Euratom-Max-Planck-Institut fuer Plasmaphysik, Garching (Germany, F.R.)
1991-09-01
Computations of the reflection coefficient based on a non-linear lower hybrid (LH) coupling theory are presented and compared with the measurements of the reflection coefficient of the ASDEX tokamak LH grill, where powers up to 4 kW/cm{sup 2} have been launched. This high LH power density modifies the electron density in front of the grill because of ponderomotive forces. Thus, the coupling and the power reflection coefficient change. To explain the observed saturation of the growth of the reflection coefficient with power, it is necessary to take into account some heating of the plasma in front of the grill by the transmitted LH power, which also leads to a poloidally inhomogeneous edge electron density. (author). Letter-to-the-editor. 14 refs, 13 figs.
Nonlinear coupling analysis of coal seam floor during mining based on FLAC3D
Institute of Scientific and Technical Information of China (English)
YAO Duo-xi; XU Ji-ying; LU Hai-feng
2011-01-01
Based on the hydro-geological conditions of 1028 mining face in Suntuan Coal Mine, mining seepage strain mechanism of seam floor was simulated by a nonlinear coupling method, which applied fluid-solid coupling analysis module of FLAC3D. The results indicate that the permeability coefficient of adjoining rock changes a lot due to mining. The maximum value reaches 1 379.9 times to the original value, where it is at immediate roof of the mined-out area. According to the analysis on the seepage field, mining does not destroy water resistance of the floor aquiclude. The mining fissure does not conduct lime-stone aquifer, and it is less likely to form damage. The plastic zone does not exactly correspond to the seepage area, and the scope of the altered seepage area is much larger than the plastic zone.
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)
Bedeaux, Dick; Kjelstrup, Signe; Öttinger, Hans Christian
2014-09-28
We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.
Bedeaux, Dick; Kjelstrup, Signe; Öttinger, Hans Christian
2014-09-01
We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.
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.
The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Linander, Hampus; Nilsson, Bengt E.W. [Department of Physics, Theoretical PhysicsChalmers University of Technology, S-412 96 Göteborg (Sweden)
2016-07-05
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 “translation”, “Lorentz” and “dilatation”) properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.
Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach
Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich
2018-04-01
Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.
Non-linear auto-regressive models for cross-frequency coupling in neural time series
Tallot, Lucille; Grabot, Laetitia; Doyère, Valérie; Grenier, Yves; Gramfort, Alexandre
2017-01-01
We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. PMID:29227989
Unexpected nonlinear effects and critical coupling in NbN superconducting microwave resonators
International Nuclear Information System (INIS)
Abdo, B.; Buks, E.
2004-01-01
Full Text:In this work, we have designed and fabricated several NbN superconducting stripline microwave resonators sputtered on sapphire substrates. The low temperature response exhibits strong and unexpected nonlinear effects, including sharp jumps as the frequency or poser are varied, frequency hysteresis loops changing direction as the input power is varied, and others. Contrary to some other superconducting resonators, a simple model of a one-dimensional Duffing resonator cannot account for the experimental results. Whereas the physical origin of the unusual nonlinear response of our samples remains an open question, our intensive experimental study of these effects under varying conditions provides some important insight. We consider a hypothesis according to which Josephson junctions forming weak links between the grains of the NbN are responsible for the observed behavior. We show that most of the experimental results are qualitatively consistent with such hypothesis. While revealing the underlying physics remains an outstanding challenge for future research, the utilization of the unusual nonlinear response for some novel applications is already demonstrated in the present work. In particular an operate the resonator as an inter modulation amplifier and find that the gain can be as high as 15 dB. To the best of our knowledge, inter modulation gain greater than unity has not been reported before in the scientific literature. In another application we demonstrate for the first time that the coupling between the resonator and its feed line can be made amplitude dependent. This novel mechanism allows us to tune the resonator into critical coupling conditions
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
Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.
2018-07-01
The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.
Toshmatov, Bobir; Stuchlík, Zdeněk; Schee, Jan; Ahmedov, Bobomurat
2018-04-01
The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordström (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-07-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Nonlinear Raman scattering behavior with Langmuir and sound waves coupling in a homogeneous plasma
International Nuclear Information System (INIS)
Bonnaud, G.; Pesme, D.; Pellat, R.
1990-01-01
By means of wave-coupling simulations, the typical nonlinear evolution of stimulated Raman scattering (SRS) is investigated in a homogeneous sub-quarter-critical plasma for present-day low laser irradiances and kilo-electron-volt electron temperatures. The decrease of the Langmuir energy observed after the SRS growth is found to be basically the result of the electrostatic decay instability (EDI) onset, which generates a high-amplitude ion-acoustic wave. The resulting strong modulation of the plasma density causes a conversion process that transforms the initial one-wave-vector Langmuir wave driven by SRS into a Bloch wave and induces SRS detuning and larger damping. The conditions involved herein have allowed isolation of these processes from the modulational instability; in addition, the Langmuir collapse is found not to occur owing to the high electron temperature
Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Shin, H J
2004-01-01
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave
International Nuclear Information System (INIS)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons
Vorotnikov, K.; Starosvetsky, Y.
2018-01-01
The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
Hajjaj, Amal Z.
2017-01-30
We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
Directory of Open Access Journals (Sweden)
A. Sheykhi
2016-01-01
Full Text Available We construct a new class of charged rotating black brane solutions in the presence of logarithmic nonlinear electrodynamics with complete set of the rotation parameters in arbitrary dimensions. The topology of the horizon of these rotating black branes is flat, while due to the presence of the dilaton field the asymptotic behavior of them is neither flat nor (anti-de Sitter [(AdS]. We investigate the physical properties of the solutions. The mass and angular momentum of the spacetime are obtained by using the counterterm method inspired by AdS/CFT correspondence. We derive temperature, electric potential, and entropy associated with the horizon and check the validity of the first law of thermodynamics on the black brane horizon. We study thermal stability of the solutions in both canonical and grand-canonical ensemble and disclose the effects of the rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions. We find the solutions are thermally stable for α1 the solutions may encounter an unstable phase, where α is dilaton-electromagnetic coupling constant.
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
Dynamics of atom-field probability amplitudes in a coupled cavity system with Kerr non-linearity
Energy Technology Data Exchange (ETDEWEB)
Priyesh, K. V.; Thayyullathil, Ramesh Babu [Department of Physics, Cochin University of Science and Technology, Cochin (India)
2014-01-28
We have investigated the dynamics of two cavities coupled together via photon hopping, filled with Kerr non-linear medium and each containing a two level atom in it. The evolution of various atom (field) state probabilities of the coupled cavity system in two excitation sub space are obtained numerically. Detailed analysis has been done by taking different initial conditions of the system, with various coupling strengths and by varying the susceptibility of the medium. The role of susceptibility factor, on the dynamics atom field probability has been examined. In a coupled cavity system with strong photon hopping it is found that the susceptibility factor modifies the behaviour of probability amplitudes.
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
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
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.
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.
Testing Universal Relations of Neutron Stars with a Nonlinear Matter-Gravity Coupling Theory
Sham, Y.-H.; Lin, L.-M.; Leung, P. T.
2014-02-01
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.
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
Ultrafast switching of the magnetic ground state in d1 titanates though nonlinear phononic coupling
Gu, Mingqiang; Rondinelli, James M.
LaTiO3 and YTiO3 are isostructure d1 titanates, which exhibit distinct magnetic and orbital properties: The former is a G-type antiferromagnet with a 150 K Neel temperature whereas the latter is a rare ferromagnetic (FM) insulator with a 30 K Curie temperature. With first-principles density functional theory calculations, we identify the local structural origin of the magnetic order difference in these orthorhombic perovskites. By increasing the tilt and rotation angles in LaTiO3, respectively, LaTiO3 is predicted to undergo a magnetic phase transition to an FM state. Similarly, decreasing the tilt and rotation angles in YTiO3 leads to a FM-to-AFM phase transition. The underlying physics is attributed to the change in the superexchange coupling between Ti-sites. Last, we propose a route to switch the magnetism in the titanates by controlling the octahedral distortions through dynamical nonlinear phononic coupling. The proposed experiment requires the use of static strain to position the crystal structure in proximity to the structural transition combined with readily achievable fluencies in an ultrafast optical pump-probe geometry The theory work is supported by the U.S Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-SC0012375.
Energy Technology Data Exchange (ETDEWEB)
Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)
2016-09-15
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
Beninato, A.; Emery, T.; Baglio, S.; Andò, B.; Bulsara, A. R.; Jenkins, C.; Palkar, V.
2013-12-01
Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi0.7Dy0.3FeO3 shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi0.7Dy0.3FeO3, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a "blueprint" for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or "target" B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
International Nuclear Information System (INIS)
Lehmann, G.; Spatschek, K. H.
2013-01-01
Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime
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.
International Nuclear Information System (INIS)
Macias-Diaz, J.E.; Puri, A.
2007-01-01
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information
Michiels, W.; Nijmeijer, H.
2009-01-01
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
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.
Study of the linear and non-linear coupling of the LH wave to the tokamak plasmas
International Nuclear Information System (INIS)
Preynas, M.
2012-10-01
In order to achieve long pulse operation with a tokamak, additional heating and current drive systems are necessary. High frequency antennas, which deliver several megawatts of power to the plasma, are currently used in several tokamaks. Moreover, a good control of the coupling of the wave launched by the antenna to the edge plasma is required to optimize the efficiency of heating and current drive LH systems. However, non-linear effects which depend on the level of injected power in the plasma strongly damage the coupling of the LH wave at particular edge parameters (density and temperature profiles). Results presented in the manuscript deal with the study of the linear and non-linear coupling of the LH wave to the plasma. In the framework of the commissioning of the Passive Active Multijunction antenna in 2009 on the Tore Supra tokamak aiming at validating the LH system suggested for ITER, the characterisation of its coupling properties was realized from low power experiments. The experimental results, which are compared with the linear coupling code ALOHA, have validated the theoretical predictions of good coupling at edge plasma density around the cut-off density. Besides, the ponderomotive effect is clearly identified as responsible for the deterioration in the coupling of the wave, which is measured under particular edge plasma conditions. A theoretical model combining the coupling of the LH wave with the ponderomotive force is suggested to explain the experimental observations. Thus, a new full wave code (named PICCOLO-2D) was developed and results from simulations validate the working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling on Tore Supra. (author)
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
Pérez Daroca, Diego; Roura-Bas, Pablo; Aligia, Armando A.
2018-04-01
We study the low-temperature properties of the differential response of the current to a temperature gradient at finite voltage in a single-level quantum dot including electron-electron interaction, nonsymmetric couplings to the leads, and nonlinear effects. The calculated response is significantly enhanced in setups with large asymmetries between the tunnel couplings. In the investigated range of voltages and temperatures with corresponding energies up to several times the Kondo energy scale, the maximum response is enhanced nearly an order of magnitude with respect to symmetric coupling to the leads.
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.
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)
Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A
2012-03-01
We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.
Directory of Open Access Journals (Sweden)
Hideki Gotoh
2014-10-01
Full Text Available Optical nonlinear effects are examined using a two-color micro-photoluminescence (micro-PL method in a coherently coupled exciton-biexciton system in a single quantum dot (QD. PL and photoluminescence excitation spectroscopy (PLE are employed to measure the absorption spectra of the exciton and biexciton states. PLE for Stokes and anti-Stokes PL enables us to clarify the nonlinear optical absorption properties in the lowest exciton and biexciton states. The nonlinear absorption spectra for excitons exhibit asymmetric shapes with peak and dip structures, and provide a distinct contrast to the symmetric dip structures of conventional nonlinear spectra. Theoretical analyses with a density matrix method indicate that the nonlinear spectra are caused not by a simple coherent interaction between the exciton and biexciton states but by coupling effects among exciton, biexciton and continuum states. These results indicate that Fano quantum interference effects appear in exciton-biexciton systems at QDs and offer important insights into their physics.
Directory of Open Access Journals (Sweden)
Yong Zhao
1997-01-01
Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.
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)
International Nuclear Information System (INIS)
Hornsby, W. A.; Peeters, A. G.; Snodin, A. P.; Casson, F. J.; Camenen, Y.; Szepesi, G.; Siccinio, M.; Poli, E.
2010-01-01
The interaction between small scale turbulence (of the order of the ion Larmor radius) and mesoscale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux and, consequently, a finite pressure gradient in the island. A finite radial temperature gradient inside the island is also shown to persist due to the trapped particles, which do not move along the field around the island. In the low collisionality regime, the finite gradient in the trapped population leads to the generation of a bootstrap current, which reduces the neoclassical drive.
International Nuclear Information System (INIS)
Martínez-Orozco, J.C.; Mora-Ramos, M.E.; Duque, C.A.
2014-01-01
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
Cross-separatrix Coupling in Nonlinear Global Electrostatic Turbulent Transport in C-2U
Lau, Calvin; Fulton, Daniel; Bao, Jian; Lin, Zhihong; Binderbauer, Michl; Tajima, Toshiki; Schmitz, Lothar; TAE Team
2017-10-01
In recent years, the progress of the C-2/C-2U advanced beam-driven field-reversed configuration (FRC) experiments at Tri Alpha Energy, Inc. has pushed FRCs to transport limited regimes. Understanding particle and energy transport is a vital step towards an FRC reactor, and two particle-in-cell microturbulence codes, the Gyrokinetic Toroidal Code (GTC) and A New Code (ANC), are being developed and applied toward this goal. Previous local electrostatic GTC simulations find the core to be robustly stable with drift-wave instability only in the scrape-off layer (SOL) region. However, experimental measurements showed fluctuations in both regions; one possibility is that fluctuations in the core originate from the SOL, suggesting the need for non-local simulations with cross-separatrix coupling. Current global ANC simulations with gyrokinetic ions and adiabatic electrons find that non-local effects (1) modify linear growth-rates and frequencies of instabilities and (2) allow instability to move from the unstable SOL to the linearly stable core. Nonlinear spreading is also seen prior to mode saturation. We also report on the progress of the first turbulence simulations in the SOL. This work is supported by the Norman Rostoker Fellowship.
International Nuclear Information System (INIS)
Yurtsever, E.; Brickmann, J.
1990-01-01
A two dimensional strongly nonharmonic vibrational system with nonlinear intermode coupling is studied both classically and quantum mechanically. The system was chosen such that there is a low lying transition (in energy) from a region where almost all trajectories move regularly to a region where chaotic dynamics strongly dominates. The corresponding quantum system is far away from the semiclassical limit. The eigenfunctions are calculated with high precision according to a linear variational scheme using conveniently chosen basis functions. It is the aim of this paper to check whether the prediction from semiclassical theory, namely that the measure of classically chaotic trajectories in phase space approaches the measure of irregular states in corresponding energy ranges, holds when the system is not close to the classical limit. It is also the aim to identify individual eigenfunctions with respect to regularity and to differentiate between local and normal vibrational states. It is found that there are quantitative and also qualitative differences between the quantum results and the semiclassical predictions. (orig./HK)
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.
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
Energy Technology Data Exchange (ETDEWEB)
Franchi, A.
2006-07-01
In this thesis a beam-based method has been developed to measure the strength and the polarity of corrector magnets (skew quadrupoles and sextupoles) in circular accelerators. The algorithm is based on the harmonic analysis (via FFT) of beam position monitor (BPM) data taken turn by turn from an accelerator in operation. It has been shown that, from the differences of the spectral line amplitudes between two consecutive BPMs, both the strength and the polarity of non-linear elements placed in between can be measured. The method has been successfully tested using existing BPM data from the SPS of CERN. A second beam-based method has been studied for a fast measurement and correction of betatron coupling driven by skew quadrupole field errors and tilted focusing quadrupoles. In this thesis it has been shown how the correction for minimizing the coupling stop band C can be performed in a single machine cycle from the harmonic analysis of multi-BPM data. The method has been successfully applied to RHIC. A third theoretical achievement is a new description of the betatron motion close to the difference resonance in presence of linear coupling. New formulae describing the exchange of RMS resonances have been derived here making use of Lie algebra providing a better description of the emittance behavior. A new way to decouple the equations of motion and explicit expressions for the individual single particle invariants have been found. For the first time emittance exchange studies have been carried out in the SIS-18 of GSI. Applications of this manipulation are: emittance equilibration under consideration for future operations of the SIS-18 as booster for the SIS-100; emittance transfer during multi-turn injection to improve the efficiency and to protect the injection septum in high intensity operations, by shifting part of the horizontal emittance into the vertical plane. Multi-particle simulations with 2D PIC space-charge solver have been run to infer heuristic scaling
Studies and measurements of linear coupling and nonlinearities in hadron circular accelerators
International Nuclear Information System (INIS)
Franchi, A.
2006-01-01
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
International Nuclear Information System (INIS)
Ünal, Hakkı Ulaş; Michiels, Wim
2013-01-01
The full synchronization of coupled nonlinear oscillators has been widely studied. In this paper we investigate conditions for which partial synchronization of time-delayed diffusively coupled systems arises. The coupling configuration of the systems is described by a directed graph. As a novel quantitative result we first give necessary and sufficient conditions for the presence of forward invariant sets characterized by partially synchronous motion. These conditions can easily be checked from the eigenvalues and eigenvectors of the graph Laplacian. Second, we perform stability analysis of the synchronized equilibria in a (gain,delay) parameter space. For this analysis the coupled nonlinear systems are linearized around the synchronized equilibria and then the resulting characteristic function is factorized. By such a factorization, it is shown that the relation between the behaviour of different agents at the zero of the characteristic function depends on the structure of the eigenvectors of the weighted Laplacian matrix. By determining the structure of the solutions in the unstable manifold, combined with the characterization of invariant sets, we predict which partially synchronous regimes occur and estimate the corresponding coupling gain and delay values. We apply the obtained results to networks of coupled Hindmarsh–Rose neurons and verify the occurrence of the expected partially synchronous regimes by using a numerical simulation. We also make a comparison with an existing approach based on Lyapunov functionals. (paper)
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.
Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M
2010-12-01
Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.
International Nuclear Information System (INIS)
Xu Guiqiong; Li Zhibin
2005-01-01
It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests
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
Ge, Li; Zhao, Nan
2018-04-01
We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.
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
International Nuclear Information System (INIS)
Ganguly, Jayanta; Ghosh, Manas
2015-01-01
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
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.
International Nuclear Information System (INIS)
Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A
2015-01-01
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. (paper)
Low cost metamodel for robust design of periodic nonlinear coupled micro-systems
Directory of Open Access Journals (Sweden)
Chikhaoui K.
2016-01-01
Full Text Available To achieve robust design, in presence of uncertainty, nonlinearity and structural periodicity, a metamodel combining the Latin Hypercube Sampling (LHS method for uncertainty propagation and an enriched Craig-Bampton Component Mode Synthesis approach (CB-CMS for model reduction is proposed. Its application to predict the time responses of a stochastic periodic nonlinear micro-system proves its efficiency in terms of accuracy and reduction of computational cost.
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)
Hamid M. Sedighi
Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.
International Nuclear Information System (INIS)
Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian
2012-01-01
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2012-12-01
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
Jana, Amiya Kumar; Ganguly, Saibal; Samanta, Amar Nath
2006-10-01
The work is devoted to design the globally linearizing control (GLC) strategy for a multicomponent distillation process. The control system is comprised with a nonlinear transformer, a nonlinear closed-loop state estimator [extended Kalman filter (EKF)], and a linear external controller [conventional proportional integral (PI) controller]. The model of a binary distillation column has been used as a state predictor to avoid huge design complexity of the EKF estimator. The binary components are the light key and the heavy key of the multicomponent system. The proposed GLC-EKF (GLC in conjunction with EKF) control algorithm has been compared with the GLC-ROOLE [GLC coupled with reduced-order open-loop estimator (ROOLE)] and the dual-loop PI controller based on set point tracking and disturbance rejection performance. Despite huge process/predictor mismatch, the superiority of the GLC-EKF has been inspected over the GLC-ROOLE control structure.
Energy Technology Data Exchange (ETDEWEB)
Choubani, M., E-mail: mohsenchoubani3@yahoo.fr; Ben Mahrsia, R.; Bouzaiene, L.; Maaref, H.
2013-12-15
In this paper we explore the effects of the structural dimensions, applied electromagnetic fields, hydrostatic pressure and temperature on the nonlinear optical rectification (NOR) in Vertically Coupled InAs/GaAs Quantum Dots (VCQDs). The analytical expression of the NOR is analyzed by using the density matrix formalism, the effective mass and the Finite Difference Method (FDM). Obtained results show that the NOR obtained with this coupled system is not a monotonic function of the barrier width, electromagnetic fields, pressure and temperature. Also, calculated results reveal that the resonant peaks of the NOR can be blue-shifted or red-shifted energies depending on the energy of the lowest confined states in the VCQDs structure. In addition, this condition can be controlled by changes in the structural dimensions and the external proofs mentioned above. -- Highlights: • In this paper we explore the effects of the barrier width, applied electromagnetic fields, hydrostatic pressure and temperature on the nonlinear optical rectification (NOR) in Vertically Coupled InAs/GaAs Quantum Dots (VCQDs). • The calculated results reveal that the resonant peaks of the NOR can be blue-shifted to large photon energies or red-shifted to lower photon energies. • In this paper, all parameters: electromagnetic fields, pressure and temperature effects are introduced and investigated. • The resonant energy and the magnitude of the NOR are controlled and adjusted.
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)
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.
Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power
Directory of Open Access Journals (Sweden)
Sado Danuta
2006-01-01
Full Text Available An ideal and nonideal autoparametrical system excited by DC motor with unbalanced mass is presented in this work. The system consists of the body of mass M which is hung on a nonlinear spring with a nonlinear damper, and a pendulum of the length l and mass m mounted to the body of mass M. It is assumed that the motion of the pendulum is damped by nonlinear resistive forces. Vibrations of both models (ideal and nonideal are researched. Solutions for the system response are presented for specific values of the parameters of system and the energy transfer between modes of vibrations is studied. Next excited vibrations for both models have been examined analytically and numerically. Except different kinds of periodic vibrations, there may also appear chaotic vibrations.
International Nuclear Information System (INIS)
Boukadida, T.
1988-01-01
The compatibility between accuracy and stability of the quasilinear equations is studied. Three stuations are analyzed: the discontinuous P-1 approximation of the first order quasilinear equation, the two dimensional version of the Lax-Friedrichs scheme and the coupling of modes in a plasma. For the one dimensional case, the proposed scheme matches the available data. In the two dimensional case, tests to show the explosion condition are performed. This investigation can be applied in laser-matter interactions, nonlinear optics and in many fields of physics [fr
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.
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.
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.
The Nonlinear Effects of Pion-Quark Coupling in the Cloudy Bag Model
Yasuhiko, FUTAMI; Satoru, AKIYAMA; Department of Physics, Faculty of Science and Technology Science University of Tokyo; Department of Physics, Faculty of Science and Technology Science University of Tokyo
1990-01-01
The nonlinear pion-quark interaction in the Cloudy Bag Model is investigated. The Hamiltonian is normal-ordered. The vacuum expectation value of pion field squared is evaluated by introducting some cutoff momentum for the virtual pions.We then calculate g_A, including other corrections.
The nonlinear effects of pion-quark coupling in the Cloudy Bag Model
International Nuclear Information System (INIS)
Futami, Yasuhiko; Akiyama, Satoru
1990-01-01
The nonlinear pion-quark interaction in the Cloudy Bag Model is investigated. The Hamiltonian is normal-ordered. The vacuum expectation value of pion field squared is evaluated by introducing some cutoff momentum for the virtual pions. We then calculate g A , including other corrections. (author)
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
Energy Technology Data Exchange (ETDEWEB)
Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu
2016-02-05
We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.
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.
International Nuclear Information System (INIS)
Wolf, Omri; Ma, Xuedan; Brener, Igal; Allerman, Andrew A.; Wendt, Joel R.; Shaner, Eric A.; Song, Alex Y.
2015-01-01
We use planar metamaterial resonators to enhance by more than two orders of magnitude the near infrared second harmonic generation obtained from intersubband transitions in III-Nitride heterostructures. The improvement arises from two factors: employing an asymmetric double quantum well design and aligning the resonators' cross-polarized resonances with the intersubband transition energies. The resulting nonlinear metamaterial operates at wavelengths where single photon detection is available, and represents a different class of sources for quantum photonics related phenomena
Nonlinear coupling of the resistive tearing modes under the unperturbed shear flow
International Nuclear Information System (INIS)
Urata, Kazuhiro
1990-01-01
The influence of the unperturbed shear flow on the nonlinear evolution of the tearing mode is studied. In the case of single helicity, the shear flow activates the unstable mode which finally saturates to a rigid rotor state. In the case of multiple helicity, a variety of flow patterns is created depending on parameters, and always forms the current bubble soon after the collapse of the 3/2 magnetic island. (author)
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions
Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.
2015-01-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256
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.
Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites
Khan, Kamran; Muliana, Anastasia Hanifah
2012-01-01
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
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.
Dynamical Chaos Rise in the System of Large Number of Nonlinear Coupled Oscillators
International Nuclear Information System (INIS)
Buts, V.A.; Koval'chuk, I.K.; Tarasov, D.V.
2007-01-01
The problem of dynamical chaos arising in distributed systems is considered. It was shown that in many cases it is possible to allocate relatively isolated subsystem which may be simpler for investigation. We suppose that chaos in this subsystem leads to chaotic behaviour of all system. Besides, the allocated subsystem may be used for describing complex dynamics of nonlinear three-wave interaction, in particular, in plasma systems. The analytical criterion of arising dynamics chaos in distributed system was obtained. This criterion was confirmed by numerical simulation
Current and Future Constraints on Higgs Couplings in the Nonlinear Effective Theory
Energy Technology Data Exchange (ETDEWEB)
de Blas, Jorge [INFN, Padua; Eberhardt, Otto [Valencia U., IFIC; Krause, Claudius [Fermilab
2018-03-02
We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.
Network synchronization in a population of star-coupled fractional nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Wang Junwei, E-mail: wangjunweilj@yahoo.com.c [School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006 (China); Zhang Yanbin [School of Computer Science, Hangzhou Dianzi University, Hangzhou 310018 (China)
2010-03-29
The topic of fractional calculus is enjoying growing interest among mathematicians, physicists and engineers in recent years. For complex network consisting of more than two fractional-order systems, however, it is difficult to establish its synchronization behavior. In this Letter, we study the synchronized motions in a star network of coupled fractional-order systems in which the major element is coupled to each of the noninteracting individual elements. On the basis of the stability theory of linear fractional-order differential equations, we derive a sufficient condition for the stability of the synchronization behavior in such a network. Furthermore, we verify our theoretical results by numerical simulations of star-coupled network with fractional-order chaotic nodes.
International Nuclear Information System (INIS)
Zhao-Bing, Liu; Hua-Guang, Zhang; Qiu-Ye, Sun
2010-01-01
This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results. (general)
Periodic oscillations in linear continuous media coupled with nonlinear discrete systems
International Nuclear Information System (INIS)
Lupini, R.
1998-01-01
A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ
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.
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P.; van Dijk, Pim
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P; van Dijk, Pim
2012-08-01
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.
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
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
Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K
2017-02-01
We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.
International Nuclear Information System (INIS)
Miskovic, Olivera; Olea, Rodrigo
2011-01-01
Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.
Lei, Dangyuan
2016-09-01
In the first part of this talk, I will show our experimental investigation on the linear and nonlinear optical properties of metal film-coupled nanosphere monomers and dimers both with nanometric gaps. We have developed a new methodology - polarization resolved spectral decomposition and color decoding to "visualizing" unambiguously the spectral and radiation properties of the complex plasmonic gap modes in these hybrid nanostructures. Single-particle spectroscopic measurements indicate that these hybrid nanostructures can simultaneously enhance several nonlinear optical processes, such as second harmonic generation, two-photon absorption induced luminescence, and hyper-Raman scattering. In the second part, I will show how the polarization state of the emissions from sub-10 nm upconversion nanocrystals (UCNCs) can be modulated when they form a hybrid complex with a gold nanorod (GNR). Our single-particle scattering experiments expose how an interplay between excitation polarization and GNR orientation gives rise to an extraordinary polarized nature of the upconversion emissions from an individual hybrid nanostructure. We support our results by numerical simulations and, using Förster resonance energy transfer theory, we uncover how an overlap between the UCNC emission and GNR extinction bands as well as the mutual orientation between emission and plasmonic dipoles jointly determine the polarization state of the UC emissions.
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Senthilkumar, D. V., E-mail: skumarusnld@gmail.com [School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016 (India); Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Kovilvenni 614 403, Tamilnadu (India); Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Chandrasekar, V. K. [Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Zou, Wei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Centre for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074 (China); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Kolkata 700032 (India); Kathamuthu, Thamilmaran [Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, Telegrafenberg, Potsdam D-14415 (Germany); Institute of Physics, Humboldt University Berlin, Berlin D-12489 (Germany); Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX (United Kingdom); Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod (Russian Federation)
2016-04-15
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Control of Nonlinear Coupled Electromagnetic Actuators for Active Drag Reduction in Turbulent Flow
Seidler, Florian; Trabert, Julius; Dück, Marcel; van Waasen, Stefan; Schiek, Michael; Abel, Dirk; Castelan, E. B.
2016-01-01
The research group FOR1779 “active drag reduction via wavy surface oscillations” develops robust methods for reduction of turbulent friction drag by flow control. The planned concentration on unsteady flow conditions requires a control of the electromagnetic actuator system for generation of transversal surface waves. The bars are positioned in parallel and coupled with an aluminum surface to generate a travelling wave perpendicular to the flow field. The actuator system can be approximately ...
Harmonic emission due to the nonlinear coupling of a Gaussian laser and a plasma wave
Energy Technology Data Exchange (ETDEWEB)
Pathak, R; Jain, R K [Department of Mathematics, SSL Jain College, Vidisha, MP, 464001 (India); Parashar, J [Department of Physics, Samrat Ashok Technological Institute, Vidisha, MP, 464001 (India)
2010-04-15
A high-power Gaussian laser propagating through a plasma couples with a large-amplitude plasma wave and undergoes scattering to produce harmonics. The process is sensitive to the phase matching angle between the laser and plasma wave numbers and the plasma wave frequency. For larger harmonics, the phase matching angle is high. The efficiency of the process is comparatively high at higher plasma wave frequencies.
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.
Hide, Raymond
1997-02-01
This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor
A less-constrained (2,0) super-Yang-Mills model: the coupling to non-linear σ-models
International Nuclear Information System (INIS)
Almeida, C.A.S.; Doria, R.M.
1990-01-01
Considering a class of (2,0) super-Yang-Mills multiplets characterised by the appearance of a pair of independent gauge potentials, we present here their coupling to non-linear σ-models in (2,0)-superspace. Contrary to the case of the coupling to (2,0) matter superfields, the extra gauge potential present in the Yang-Mills sector does not decouple from the theory in the case one gauges isometry groups of σ-models. (author)
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.
Evidence for nonlinear coupling of the lower hybrid grill in ASDEX
International Nuclear Information System (INIS)
Leuterer, F.; Soeldner, F.X.; Giannone, L.; Schubert, R.; Petrzilka, V.
1991-01-01
The grill in ASDEX consists of two stacked arrays of 24 waveguides each (upper and lower grill) with inner dimensions of 10x109 mm and 4 mm walls in between. A phasing of Δφ=180deg generates a symmetric spectrum with N parallel =±4.4, while Δφ=90deg generates an asymmetric spectrum with N parallel =2.2. The grill (i.e. its metallic surface) was usually at a radial position of R g =212.5 cm, the major radius of the plasma was R p =168 cm, the positions of separatrix and protection limiters were R S =208 cm and R I =212 cm. In a first campaign the grill was surrounded by protection tiles which protruded beyond the waveguides by 3 mm. In these conditions the average reflection coefficient R was between 10% and 50% depending on the phasing and power. Later these tiles had been cut back to be flush with the waveguides. This improved the coupling considerably. The difference can be understood on the basis of the linear coupling theory with a step and ramp electron density profile, if a vacuum gap X p ≤ 2 mm is, or is not, allowed between the grill and the plasma. However, in both cases increased with power with a tendency to saturate. We have applied a simple model to estimate this variation of . (orig./AH)
Veltz, Romain; Sejnowski, Terrence J.
2016-01-01
Inhibition-stabilized networks (ISNs) are neural architectures with strong positive feedback among pyramidal neurons balanced by strong negative feedback from inhibitory interneurons, a circuit element found in the hippocampus and the primary visual cortex. In their working regime, ISNs produce damped oscillations in the γ-range in response to inputs to the inhibitory population. In order to understand the properties of interconnected ISNs, we investigated periodic forcing of ISNs. We show that ISNs can be excited over a range of frequencies and derive properties of the resonance peaks. In particular, we studied the phase-locked solutions, the torus solutions, and the resonance peaks. Periodically forced ISNs respond with (possibly multistable) phase-locked activity, whereas networks with sustained intrinsic oscillations respond more dynamically to periodic inputs with tori. Hence, the dynamics are surprisingly rich, and phase effects alone do not adequately describe the network response. This strengthens the importance of phaseamplitude coupling as opposed to phase-phase coupling in providing multiple frequencies for multiplexing and routing information. PMID:26496044
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.
International Nuclear Information System (INIS)
Edery, D.; Pellat, R.; Soule, J.L.
1981-01-01
The resistive MHD equations have been handled in toroidal geometry following the tokamak ordering, in order to obtain a simplified set of non-linear equations. This system of equations is compact, closed, consistent and exact to the first two orders in the expansion in the inverse aspect ratio. Studies of the non-linear evolution of tearing modes in the real geometry of tokamak discharges are now in progress, and quite significant results have been obtained from the numerical code REVE of Fontenay based on our above model. From the analytical results, strong linear coupling between neighbouring modes is expected as is demonstrated by the numerical results in the linear, and non-linear regimes. Moreover, coupling exhibits a stochastic structure of the magnetic field lines, the threshold of which is seen to be easily computed by a simple analytical criterion. (orig.)
Liang, Hong-Qin; Liu, Bin; Hu, Jin-Feng; He, Xing-Dao
2018-05-01
An all-optical plasmonic diode, comprising a metal-insulator-metal waveguide coupled with a stub cavity, is proposed based on a nonlinear Fano structure. The key technique used is to break structural spatial symmetry by a simple reflector layer in the waveguide. The spatial asymmetry of the structure gives rise to the nonreciprocity of coupling efficiencies between the Fano cavity and waveguides on both sides of the reflector layer, leading to a nonreciprocal nonlinear response. Transmission properties and dynamic responses are numerically simulated and investigated by the nonlinear finite-difference time-domain method. In the proposed structure, high-efficiency nonreciprocal transmission can be achieved with a low power threshold and an ultrafast response time (subpicosecond level). A high maximum transmittance of 89.3% and an ultra-high transmission contrast ratio of 99.6% can also be obtained. The device can be flexibly adjusted for working wavebands by altering the stub cavity length.
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
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.
Evidence for nonlinear coupling of the lower hybrid grill in ASDEX
Energy Technology Data Exchange (ETDEWEB)
Leuterer, F; Soeldner, F X; Giannone, L.; Schubert, R [Max-Planck-Institut fuer Plasmaphysik, Garching (Germany); Petrzilka, V [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu
1991-01-01
The grill in ASDEX consists of two stacked arrays of 24 waveguides each (upper and lower grill) with inner dimensions of 10x109 mm and 4 mm walls inbetween. A phasing of [Delta][phi]=180[sup o] generates a symmetric spectrum with N[sub ]=[+-]4.4, while [Delta][phi]=90[sup o] generates an asymmetric spectrum with N[sub ]=2.2. The grill (i.e. its metallic surface) was usually at a radial position of R[sub g]=212.5 cm, the major radius of the plasma was R[sub p]=168 cm, the positions of separatrix and protection limiters were R[sub s]=208 cm and R[sub ]=212 cm. In a first campaign the grill was surrounded by protection tiles which protruded beyond the waveguides by 3 mm. In these conditions the average reflection coefficient R was between 10% and 50% depending on the phasing and power. Later these tiles had been cut back to be flush with the waveguides. This improved the coupling considerably. The difference can be understood on the basis of the linear coupling theory with a step and ramp electron density profile, if a vacuum gap X[sub p][<=]2 mm is, or is not, allowed between the grill and the plasma. However, in both cases
Dark matter-baryon segregation in the nonlinear evolution of coupled dark energy models
International Nuclear Information System (INIS)
Mainini, Roberto
2005-01-01
The growth and virialization of spherical top-hat fluctuations, in coupled dark energy models, causes segregation between dark matter (DM) and baryons, as the gravitational infall into the potential well proceeds more slowly for the baryons than for DM. As a consequence, after attaining their turnaround and before full virialization, halos have outer layers rich of baryons. Accordingly, a natural ambiguity exists on the definition of the virial density contrast. In fact, when the outer baryon layers infall onto the DM-richer core, they carry with them DM materials outside the original fluctuation; hence, no time exists when all materials originally belonging to the fluctuation--and only they--have virialized. Baryon-DM segregation can have various astrophysical consequences on different length scales. The smallest halos may loose up to 50% of the original baryonic contents and become hardly visible. Subhalos in cluster-size halos may loose much baryonic materials, which could then be observed as intracluster light. Isolated halos, in general, can be expected to have a baryon component richer than the cosmological proportions, due to the cosmic enrichement of baryons lost in small halo encounters
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong
2017-07-01
The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.
On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2014-01-01
The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second...... or the first order differential equation (or a set of equations) for electrical system, depending on properties of the electrical circuit. For the sake of brevity, we assume a 1DOF mechanical system, coupled to 1 or 1/2DOF electrical system (depending whether the capacitance is, or is not considered......). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications...
National Research Council Canada - National Science Library
Soref, Richard A; Sun, Gregory; Khurgin, Jacob B
2005-01-01
We investigate nonlinear optical properties of coup led GaN/AlGaN quantum wells and show that one can engineer the response time and nonlinear phase shift within wide limits and thus achieve optimized...
Sun, F. Z.; Zhang, P.; Liang, Y. C.; Lu, L. H.
2014-09-01
In the non-critical phase-matching (NCPM) along the Θ =90° direction, ADP and DKDP crystals which have many advantages, including a large effective nonlinear optical coefficient, a small PM angular sensitivity and non beam walk-off, at the non-critical phase-matching become the competitive candidates in the inertial confinement fusion(ICF) facility, so the reasonable temperature control of crystals has become more and more important .In this paper, the fluid-solid coupling models of ADP crystal and DKDP crystal which both have anisotropic thermal conductivity in the states of vacuum and non-vacuum were established firstly, and then simulated using the fluid analysis software Fluent. The results through the analysis show that the crystal surface temperature distribution is a ring shape, the temperature gradients in the direction of the optical axis both the crystals are 0.02°C and 0.01°C due to the air, the lowest temperature points of the crystals are both at the center of surface, and the temperatures are lower than 0.09°C and 0.05°C compared in the vacuum and non-vacuum environment, then propose two designs for heating apparatus.
Li, Huanan
2013-03-01
Based on a two-time observation protocol, we consider heat transfer in a given time interval tM in a lead-junction-lead system taking coupling between the leads into account. In view of the two-time observation, consistency conditions are carefully verified in our specific family of quantum histories. Furthermore, its implication is briefly explored. Then using the nonequilibrium Green's function method, we obtain an exact formula for the cumulant generating function for heat transfer between the two leads, valid in both transient and steady-state regimes. Also, a compact formula for the cumulant generating function in the long-time limit is derived, for which the Gallavotti-Cohen fluctuation symmetry is explicitly verified. In addition, we briefly discuss Di Ventra's repartitioning trick regarding whether the repartitioning procedure of the total Hamiltonian affects the nonequilibrium steady-state current fluctuation. All kinds of properties of nonequilibrium current fluctuations, such as the fluctuation theorem in different time regimes, could be readily given according to these exact formulas. Finally a practical formalism dealing with cumulants of heat transfer across general nonlinear quantum systems is established based on field theoretical/algebraic method.
Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.
2009-12-01
A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.
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.
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)
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.
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.
International Nuclear Information System (INIS)
Liu Lan-Lan; Wu Chong-Qing; Wang Jian; Gao Kai-Qiang; Shang Chao
2015-01-01
The quaternion approach to solve the coupled nonlinear Schrödinger equations (CNSEs) in fibers is proposed, converting the CNSEs to a single variable equation by using a conception of eigen-quaternion of coupled quaternion. The crosstalk of quarter-phase-shift-key signals caused by fiber nonlinearity in polarization multiplexing systems with 100 Gbps bit-rate is investigated and simulated. The results demonstrate that the crosstalk is like a rotated ghosting of input constellation. For the 50 km conventional fiber link, when the total power is less than 4 mW, the crosstalk effect can be neglected; when the power is larger than 20 mW, the crosstalk is very obvious. In addition, the crosstalk can not be detected according to the output eye diagram and state of polarization in Poincaré sphere in the trunk fiber, making it difficult for the monitoring of optical trunk link. (paper)
Sun, P. J.; Li, Y. D.; Ren, Y.; Zhang, X. D.; Wu, G. J.; Xu, L. Q.; Chen, R.; Li, Q.; Zhao, H. L.; Zhang, J. Z.; Shi, T. H.; Wang, Y. M.; Lyu, B.; Hu, L. Q.; Li, J.; The EAST Team
2018-01-01
In this paper, we present clear experimental evidence of core region nonlinear coupling between (intermediate, small)-scale microturbulence and an magnetohydrodynamics (MHD) mode during the current ramp-down phase in a set of L-mode plasma discharges in the experimental advanced superconducting tokamak (EAST, Wan et al (2006 Plasma Sci. Technol. 8 253)). Density fluctuations of broadband microturbulence (k\\perpρi˜2{-}5.2 ) and the MHD mode (toroidal mode number m = -1 , poloidal mode number n = 1 ) are measured simultaneously, using a four-channel tangential CO2 laser collective scattering diagnostic in core plasmas. The nonlinear coupling between the broadband microturbulence and the MHD mode is directly demonstrated by showing a statistically significant bicoherence and modulation of turbulent density fluctuation amplitude by the MHD mode.
International Nuclear Information System (INIS)
Mughnetsyan, V.N.; Manaselyan, A.Kh.; Barseghyan, M.G.; Kirakosyan, A.A.
2013-01-01
In this paper the simultaneous effect of hydrostatic pressure and Rashba spin–orbit interaction on intraband linear and nonlinear light absorption has been investigated in cylindrical quantum ring. The one electron energy spectrum has been found using the effective mass approximation and diagonalization procedure. We have found that the Rashba interaction can lead both to the blue- or to the red-shift of the absorption spectrum depending on the transitions character, while the only red-shift is observed due to the hydrostatic pressure. - Highlights: ► The effects of hydrostatic pressure and spin–orbit coupling are investigated for quantum ring. ► The non-linear absorption coefficient is calculated. ► The hydrostatic pressure leads to the decrease in the absorption coefficient. ► Spin–orbit coupling weakens some transitions and strengthens others.
International Nuclear Information System (INIS)
Bora, B.
2015-01-01
On the basis of nonlinear global model, a dual frequency capacitively coupled radio frequency plasma driven by 13.56 MHz and 27.12 MHz has been studied to investigate the influences of driving voltages on the generation of dc self-bias and plasma heating. Fluid equations for the ions inside the plasma sheath have been considered to determine the voltage-charge relations of the plasma sheath. Geometrically symmetric as well as asymmetric cases with finite geometrical asymmetry of 1.2 (ratio of electrodes area) have been considered to make the study more reasonable to experiment. The electrical asymmetry effect (EAE) and finite geometrical asymmetry is found to work differently in controlling the dc self-bias. The amount of EAE has been primarily controlled by the phase angle between the two consecutive harmonics waveforms. The incorporation of the finite geometrical asymmetry in the calculations shift the dc self-bias towards negative polarity direction while increasing the amount of EAE is found to increase the dc self-bias in either direction. For phase angle between the two waveforms ϕ = 0 and ϕ = π/2, the amount of EAE increases significantly with increasing the low frequency voltage, whereas no such increase in the amount of EAE is found with increasing high frequency voltage. In contrast to the geometrically symmetric case, where the variation of the dc self-bias with driving voltages for phase angle ϕ = 0 and π/2 are just opposite in polarity, the variation for the geometrically asymmetric case is different for ϕ = 0 and π/2. In asymmetric case, for ϕ = 0, the dc self-bias increases towards the negative direction with increasing both the low and high frequency voltages, but for the ϕ = π/2, the dc-self bias is increased towards positive direction with increasing low frequency voltage while dc self-bias increases towards negative direction with increasing high frequency voltage
Tetsassi Feugmo, Conrard Giresse; Liégeois, Vincent; Champagne, Benoît
2017-11-15
The first vibrational sum frequency generation (SFG) spectra based on molecular properties calculated at the coupled cluster singles and doubles (CCSD) level of approximation have been simulated for interfacial model alkyl chains, providing benchmark data for comparisons with approximate methods, including density functional theory (DFT). The approach proceeds in three steps. In the first two steps, the molecular spectral properties are determined: the vibrational normal modes and frequencies and then the derivatives of the dipole moment and of the polarizability with respect to the normal coordinates. These derivatives are evaluated with a numerical differentiation approach, of which the accuracy was monitored using Romberg's procedure. Then, in the last step, a three-layer model is employed to evaluate the macroscopic second-order nonlinear optical responses and thereby the simulated SFG spectra of the alkyl interface. Results emphasize the following facts: (i) the dipole and polarizability derivatives calculated at the DFT level with the B3LYP exchange-correlation functional can differ, with respect to CCSD, by as much as ±10 to 20% and ±20 to 50% for the CH 3 and CH 2 vibrations, respectively; (ii) these differences are enhanced when considering the SFG intensities as well as their variations as a function of the experimental configuration (ppp versus ssp) and as a function of the tilt and rotation angles, defining the orientation of the alkyl chain at the interface; (iii) these differences originate from both the vibrational normal coordinates and the Cartesian derivatives of the dipole moment and polarizability; (iv) freezing the successive fragments of the alkyl chain strongly modifies the SFG spectrum and enables highlighting the delocalization effects between the terminal CH 3 group and its neighboring CH 2 units; and finally (v) going from the free chain to the free methyl model, and further to C 3v constraints on leads to large variations of two ratios
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
Stošić, Dušan; Auroux, Aline
Basic principles of calorimetry coupled with other techniques are introduced. These methods are used in heterogeneous catalysis for characterization of acidic, basic and red-ox properties of solid catalysts. Estimation of these features is achieved by monitoring the interaction of various probe molecules with the surface of such materials. Overview of gas phase, as well as liquid phase techniques is given. Special attention is devoted to coupled calorimetry-volumetry method. Furthermore, the influence of different experimental parameters on the results of these techniques is discussed, since it is known that they can significantly influence the evaluation of catalytic properties of investigated materials.
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.
Directory of Open Access Journals (Sweden)
Solenna Blanchard
Full Text Available Developing a clear understanding of the relationship between cerebral blood flow (CBF response and neuronal activity is of significant importance because CBF increase is essential to the health of neurons, for instance through oxygen supply. This relationship can be investigated by analyzing multimodal (fMRI, PET, laser Doppler… recordings. However, the important number of intermediate (non-observable variables involved in the underlying neurovascular coupling makes the discovery of mechanisms all the more difficult from the sole multimodal data. We present a new computational model developed at the population scale (voxel with physiologically relevant but simple equations to facilitate the interpretation of regional multimodal recordings. This model links neuronal activity to regional CBF dynamics through neuro-glio-vascular coupling. This coupling involves a population of glial cells called astrocytes via their role in neurotransmitter (glutamate and GABA recycling and their impact on neighboring vessels. In epilepsy, neuronal networks generate epileptiform discharges, leading to variations in astrocytic and CBF dynamics. In this study, we took advantage of these large variations in neuronal activity magnitude to test the capacity of our model to reproduce experimental data. We compared simulations from our model with isolated epileptiform events, which were obtained in vivo by simultaneous local field potential and laser Doppler recordings in rats after local bicuculline injection. We showed a predominant neuronal contribution for low level discharges and a significant astrocytic contribution for higher level discharges. Besides, neuronal contribution to CBF was linear while astrocytic contribution was nonlinear. Results thus indicate that the relationship between neuronal activity and CBF magnitudes can be nonlinear for isolated events and that this nonlinearity is due to astrocytic activity, highlighting the importance of astrocytes in
Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20
DEFF Research Database (Denmark)
Andersen, Peter E.; Buchhave, P.; Petersen, Paul Michael
1996-01-01
Nonlinear interactions between multiple coherent photorefractive gratings in Bi12SiO20 are investigated. It is demonstrated that the nonlinear mixing, or cross talk, is strongly influenced by the intensity ration kappa between the two object beams. The diffraction efficiency of a specific grating...... may be increased or strongly decreased depending on kappa. In the limit of a weak reference beam intensity compared to the sum of the object beam intencities, we derive an analytical expression for the cross talk valid for all kappa. Furthermore, we find the value of kappa yielding zero cross talk. We...
Energy Technology Data Exchange (ETDEWEB)
Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo (Brazil); Balthazar, José M., E-mail: jmbaltha@gmail.com [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Universidade Estadual Paulista, Faculdade de Engenharia Mec and #x00E (Brazil); Francisco, Cayo Prado Fernandes [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Instituto de Aeronáutica e Espaço, Departamento de (Brazil)
2014-12-10
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.
Li, Ming-Zhen; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Liu, Lei; Du, Zhong
2017-12-01
In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.
International Nuclear Information System (INIS)
Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel; Balthazar, José M.; Francisco, Cayo Prado Fernandes
2014-01-01
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam
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.
Colosi, John A
2008-09-01
While many results have been intuited from numerical simulation studies, the precise connections between shallow-water acoustic variability and the space-time scales of nonlinear internal waves (NLIWs) as well as the background environmental conditions have not been clearly established analytically. Two-dimensional coupled mode propagation through NLIWs is examined using a perturbation series solution in which each order n is associated with nth-order multiple scattering. Importantly, the perturbation solution gives resonance conditions that pick out specific NLIW scales that cause coupling, and seabed attenuation is demonstrated to broaden these resonances, fundamentally changing the coupling behavior at low frequency. Sound-speed inhomogeneities caused by internal solitary waves (ISWs) are primarily considered and the dependence of mode coupling on ISW amplitude, range width, depth structure, location relative to the source, and packet characteristics are delineated as a function of acoustic frequency. In addition, it is seen that significant energy transfer to modes with initially low or zero energy involves at least a second order scattering process. Under moderate scattering conditions, comparisons of first order, single scattering theoretical predictions to direct numerical simulation demonstrate the accuracy of the approach for acoustic frequencies upto 400 Hz and for single as well as multiple ISW wave packets.
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
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2013-01-01
An electro-magneto-mechanical system combines three physical domains - a mechanical structure, a magnetic field and an electric circuit. The interaction between these domains is analysed for a structure with two degrees of freedom (translational and rotational) and two electrical circuits. Each...... electrical circuit is described by a differential equation of the 1st order, which is considered to contribute to the coupled system by 0.5 DOF. The electrical and mechanical systems are coupled via a magnetic circuit, which is inherently non-linear, due to a non-linear nature of the electro-magnetic force...
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)
International Nuclear Information System (INIS)
Zhang, Z. L.; Nie, Q. Y.; Wang, Z. B.; Gao, X. T.; Kong, F. R.; Sun, Y. F.; Jiang, B. H.
2016-01-01
Dielectric barrier discharges (DBDs) provide a promising technology of generating non-equilibrium cold plasmas in atmospheric pressure gases. For both application-focused and fundamental studies, it is important to explore the strategy and the mechanism for enabling effective independent tuning of key plasma parameters in a DBD system. In this paper, we report numerical studies of effects of dual-frequency excitation on atmospheric DBDs, and modulation as well as separate tuning mechanism, with emphasis on dual-frequency coupling to the key plasma parameters and discharge evolution. With an appropriately applied low frequency to the original high frequency, the numerical calculation demonstrates that a strong nonlinear coupling between two frequencies governs the process of ionization and energy deposition into plasma, and thus raises the electron density significantly (e.g., three times in this case) in comparisons with a single frequency driven DBD system. Nevertheless, the gas temperature, which is mainly determined by the high frequency discharge, barely changes. This method then enables a possible approach of controlling both averaged electron density and gas temperature independently.
International Nuclear Information System (INIS)
Strenski, P.N.
1985-01-01
The first part of this thesis deals with the analysis of a small array of Josephson junctions, superconducting devices of markedly nonlinear behavior. The components of the array are modeled as resistively-shunted junctions and are driven by direct current. A chapter is provided that reviews the validity and features of such a model for the case of a single junction. This chapter also includes background information on the subjects of bifurcation, chaos, and fractals. In the following chapters, the array of three junctions is studied, first with one driving current and later with an additional bias current. The analysis includes both numerical results from computer simulations and analytic computations using a perturbative approach. The two approaches are shown to be in good agreement. The behavior of the array is dominated by hysteresis effects. The second part of the thesis describes an exact bound-to-site transformation for diffusion-limited aggregation. A review is provided that summarizes the field of aggregation and demonstrates the need for such exact results. The equivalence maps a class of partial adhesion problems on arbitrary lattices to absolute adhesion problems on transformed lattices. Examples are given for diffusion in the presence and absence of an external field
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.
International Nuclear Information System (INIS)
Bressloff, P.C.; Bressloff, N.W.
2000-01-01
Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neurons is analyzed in terms of spontaneous pattern formation. It is shown how the ring bifurcates from a synchronous state to a non-phase-locked state whose spike trains are characterized by quasiperiodic variations of the inter-spike intervals (ISIs) on closed invariant circles. The separation of these invariant circles in phase space results in a localized peak of activity as measured by the time-averaged firing rate of the neurons. This generates a sharp orientation tuning curve that can lock to a slowly rotating, weakly tuned external stimulus. For fast synapses, breakup of the quasiperiodic orbits occurs leading to high spike time variability suggestive of chaos
Bressloff, P. C.; Bressloff, N. W.
2000-02-01
Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neurons is analyzed in terms of spontaneous pattern formation. It is shown how the ring bifurcates from a synchronous state to a non-phase-locked state whose spike trains are characterized by quasiperiodic variations of the inter-spike intervals (ISIs) on closed invariant circles. The separation of these invariant circles in phase space results in a localized peak of activity as measured by the time-averaged firing rate of the neurons. This generates a sharp orientation tuning curve that can lock to a slowly rotating, weakly tuned external stimulus. For fast synapses, breakup of the quasiperiodic orbits occurs leading to high spike time variability suggestive of chaos.
Rose, Brian E. J.
2015-02-01
Ongoing controversy about Neoproterozoic Snowball Earth events motivates a theoretical study of stability and hysteresis properties of very cold climates. A coupled atmosphere-ocean-sea ice general circulation model (GCM) has four stable equilibria ranging from 0% to 100% ice cover, including a "Waterbelt" state with tropical sea ice. All four states are found at present-day insolation and greenhouse gas levels and with two idealized ocean basin configurations. The Waterbelt is stabilized against albedo feedback by intense but narrow wind-driven ocean overturning cells that deliver roughly 100 W m-2 heating to the ice edges. This requires three-way feedback between winds, ocean circulation, and ice extent in which circulation is shifted equatorward, following the baroclinicity at the ice margins. The thermocline is much shallower and outcrops in the tropics. Sea ice is snow-covered everywhere and has a minuscule seasonal cycle. The Waterbelt state spans a 46 W m-2 range in solar constant, has a significant hysteresis, and permits near-freezing equatorial surface temperatures. Additional context is provided by a slab ocean GCM and a diffusive energy balance model, both with prescribed ocean heat transport (OHT). Unlike the fully coupled model, these support no more than one stable ice margin, the position of which is slaved to regions of rapid poleward decrease in OHT convergence. Wide ranges of different climates (including the stable Waterbelt) are found by varying the magnitude and spatial structure of OHT in both models. Some thermodynamic arguments for the sensitivity of climate, and ice extent to OHT are presented.
International Nuclear Information System (INIS)
Dokhane, A.; Henning, D.; Chawla, R.; Rizwan-Uddin
2003-01-01
BWR stability analysis at PSI, as at other research centres, is usually carried out employing complex system codes. However, these do not allow a detailed investigation of the complete manifold of all possible solutions of the associated nonlinear differential equation set. A novel analytical, reduced order model for BWR stability has been developed at PSI, in several successive steps. In the first step, the thermal-hydraulic model was used for studying the thermal-hydraulic instabilities. A study was then conducted of the one-channel nuclear-coupled thermal-hydraulic dynamics in a BWR by adding a simple point kinetic model for neutron kinetics and a model for the fuel heat conduction dynamics. In this paper, a two-channel nuclear-coupled thermal-hydraulic model is introduced to simulate the out-of phase oscillations in a BWR. This model comprises three parts: spatial mode neutron kinetics with the fundamental and fist azimuthal modes; fuel heat conduction dynamics; and thermal-hydraulics model. This present model is an extension of the Karve et al. model i.e., a drift flux model is used instead of the homogeneous equilibrium model for two-phase flow, and lambda modes are used instead of the omega modes for the neutron kinetics. This two-channel model is employed in stability and bifurcation analyses, carried out using the bifurcation code BIFDD. The stability boundary (SB) and the nature of the Poincare-Andronov-Hopf bifurcation (PAF-B) are determined and visualized in a suitable two-dimensional parameter/state space. A comparative study of the homogeneous equilibrium model (HEM) and the drift flux model (DFM) is carried out to investigate the effects of the DFM parameters the void distribution parameter C 0 and the drift velocity V gi -on the SB, the nature of PAH bifurcation, and on the type of oscillation mode (in-phase or out-of-phase). (author)
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
Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Yuan, Yu-Qiang
2018-05-01
Studied in this paper is a (2+1)-dimensional coupled nonlinear Schrödinger system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-I and type-II rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves. When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.
Directory of Open Access Journals (Sweden)
Chenji Wei
2018-02-01
Full Text Available Gas transport in shale gas reservoirs is largely affected by rock properties such as permeability. These properties are often sensitive to the in-situ stress state changes. Accurate modeling of shale gas transport in shale reservoir rocks considering the stress sensitive effects on rock petrophysical properties is important for successful shale gas extraction. Nonlinear elasticity in stress sensitive reservoir rocks depicts the nonlinear stress-strain relationship, yet it is not thoroughly studied in previous reservoir modeling works. In this study, an improved coupled flow and geomechanics model that considers nonlinear elasticity is proposed. The model is based on finite element methods, and the nonlinear elasticity in the model is validated with experimental data on shale samples selected from the Longmaxi Formation in Sichuan Basin China. Numerical results indicate that, in stress sensitive shale rocks, nonlinear elasticity affects shale permeability, shale porosity, and distributions of effective stress and pore pressure. Elastic modulus change is dependent on not only in-situ stress state but also stress history path. Without considering nonlinear elasticity, the modeling of shale rock permeability in Longmaxi Formation can overestimate permeability values by 1.6 to 53 times.
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
Problems in nonlinear resistive MHD
International Nuclear Information System (INIS)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-01-01
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1
Directory of Open Access Journals (Sweden)
Azizian Davood
2016-12-01
Full Text Available Regarding the importance of short circuit and inrush current simulations in the split-winding transformer, a novel nonlinear equivalent circuit is introduced in this paper for nonlinear simulation of this transformer. The equivalent circuit is extended using the nonlinear inductances. Employing a numerical method, leakage and magnetizing inductances in the split-winding transformer are extracted and the nonlinear model inductances are estimated using these inductances. The introduced model is validated and using this nonlinear model, inrush and short-circuit currents are calculated. It has been seen that the introduced model is valid and suitable for simulations of the split-winding transformer due to various loading conditions. Finally, the effects of nonlinearity of the model inductances are discussed in the following.
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
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...
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.
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.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
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
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...
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
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...
Nonlinear electrodynamics and cosmology
International Nuclear Information System (INIS)
Breton, Nora
2010-01-01
Nonlinear electrodynamics (NLED) generalizes Maxwell's theory for strong fields. When coupled to general relativity NLED presents interesting features like the non-vanishing of the trace of the energy-momentum tensor that leads to the possibility of violation of some energy conditions and of acting as a repulsive contribution in the Raychaudhuri equation. This theory is worth to study in cosmological and astrophysical situations characterized by strong electromagnetic and gravitational fields.
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...
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
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Nonlinear 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....
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.
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
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.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.
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.
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...
Experimental studies of nonlinear beam dynamics
International Nuclear Information System (INIS)
Caussyn, D.D.; Ball, M.; Brabson, B.; Collins, J.; Curtis, S.A.; Derenchuck, V.; DuPlantis, D.; East, G.; Ellison, M.; Ellison, T.; Friesel, D.; Hamilton, B.; Jones, W.P.; Lamble, W.; Lee, S.Y.; Li, D.; Minty, M.G.; Sloan, T.; Xu, G.; Chao, A.W.; Ng, K.Y.; Tepikian, S.
1992-01-01
The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility cooler ring. Motion in one dimension was measured for betatron tunes near the third, fourth, fifth, and seventh integer resonances. This motion is described by coupling between the transverse modes of motion and nonlinear field errors. The Hamiltonian for nonlinear particle motion near the third- and fourth-integer-resonance conditions has been deduced
Integrable KP Coupling and Its Exact Solution
International Nuclear Information System (INIS)
Peng Ling; Yang Xuxong; Lou Senyue
2012-01-01
The integrable coupling is one of the most important topics in the nonlinear physics. This paper creates a novel integrable KP coupling and solves it via a recently-developed dark parameterization procedure. (general)
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....
Ocean wave nonlinearity and phase couplings
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J
stream_size 4 stream_content_type text/plain stream_name Indian_J_Mar_Sci_20_93.pdf.txt stream_source_info Indian_J_Mar_Sci_20_93.pdf.txt Content-Encoding ISO-8859-1 Content-Type text/plain; charset=ISO-8859-1 ...
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...
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
Nonlinear waves in plasma with negative ion
International Nuclear Information System (INIS)
Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.
1984-01-01
The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Nonlinear phenomena at cyclotron resonance
International Nuclear Information System (INIS)
Subbarao, D.; Uma, R.
1986-01-01
Finite amplitude electromagnetic waves in a magnetoplasma which typically occur in situations as in present day wave heating, current drives and other schemes in magnetically confined fusion systems, can show qualitatively different absorption and emission characteristics around resonant frequencies of the plasma because of anharmonicity. Linear wave plasma coupling as well as weak nonlinear effects such as parametric instabilities generally overlook this important effect even though the thresholds for the two phenomena as shown here are comparable. Though the effects described here are relevant to a host of nonlinear resonance effects in fusion plasmas, the authors mainly limit themselves to ECRH
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...
Linear and nonlinear piezoelectric shunting strategies for vibration mitigation
Directory of Open Access Journals (Sweden)
Soltani P.
2014-01-01
Full Text Available This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based on the equal-peak method. A comparison between the performance of linear mechanical and electrical tuned vibration absorbers coupled to a linear oscillator is first performed. Nonlinearity is then introduced in the primary oscillator to which a new nonlinear electrical tuned vibration absorber is attached. Despite the frequency-energy dependence of nonlinear oscillations, we show that the nonlinear absorber is capable of effectively mitigating the vibrations of the nonlinear primary system in a large range of forcing amplitudes.
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.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah; Hajjaj, Amal Z.; Younis, Mohammad I.
2016-01-01
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.
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
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...
Gradient-based optimization in nonlinear structural dynamics
DEFF Research Database (Denmark)
Dou, Suguang
The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...
Simulating nonlinear neutrino flavor evolution
Duan, H.; Fuller, G. M.; Carlson, J.
2008-10-01
We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev Smirnov Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle θ13.
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
Nonlinear and stochastic dynamics of coherent structures
DEFF Research Database (Denmark)
Rasmussen, Kim
1997-01-01
This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...
Nonlinear analysis on power reactor dynamics
International Nuclear Information System (INIS)
Konno, H.; Hayashi, K.
1997-01-01
We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)
Wave modulation in a nonlinear dispersive medium
International Nuclear Information System (INIS)
Kim, Y.C.; Khadra, L.; Powers, E.J.
1980-01-01
A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model
Vibronic coupling density and related concepts
International Nuclear Information System (INIS)
Sato, Tohru; Uejima, Motoyuki; Iwahara, Naoya; Haruta, Naoki; Shizu, Katsuyuki; Tanaka, Kazuyoshi
2013-01-01
Vibronic coupling density is derived from a general point of view as a one-electron property density. Related concepts as well as their applications are presented. Linear and nonlinear vibronic coupling density and related concepts, orbital vibronic coupling density, reduced vibronic coupling density, atomic vibronic coupling constant, and effective vibronic coupling density, illustrate the origin of vibronic couplings and enable us to design novel functional molecules or to elucidate chemical reactions. Transition dipole moment density is defined as an example of the one-electron property density. Vibronic coupling density and transition dipole moment density open a way to design light-emitting molecules with high efficiency.
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
Yang, Y.; Solis Escalante, T.; van der Helm, F.C.T.; Schouten, A.C.
2016-01-01
Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present
Advances in nonlinear vibration analysis of structures. Part-I. Beams
Indian Academy of Sciences (India)
Unknown
element analysis of nonlinear beams under static and dynamic loads. ... linearization, substitution of inplane boundary conditions at element level rather .... Modelling the nonlinear vibration problems using finite elements, albeit with a couple.
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...
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr
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.
Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.
Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F
2016-10-21
Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.
Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles
Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.
2016-10-01
Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.
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
Engineering high-order nonlinear dissipation for quantum superconducting circuits
Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.
Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.
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
Theory and design of nonlinear metamaterials
Rose, Alec Daniel
If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers
A study of discrete nonlinear systems
International Nuclear Information System (INIS)
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
Complete synchronization in coupled type-I neurons
Indian Academy of Sciences (India)
Keywords. Complete synchronization; noise; coupled type-I neurons. Abstract. For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of ... Pramana – Journal of Physics | News.
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).
Spin-current emission governed by nonlinear spin dynamics.
Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya
2015-10-16
Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.
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
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.
A solution to nonlinearity problems
International Nuclear Information System (INIS)
Neuffer, D.V.
1989-01-01
New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab
Nonlinear resonance phenomena of a doped fibre laser under cavity ...
Indian Academy of Sciences (India)
quence and other routes to chaos, generalized multistability and crisis. But, doped ... of chaos and synchronization of coupled chaotic lasers (for communication with a ... The two basic issues in focus here for the nonlinear dynamical studies.
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 ...
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
Nonlinear theory of the free-electron laser
International Nuclear Information System (INIS)
Chian, A.C.-L.; Padua Brito Serbeto, A. de.
1984-01-01
A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
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
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.
Slow-light dynamics in nonlinear periodic waveguides couplers
DEFF Research Database (Denmark)
Sukhorukov, A.A.; Ha, S.; Powell, D.A.
2009-01-01
We predict pulse switching and reshaping through nonlinear mixing of two slow-light states with different phase velocities in the same frequency range, and report on the first experimental observation of slow-light tunneling between coupled periodic waveguides.......We predict pulse switching and reshaping through nonlinear mixing of two slow-light states with different phase velocities in the same frequency range, and report on the first experimental observation of slow-light tunneling between coupled periodic waveguides....
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....
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
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...
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.)
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
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.
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.
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.
Hanamura, Eiichi; Yamanaka, Akio
2007-01-01
This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Simultaneous viscous-inviscid coupling via transpiration
International Nuclear Information System (INIS)
Yiu, K.F.C.; Giles, M.B.
1995-01-01
In viscous-inviscid coupling analysis, the direct coupling technique and the inverse coupling technique are commonly adopted. However, stability and convergence of the algorithms derived are usually very unsatisfactory. Here, by using the transpiration technique to simulate the effect of the displacement thickness, a new simultaneous coupling method is derived. The integral boundary layer equations and the full potential equation are chosen to be the viscous-inviscid coupled system. After discretization, the Newton-Raphson technique is proposed to solve the coupled nonlinear system. Several numerical results are used to demonstrate the accuracy and efficiency of the proposed method. 15 refs., 23 figs
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....
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...
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
The application of He's exp-function method to a nonlinear differential-difference equation
International Nuclear Information System (INIS)
Dai Chaoqing; Cen Xu; Wu Shengsheng
2009-01-01
This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
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.
Topological approximation of the nonlinear Anderson model
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Nonlinear Single Spin Spectrum Analayzer
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-05-01
Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.
Dumeige, Yannick; Féron, Patrice
2011-10-01
Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.
International Nuclear Information System (INIS)
Dumeige, Yannick; Feron, Patrice
2011-01-01
Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.
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
Transient chaos in weakly coupled Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Koch, B P; Bruhn, B
1988-01-01
This paper considers periodic excitations and coupling of nonlinear Josephson oscillators. The Melnikov method is used to prove the existence of horseshoes in the dynamics. The coupling of two systems yields a reduction of the chaos threshold in comparison with the corresponding threshold of a single system. For some selected parameter values the theoretical predictions are checked by numerical methods.
Coupling single emitters to quantum plasmonic circuits
DEFF Research Database (Denmark)
Huck, Alexander; Andersen, Ulrik Lund
2016-01-01
In recent years, the controlled coupling of single-photon emitters to propagating surface plasmons has been intensely studied, which is fueled by the prospect of a giant photonic nonlinearity on a nanoscaled platform. In this article, we will review the recent progress on coupling single emitters...
Simulating nonlinear neutrino flavor evolution
Energy Technology Data Exchange (ETDEWEB)
Duan, H [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195 (United States); Fuller, G M [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Carlson, J [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: hduan@phys.washington.edu, E-mail: gfuller@ucsd.edu, E-mail: carlson@lanl.gov
2008-10-01
We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev-Smirnov-Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle {theta}{sub 13}.
Linear and nonlinear low-frequency electrostatic waves in a nonuniform pair-ion-dust magnetoplasma
International Nuclear Information System (INIS)
Saleem, H; Shukla, P K; Eliasson, B
2008-01-01
Linear and nonlinear properties of the low-frequency (in comparison with the ion gyrofrequency) electrostatic oscillations in pair-ion-dust magnetoplasma are presented. In the linear limit, the Shukla-Varma mode is coupled with the ion oscillations while the nonlinearly coupled modes appear in the form of a dipolar or a monopolar vortex
Nonlinear electron transport in magnetized laser plasmas
International Nuclear Information System (INIS)
Kho, T.H.; Haines, M.G.
1986-01-01
Electron transport in a magnetized plasma heated by inverse bremsstrahlung is studied numerically using a nonlinear Fokker--Planck model with self-consistent E and B fields. The numerical scheme is described. Nonlocal transport is found to alter many of the transport coefficients derived from linear transport theory, in particular, the Nernst and Righi--Leduc effects, in addition to the perpendicular heat flux q/sub perpendicular/, are substantially reduced near critical surface. The magnetic field, however, remains strongly coupled to the nonlinear q/sub perpendicular/ and, as has been found in hydrosimulations, convective amplification of the magnetic field occurs in the overdense plasma
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
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15
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.
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.
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.
Wave Propagation of Coupled Modes in the DNA Double Helix
International Nuclear Information System (INIS)
Tabi, Conrad B.; Mohamadou, Alidou; Kofane, Timoleon C.
2010-06-01
The dynamics of waves propagating along the DNA molecule is described by the coupled nonlinear Schroedinger equations. We consider both the single and the coupled nonlinear excitation modes, and we discuss their biological implications. Furthermore, the characteristics of the coupled mode solution are discussed and we show that such a solution can describe the local opening observed within the transcription and the replication phenomena. (author)
Coupled oscillators with parity-time symmetry
Energy Technology Data Exchange (ETDEWEB)
Tsoy, Eduard N., E-mail: etsoy@uzsci.net
2017-02-05
Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed. - Highlights: • A generalization of a Hamiltonian system of linear coupled oscillators with the parity-time (PT) symmetry is suggested. • It is found that an increase of the gain-loss parameter can stabilize the system. • A family of Hamiltonian functions for two coupled nonlinear oscillators with PT-symmetry is obtained.
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.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-01-01
With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth...
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
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
International Nuclear Information System (INIS)
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-01-01
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules
Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound
Solodov, Igor; Busse, Gerd
The concept of defect-selective ultrasonic nonlinear imaging is based on visualization of strongly nonlinear inclusions in the form of localized cracked defects. For intense excitation, the ultrasonic response of defects is affected by mechanical constraint between their fragments that makes their vibrations extremely nonlinear. The cracked flaws, therefore, efficiently generate multiple new frequencies, which can be used as a nonlinear "tag" to detect and image them. In this paper, the methodologies of nonlinear scanning laser vibrometry (NSLV) and nonlinear air-coupled emission (NACE) are applied for nonlinear imaging of various defects in hi-tech and constructional materials. A broad database obtained demonstrates evident advantages of the nonlinear approach over its linear counterpart. The higher-order nonlinear frequencies provide increase in signal-to-noise ratio and enhance the contrast of imaging. Unlike conventional ultrasonic instruments, the nonlinear approach yields abundant multi-frequency information on defect location. The application of image recognition and processing algorithms is described and shown to improve reliability and quality of ultrasonic imaging.
Self-synchronization in an ensemble of nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Ostrovsky, L. A., E-mail: lev.ostrovsky@gmail.com [Physical Science Division, NOAA Earth Science Research Laboratory, and University of Colorado, Boulder, Colorado 80305 (United States); Galperin, Y. V.; Skirta, E. A. [Department of Mathematics, East Stroudsburg University, East Stroudsburg, Pennsylvania 18301 (United States)
2016-06-15
The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system.
Nonlinear dynamics in Nuclotron
International Nuclear Information System (INIS)
Dinev, D.
1997-01-01
The paper represents an extensive study of the nonlinear beam dynamics in the Nuclotron. Chromatic effects, including the dependence of the betatron tunes on the amplitude, and chromatic perturbations have been investigated taking into account the measured field imperfections. Beam distortion, smear, dynamic aperture and nonlinear acceptance have been calculated for different particle energies and betatron tunes
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.
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 programming with feedforward neural networks.
Energy Technology Data Exchange (ETDEWEB)
Reifman, J.
1999-06-02
We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.
General solution of string inspired nonlinear equations
International Nuclear Information System (INIS)
Bandos, I.A.; Ivanov, E.; Kapustnikov, A.A.; Ulanov, S.A.
1998-07-01
We present the general solution of the system of coupled nonlinear equations describing dynamics of D-dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2) dimensional spheres S D-2 = SO(1,D-1)/SO(1,1)xSO(D-2) contained in K D-2 . (author)
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
Self-similar solutions of certain coupled integrable systems
Chakravarty, S; Kent, S L
2003-01-01
Similarity reductions of the coupled nonlinear Schroedinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painleve transcendents, leading to new exact self-similar solutions for these integrable equations.
Self-similar solutions of certain coupled integrable systems
International Nuclear Information System (INIS)
Chakravarty, S; Halburd, R G; Kent, S L
2003-01-01
Similarity reductions of the coupled nonlinear Schroedinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painleve transcendents, leading to new exact self-similar solutions for these integrable equations
Chaotic synchronization of three coupled oscillators with ring connection
International Nuclear Information System (INIS)
Kyprianidis, I.M.; Stouboulos, I.N.
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)
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).
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.
Nonlinear amplitude dynamics in flagellar beating.
Oriola, David; Gadêlha, Hermes; Casademunt, Jaume
2017-03-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
Nonlinear photonic metasurfaces
Li, Guixin; Zhang, Shuang; Zentgraf, Thomas
2017-03-01
Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.
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
Fourier imaging of non-linear structure formation
International Nuclear Information System (INIS)
Brandbyge, Jacob; Hannestad, Steen
2017-01-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
Fourier imaging of non-linear structure formation
Energy Technology Data Exchange (ETDEWEB)
Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)
2017-04-01
We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.
Nonlinear wave chaos: statistics of second harmonic fields.
Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M
2017-10-01
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.
DEFF Research Database (Denmark)
Dahl, Michael S.; Van Praag, Mirjam; Thompson, Peter
2015-01-01
We study possible motivations for co-entreprenurial couples to start up a joint firm, using a sample of 1,069 Danish couples that established a joint enterprise between 2001 and 2010. We compare their pre-entry characteristics, firm performance and post-dissolution private and financial outcomes...
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
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.
Heterotic sigma models and non-linear strings
International Nuclear Information System (INIS)
Hull, C.M.
1986-01-01
The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)
Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction
Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.
2005-03-01
We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.
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.
Some non-linear physics in crystallographic structures
International Nuclear Information System (INIS)
Aubry, S.
1977-10-01
A summary of studies on simple but strongly nonlinear crystallographic models that make use of some methods in stochasticity is presented. Two one-dimensional models are described; one has been studied to understand some aspects of the nonlinear dynamics in crystals when close to the transition temperature, the other is for commensurability and incommensurability problems. Periodic orbits and the dynamics of a one-dimensional coupled double-well chain are considered, along with lattice locking and stochasticity
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...
Canonical action-angle formalism for quantized nonlinear fields
International Nuclear Information System (INIS)
Garbaczewki, P.
1987-01-01
The canonical quantizations of field and action-angle coordinates which (locally) parameterize the phase manifold for the same nonlinear field theory model (e.g. sine-Gordon and nonlinear Schrodinger with the attractive coupling) are reconciled on the common for both cases state space. The classical-quantum relationship is maintained in the mean: coherent state expectation values of operators give rise to classical objects
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.
Nonlinear switching dynamics in a photonic-crystal nanocavity
International Nuclear Information System (INIS)
Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper
2014-01-01
We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.
Nonlinear switching dynamics in a photonic-crystal nanocavity
DEFF Research Database (Denmark)
Yu, Yi; Palushani, Evarist; Heuck, Mikkel
2014-01-01
We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...
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.
Photostable nonlinear optical polycarbonates
Faccini, M.; Balakrishnan, M.; Diemeer, Mart; Torosantucci, Riccardo; Driessen, A.; Reinhoudt, David; Verboom, Willem
2008-01-01
Highly thermal and photostable nonlinear optical polymers were obtained by covalently incorporating the tricyanovinylidenediphenylaminobenzene (TCVDPA) chromophore to a polycarbonate backbone. NLO polycarbonates with different chromophore attachment modes and flexibilities were synthesized. In spite
Nonlinear singular elliptic equations
International Nuclear Information System (INIS)
Dong Minh Duc.
1988-09-01
We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs
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.
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...... nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...... to a decrease of plasma frequency in semiconductor and produces a substantial modification of THz-range material dielectric function, described by the Drude model. As a result, the nonlinearity of both absorption coefficient and refractive index of the semiconductor is observed. In particular we demonstrate...
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...