Nonlinear evolution of astrophysical Alfven waves
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Nonlinear hybrid simulation of toroidicity-induced alfven eigenmode
International Nuclear Information System (INIS)
Fu, G.Y.; Park, W.
1994-11-01
Gyrokinetic/Magnetohydrodynamics hybrid simulations have been carried out using MH3D-K code to study the nonlinear saturation of the toroidicity-induced Alfven eigenmode driven by energetic particles in a tokamak plasma. It is shown that the wave particle trapping is the nonlinear saturation mechanism for the parameters considered. The corresponding density profile flattening of hot particles is observed. The saturation amplitude is proportional to the square of linear growth rate. In addition to TAE modes, a new n = 1, m = 0 global Alfven eigenmode is shown to be excited by the energetic particles
Direct excitation of resonant torsional Alfven waves by footpoint motions
Ruderman, M. S.; Berghmans, D.; Goossens, M.; Poedts, S.
1997-01-01
The present paper studies the heating of coronal loops by linear resonant Alfven waves that are excited by the motions of the photospheric footpoints of the magnetic field lines. The analysis is restricted to torsionally polarised footpoint motions in an axially symmetric system so that only
Resonant Alfven wave instabilities driven by streaming fast particles
International Nuclear Information System (INIS)
Zachary, A.
1987-01-01
A plasma simulation code is used to study the resonant interactions between streaming ions and Alfven waves. The medium which supports the Alfven waves is treated as a single, one-dimensional, ideal MHD fluid, while the ions are treated as kinetic particles. The code is used to study three ion distributions: a cold beam; a monoenergetic shell; and a drifting distribution with a power-law dependence on momentum. These distributions represent: the field-aligned beams upstream of the earth's bow shock; the diffuse ions upstream of the bow shock; and the cosmic ray distribution function near a supernova remnant shock. 92 refs., 31 figs., 12 tabs
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...
The effect of compressibility on the Alfven spatial resonance heating
International Nuclear Information System (INIS)
Azevedo, C.A.
1984-01-01
The effect of compressibility of magnetic field line on the damping rate of Alfven spatial resonance heating for a high beta plasma (Kinetic pressure/magnetic pressure) was analysed, using the ideal MHD (Magnetohydrodynamic) model in cylindrical geometry for a diffuse θ-pinch with conducting wall. The dispersion relation was obtained solving the equation of motion in the plasma and vacuum regions together with boundary conditions. (Author) [pt
Nonlinear standing shear Alfven waves in the Earth`s magnetosphere
Energy Technology Data Exchange (ETDEWEB)
Rankin, R.; Frycz, P.; Tikhonchuk, V.T.; Samson, J. C. [Univ. of Alberta, Edmonton, Alberta (Canada)
1994-11-01
We present theory and numerical simulations of strong nonlinear effects in standing shear Alfven waves (SAWs) in the Earth`s magnetosphere, which is modeled as a finite size box with straight magnetic lines and (partially) reflecting boundaries. In a low beta plasma it is shown that the ponderomotive force can lead to a large-amplitude SAW spatial harmonic generation due to nonlinear coupling between the SAW and a slow magnetosonic wave. The nonlinear coupling leads to secularly growing frequency shifts, and in the case of driven systems, nonlinear dephasing can lead to saturation of the driven wave fields. The results are discussed on the context of their possible relevance to the theory of standing ionospheric cavity wave modes and field line resonances in the high-latitude magnetosphere.
On field line resonances of hydromagnetic Alfven waves in dipole magnetic field
International Nuclear Information System (INIS)
Chen, Liu; Cowley, S.C.
1989-07-01
Using the dipole magnetic field model, we have developed the theory of field line resonances of hydromagnetic Alfven waves in general magnetic field geometries. In this model, the Alfven speed thus varies both perpendicular and parallel to the magnetic field. Specifically, it is found that field line resonances do persist in the dipole model. The corresponding singular solutions near the resonant field lines as well as the natural definition of standing shear Alfven eigenfunctions have also been systematically derived. 11 refs
Kelvin-Helmholtz instability in an Alfven resonant layer of a solar coronal loop
Uchimoto, E.; Strauss, H. R.; Lawson, W. S.
1991-01-01
A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfven resonant layer in an axially bounded, straight cylindrical coronal loop. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfven driving amplitude and inversely proportional to the width of the Alfven resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfven resonant layer width, and decreases at higher azimuthal mode number.
Shear Alfven wave excitation by direct antenna coupling and fast wave resonant mode conversion
International Nuclear Information System (INIS)
Borg, G.G.
1994-01-01
Antenna coupling to the shear Alfven wave by both direct excitation and fast wave resonant mode conversion is modelled analytically for a plasma with a one dimensional linear density gradient. We demonstrate the existence of a shear Alfven mode excited directly by the antenna. For localised antennas, this mode propagates as a guided beam along the steady magnetic field lines intersecting the antenna. Shear Alfven wave excitation by resonant mode conversion of a fast wave near the Alfven resonance layer is also demonstrated and we prove that energy is conserved in this process. We compare the efficiency of these two mechanisms of shear Alfven wave excitation and present a simple analytical formula giving the ratio of the coupled powers. Finally, we discuss the interpretation of some experimental results. 45 refs., 7 figs
The soliton transform and a possible application to nonlinear Alfven waves in space
Hada, T.; Hamilton, R. L.; Kennel, C. F.
1993-01-01
The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.
Heating of solar coronal loops by resonant absorption of Alfven waves
Grossmann, William; Smith, Robert A.
1988-01-01
Numerical calculations governing the efficiency of coronal loop heating by the resonant absorption of shear Alfven waves are reported. The loop structure is modeled by a class of axisymmetric force-free equilibria of a long straight cylinder, approximating a large aspect ratio loop. For a range of parameters characterizing the evolution of solar coronal loops, the absorption bandwidth falls in the frequency range of the photospheric motions due to granulation and p-modes. Resonant Alfven wave absorption is thus a viable mechanism for coronal loop heating.
Crossing a Nonlinear Resonance
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Crossing a Nonlinear Resonance: Adiabatic Invariants and the Melnikov-Arnold Integral. Sudhir R Jain. General Article Volume 19 Issue 9 September 2014 pp 797-813 ...
Energy Technology Data Exchange (ETDEWEB)
Biglari, H.; Zonca, F.; Chen, L.
1991-10-01
Toroidal Alfven eigenmodes are shown to be resonantly destabilized by both circulating and trapped energetic ions/alpha particles. In particular, the energetic circulating ions are shown to resonate with the mode not only at the Alfven speed ({upsilon}{sub A}), but also one-third of this speed, while resonances exist between trapped energetic ions and the wave when {upsilon} = {upsilon}{sub A}/21{epsilon}{sup {1/2}} (l=integer, {epsilon}=r/R is the local inverse aspect ratio), although the instability becomes weaker for resonances other than the fundamental. The oft-quoted criterion that instability requires super-Alfvenic ion velocities is thus sufficient but not necessary. 14 refs.
Nonlinear Dynamics of Fast-electron Driven Beta-induced Alfven eigenmode
Cheng, Junyi; Zhang, Wenlu; Lin, Zhihong; Li, Ding
2017-10-01
The fast-electron driven beta-induced Alfven eigenmode (e-BAE) has been routinely observed in HL-2A tokamak. We study e-BAE for the first time using global gyrokinetic GTC simulations, where the fast electrons are described by the drift kinetic model. Frequency chirping is observed in nonlinear simulations in the absence of sources and sinks, which provides a new nonlinear paradigm beyond the standard ``bump-on-tail'' model. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of the coherent structures in the fast electron phase space, where the dynamics of the coherent structure is controlled by the formation and destruction of phase space islands in the canonical variables. Furthermore, we put forward a new theory frame to demonstrate that the evolution of chirping phenomenon is essentially induced by balance and destruction of net shear flow in the toroidal direction combined by the background shear flow and perturbed shear flow, which provides a novel and clear physical image.
Resonant interaction of energetic ions with Alfven-like perturbations in stellarators
International Nuclear Information System (INIS)
Karulin, N.; Wobig, H.
1994-04-01
The modification of passing guiding center orbits of 3.5 MeV alpha particles and 45 keV protons in the presence of global Alfven eigenmodes (GAE's) is studied in modular advanced stellarators. It is found that if resonances between particles and waves occur, drift surfaces form a set of island structures. The mode numbers of the perturbations, which are dangerous for the energetic particle confinement, are discussed for two particular stellarators (Helias reactor and Wendelstein 7-AS). The perturbation amplitudes corresponding to the onset of orbit stochasticity are studied numerically. The coefficient of the collisionless stochastic diffusion is estimated using the island width derived analytically. (orig.)
Heating of the solar corona by the resonant absorption of Alfven waves
International Nuclear Information System (INIS)
Davila, J.M.
1987-01-01
An improved method for calculating the resonance absorption heating rate is discussed and the results are compared with observations in the solar corona. To accomplish this, the wave equation for a dissipative, compressible plasma is derived from the linearized magnetohydrodynamic equations for a plasma with transverse Alfven speed gradients. For parameters representative of the solar corona, it is found that a two-scale description of the wave motion is appropriate. The large-scale motion, which can be approximated as nearly ideal, has a scale which is on the order of the width of the loop. The small-scale wave, however, has a transverse scale much smaller than the width of the loop, with a width of about 0.3-250 km, and is highly dissipative. These two wave motions are coupled in a narrow resonance region in the loop where the global wave frequency equals the local Alfven wave frequency. Formally, this coupling comes about from using the method of matched asymptotic expansions to match the inner and outer (small and large scale) solutions. The resultant heating rate can be calculated from either of these solutions. A formula derived using the outer (ideal) solution is presented, and shown to be consistent with observations of heating and line broadening in the solar corona. 34 references
ULF Waves in the Ionospheric Alfven Resonator: Modeling of MICA Observations
Streltsov, A. V.; Tulegenov, B.
2017-12-01
We present results from a numerical study of physical processes responsible for the generation of small-scale, intense electromagnetic structures in the ultra-low-frequency range frequently observed in the close vicinity of bright discrete auroral arcs. In particular, our research is focused on the role of the ionosphere in generating these structures. A significant body of observations demonstrate that small-scale electromagnetic waves with frequencies below 1 Hz are detected at high latitudes where the large-scale, downward magnetic field-aligned current (FAC) interact with the ionosphere. Some theoretical studies suggest that these waves can be generated by the ionospheric feedback instability (IFI) inside the ionospheric Alfven resonator (IAR). The IAR is the region in the low-altitude magnetosphere bounded by the strong gradient in the Alfven speed at high altitude and the conducting bottom of the ionosphere (ionospheric E-region) at low altitude. To study ULF waves in this region we use a numerical model developed from reduced two fluid MHD equations describing shear Alfven waves in the ionosphere and magnetosphere of the earth. The active ionospheric feedback on structure and amplitude of magnetic FACs that interact with the ionosphere is implemented through the ionospheric boundary conditions that link the parallel current density with the plasma density and the perpendicular electric field in the ionosphere. Our numerical results are compared with the in situ measurements performed by the Magnetosphere-Ionosphere Coupling in the Alfven Resonator (MICA) sounding rocket, launched on February 19, 2012 from Poker Flat Research Range in Alaska to measure fields and particles during a passage through a discreet auroral arc. Parameters of the simulations are chosen to match actual MICA parameters, allowing the comparison in the most precise and rigorous way. Waves generated in the numerical model have frequencies between 0.30 and 0.45 Hz, while MICA measured
International Nuclear Information System (INIS)
Stix, H.
1981-01-01
The physics of Alfven-wave heating is particularly sensitive to the character of the linear mode conversion which occurs at the Alfven resonance layer. Parameter changes can profoundly affect both the location within the plasma and the mechanism for the power absorption. Under optimal conditions the heating power may be absorbed by electron Landau damping and by electron transit-time magnetic pumping in the plasma interior, or by the same processes acting near the resonance layer on the mode-converted kinetic Alfven wave. The method is outlined for computing the coefficients for reflection, transmission and absorption at the resonance layer and some representative results are offered
International Nuclear Information System (INIS)
Bergkvist, T.; Hellsten, T.; Johnson, T.
2006-01-01
Alfven eigenmodes (AEs) excited by fusion born α particles can degrade the heating efficiency of a burning plasma and throw out αs. To experimentally study the effects of excitation of AEs and the redistribution of the fast ions, ion cyclotron resonance heating (ICRH) is often used. The distribution function of thermonuclear αs in a reactor is expected to be isotropic and constantly renewed through DT reactions. The distribution function of cyclotron heated ions is strongly anisotropic, and the ICRH do not only renew the distribution function but also provide a strong decorrelation mechanism between the fast ions and the AE. Because of the sensitivity of the AE dynamics on the details of the distribution function, the location of the resonance surfaces in phase space and the extent of the overlapping resonant regions for different AEs, a self-consistent treatment of the AE excitation and the ICRH is necessary. Interactions of fast ions with AEs during ICRH has been implemented in the SELFO code. Simulations are in good agreement with the experimentally observer pitch-fork splitting and rapid damping of the AE as ICRH is turned off. The redistribution of fast ions have been studied in the presence of several driven AEs. (author)
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).
Noise in nonlinear nanoelectromechanical resonators
Guerra Vidal, Diego N.
Nano-Electro-Mechanical Systems (NEMS), due to their nanometer scale size, possess a number of desirable attributes: high sensitivity to applied forces, fast response times, high resonance frequencies and low power consumption. However, ultra small size and low power handling result in unwanted consequences: smaller signal size and higher dissipation, making the NEMS devices more susceptible to external and intrinsic noise. The simplest version of a NEMS, a suspended nanomechanical structure with two distinct excitation states, can be used as an archetypal two state system to study a plethora of fundamental phenomena such as Duffing nonlinearity, stochastic resonance, and macroscopic quantum tunneling at low temperatures. From a technical perspective, there are numerous applications such nanomechanical memory elements, microwave switches and nanomechanical computation. The control and manipulation of the mechanical response of these two state systems can be realized by exploiting a (seemingly) counterintuitive physical phenomenon, Stochastic Resonance: in a noisy nonlinear mechanical system, the presence of noise can enhance the system response to an external stimulus. This Thesis is mainly dedicated to study possible applications of Stochastic Resonance in two-state nanomechanical systems. First, on chip signal amplification by 1/falpha is observed. The effectiveness of the noise assisted amplification is observed to decrease with increasing a. Experimental evidence shows an increase in asymmetry between the two states with increasing noise color. Considering the prevalence of 1/f alpha noise in the materials in integrated circuits, the signal enhancement demonstrated here, suggests beneficial use of the otherwise detrimental noise. Finally, a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR is presented. The logic function can be programmed (from AND to OR) dynamically, by
Alfven Eigenmode excitation by ICRH beat-waves
International Nuclear Information System (INIS)
Fasoli, A.; Lister, J.B.; Dobbing, J.A.; Gormezano, C.; Jacquinot, J.; Sharapov, S.; Sibley, A.
1995-08-01
The resonant excitation of Alfven Eigenmodes by ICRH beat waves has been attempted experimentally on JET tokamak plasmas. Toroidicity induced AE are excited when the difference frequency between two ICRH antennas is of the order of the central frequency of the relative Alfven continuum gap. The relatively large amplitudes for the TAE driven ICRH beat waves suggest that this new non-linear excitation mechanism could allow investigations into the effects of AE on particle orbits and should be taken into account in ICRH heated thermonuclear plasmas. (author) 6 figs., 9 refs
Nonlinearity and nonclassicality in a nanomechanical resonator
Energy Technology Data Exchange (ETDEWEB)
Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)
2015-12-15
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)
The nonlinearity cancellation phenomenon in micromechanical resonators
International Nuclear Information System (INIS)
Shao, L C; Tan, W W; Palaniapan, M
2008-01-01
In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr; Matsumoto, H.
2001-01-01
Roč. 106, - (2001), s. 13,215-13,224 ISSN 0148-0227 R&D Projects: GA AV ČR IAB3042106 Institutional research plan: CEZ:AV0Z3042911 Keywords : instability * whistler * Alfven wave Subject RIV: BE - Theoretical Physics Impact factor: 2.609, year: 2001
Shukla, P. K.
2012-01-01
It is shown that a three-dimensional (3D) modified-kinetic Alfv\\'en waves (m-KAWs) can propagate in the form of Alfv\\'enic tornadoes characterized by plasma density whirls or magnetic flux ropes carrying orbital angular momentum (OAM). By using the two fluid model, together with Amp\\`ere's law, we derive the wave equation for a 3D m-KAWs in a magnetoplasma with $m_e/m_i \\ll \\beta \\ll 1$, where $m_e$ $(m_i)$ is the electron (ion) mass, $\\beta =4 \\pi n_0 k_B (T_e + T_i)/B_0^2$, $n_0$ the unpert...
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.
Nonlinear effects in varactor-tuned resonators.
Everard, Jeremy; Zhou, Liang
2006-05-01
This paper describes the effects of RF power level on the performance of varactor-tuned resonator circuits. A variety of topologies are considered, including series and parallel resonators operating in both unbalanced and balanced modes. As these resonators were designed to produce oscillators with minimum phase noise, the initial small signal insertion loss was set to 6 dB and, hence, QL/Q0 = 1/2. To enable accurate analysis and simulation, S parameter and PSPICE models for the varactors were optimized and developed. It is shown that these resonators start to demonstrate nonlinear operation at very low power levels demonstrating saturation and lowering of the resonant frequency. On occasion squegging is observed for modified bias conditions. The nonlinear effects are dependent on the unloaded Q (Q0), the ratio of loaded to unloaded Q (QL/Q0), the bias voltage, and circuit configurations with typical nonlinear effects occurring at -8 dBm in a circuit with a loaded Q of 63 and a varactor bias voltage of 3 V. Analysis, simulation, and measurements that show close correlation are presented.
Stochastic resonance in biological nonlinear evolution models
Dunkel, Jörn; Hilbert, Stefan; Schimansky-Geier, Lutz; Hänggi, Peter
2004-05-01
We investigate stochastic resonance in the nonlinear, one-dimensional Fisher-Eigen model (FEM), which represents an archetypal model for biological evolution based on a global coupling scheme. In doing so we consider different periodically driven fitness functions which govern the evolution of a biological phenotype population. For the case of a simple harmonic fitness function we are able to derive the exact analytic solution for the asymptotic probability density. A distinct feature of this solution is a phase lag between the driving signal and the linear response of the system. Furthermore, for more complex systems a general perturbation theory (linear response approximation) is put forward. Using the latter approach, we investigate stochastic resonance in terms of the spectral amplification measure for a quadratic, a quartic single-peaked, and for a bistable fitness function. Our analytical results are also compared with those of detailed numerical simulations. Our findings vindicate that stochastic resonance does occur in these nonlinear, globally coupled biological systems.
Alfven wave. DOE Critical Review Series
International Nuclear Information System (INIS)
Hasegawa, A.; Uberoi, C.
1982-01-01
This monograph deals with the properties of Alfven waves and with their application to fusion. The book is divided into 7 chapters dealing with linear properties in homogeneous and inhomogeneous plasmas. Absorption is treated by means of kinetic theory. Instabilities and nonlinear processes are treated in Chapters 1 to 6, and the closing chapter is devoted to theory and experiments in plasma heating by Alfven waves
Alfven wave. DOE Critical Review Series
Energy Technology Data Exchange (ETDEWEB)
Hasegawa, A.; Uberoi, C.
1982-01-01
This monograph deals with the properties of Alfven waves and with their application to fusion. The book is divided into 7 chapters dealing with linear properties in homogeneous and inhomogeneous plasmas. Absorption is treated by means of kinetic theory. Instabilities and nonlinear processes are treated in Chapters 1 to 6, and the closing chapter is devoted to theory and experiments in plasma heating by Alfven waves. (MOW)
Kinetic Damping of Toroidal Alfven Eigenmodes
International Nuclear Information System (INIS)
Fu, G.Y.; Berk, H.L.; Pletzer, A.
2005-01-01
The damping of Toroidal Alfven Eigenmodes in JET plasmas is investigated by using a reduced kinetic model. Typically no significant damping is found to occur near the center of the plasma due to mode conversion to kinetic Alfven waves. In contrast, continuum damping from resonance near the plasma edge may be significant, and when it is, it gives rise to damping rates that are compatible with the experimental observations
Counter operation in nonlinear micro-electro-mechanical resonators
International Nuclear Information System (INIS)
Yao, Atsushi; Hikihara, Takashi
2013-01-01
This Letter discusses a logical operation of multi-memories that consist of coupled nonlinear micro-electro-mechanical systems (MEMS) resonators. A MEMS resonator shows two coexisting stable states when nonlinear responses appear. Previous studies addressed that a micro- or nano-electrical-mechanical resonator can be utilized as a mechanical 1-bit memory or mechanical logic gates. The next phase is the development of logic system with coupled multi-resonators. From the viewpoint of application of nonlinear dynamics in coupled MEMS resonators, we show the first experimental success of the controlling nonlinear behavior as a 2-bit binary counter.
Plasma heating by kinetic Alfven wave
International Nuclear Information System (INIS)
Assis, A.S. de.
1982-01-01
The heating of a nonuniform plasma (electron-ion) due to the resonant excitation of the shear Alfven wave in the low β regime is studied using initially the ideal MHD model and posteriorly using the kinetic model. The Vlasov equation for ions and the drift kinetic equation for electrons have been used. Through the ideal MHD model, it is concluded that the energy absorption is due to the continuous spectrum (phase mixing) which the shear Alfven wave has in a nonuniform plasma. An explicit expression for the energy absorption is derived. Through the kinetic model it is concluded that the energy absorption is due to a resonant mode convertion of the incident wave into the kinetic Alfven wave which propagates away from the resonant region. Its electron Landau damping has been observed. There has been a concordance with the MHD calculations. (Author) [pt
Magnetosphere as an Alfven maser
International Nuclear Information System (INIS)
Trakhtengerts, V.Yu.
1979-01-01
The Earth magnetosphere is considered as an Alfven maser. The operation mechanism of such a maser is duscussed. The main fact of this mechanism is ''overpopulation'' of the Earth radiation belt with particles moving with cross velocities. The cross velocity particles excess results in the excitation of cyclotron instability in the radiation belt and in the self-arbitrary increase of Alfven waves. At late the theory of cyclotron instability of radiation belts has been universally developed. On the basis of ideas on magnetosphere maser on cyclotron resonance it was possible to explain many geophysical phenomena such as periodical spillings out of particles from the radiation belts, pulsing polar lights, oscillations of magnetic force tubes etc. It is proposed to carry out active cosmic experiments to understand deeper the processes occuring in radiation belts
International Nuclear Information System (INIS)
Besson, G.; Borg, G.G.; Lister, J.B.; Marmillod, Ph.; Braun, F.; Murphy, A.B.; Noterdaeme, J.M.; Ryter, F.; Wesner, F.
1990-01-01
An experiment has been completed on ASDEX to study the response of the plasma to Alfven wave heating (AWH). Antenna excitation was provided by the old TCA rf generator with an output power capability of 500 kW. Two poloidal loop antennas were installed at the east and west ends of the tokamak allowing either N=1 or N=2 phasings. Since the largest antenna coupling to the Alfven resonance is provided by the m=1 surface wave, the antenna consisted only of a single element on the low field side, whereas in TCA the antennas are located on the top and the bottom of the torus. The antenna elements consisted of 2 parallel bars of inductance 730 nH and, as in TCA, were left unshielded. A typical antenna circulating current of 2 kA peak at 1.80 MHz was provided for the experiments. (author) 3 refs., 4 figs
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.
Study of nonlinear resonance effect in Paul trap.
Zhou, Xiaoyu; Xiong, Caiqiao; Zhang, Shuo; Zhang, Ning; Nie, Zongxiu
2013-05-01
In this article, we investigated the nonlinear resonance effect in the Paul trap with a superimposed hexapole field, which was assumed as a perturbation to the quadrupole field. On the basis of the Poincare-Lighthill-Kuo (PLK) perturbation method, ion motional equation, known as nonlinear Mathieu equation (NME) was expressed as the addition of approximation equations in terms of perturbation order. We discussed the frequency characteristics of ion axial-radial (z-r) coupled motion in the nonlinear field, derived the expressions of ion trajectories and nonlinear resonance conditions, and found that the mechanism of nonlinear resonance is similar to the normal resonance. The frequency spectrum of ion motion in nonlinear field includes not only the natural frequency series but also nonlinear introduced frequency series, which provide the driving force for the nonlinear resonance. The nonlinear field and the nonlinear effects are inevitable in practical ion trap experiments. Our method provides better understanding of these nonlinear effects and would be helpful for the instrumentation for ion trap mass spectrometers.
Dynamical and spectral properties of interacting quantum nonlinear resonances
International Nuclear Information System (INIS)
Berman, G.P.; Vlasova, O.F.; Kolovskij, A.R.; Izrajlev, F.M.
1987-01-01
While considering nonlinear quantum systems in the quasiclassical occupation region interacting with an external periodical field, the renormalization method is used. In case of interactions of two nonlinear resonances renormalization is associated with occurence of higher order nonlinear resonances. There is a limit in the renormalization pattern related to existence of higher resonances, for which the number of quasienergy levels in the potential pit is small. Analysis of distributions of delocalized quasi-energy functions, corresponding to destroyed resonances, and those of distances between the adjastment quasienergy levels has shown the presence of considerable correlations. The correlations are due to phase space restricted in action and quantum effects leading to classical chaos restriction
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.
Steinolfson, Richard S.; Davila, Joseph M.
1993-01-01
Numerical simulations of the MHD equations for a fully compressible, low-beta, resistive plasma are used to study the resonance absorption process for the heating of coronal active region loops. Comparisons with more approximate analytic models show that the major predictions of the analytic theories are, to a large extent, confirmed by the numerical computations. The simulations demonstrate that the dissipation occurs primarily in a thin resonance layer. Some of the analytically predicted features verified by the simulations are (a) the position of the resonance layer within the initial inhomogeneity; (b) the importance of the global mode for a large range of loop densities; (c) the dependence of the resonance layer thickness and the steady-state heating rate on the dissipation coefficient; and (d) the time required for the resonance layer to form. In contrast with some previous analytic and simulation results, the time for the loop to reach a steady state is found to be the phase-mixing time rather than a dissipation time. This disagreement is shown to result from neglect of the existence of the global mode in some of the earlier analyses. The resonant absorption process is also shown to behave similar to a classical driven harmonic oscillator.
Tailoring the nonlinear response of MEMS resonators using shape optimization
DEFF Research Database (Denmark)
Li, Lily L.; Polunin, Pavel M.; Dou, Suguang
2017-01-01
We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge-type mic...
Nonlinear resonance in Duffing oscillator with fixed and integrative ...
Indian Academy of Sciences (India)
We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Dufﬁng oscillator with two types of time-delayed feedbacks, namely, ﬁxed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...
Nonlinear resonance in Duffing oscillator with fixed and integrative ...
Indian Academy of Sciences (India)
2012-03-02
Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...
Nonlinear resonance phenomena of a doped fibre laser under cavity ...
Indian Academy of Sciences (India)
Harmonic resonance leads to period-1 bistability and hysteresis. Inside the period-2 sub-harmonic resonance region, the laser exhibits Feigenbaum sequence and generalized bistability. Keywords. Fibre lasers; chaos; modulation; nonlinear oscillators; optical bistability. PACS Nos 05.45.Ac; 42.55.Wd; 05.45.Tp; 42.55.Rz.
Nonlinear resonances in the ABC-flow
Didov, A. A.; Uleysky, M. Yu.
2018-01-01
In this paper, we study resonances of the ABC-flow in the near integrable case ( C ≪1 ). This is an interesting example of a Hamiltonian system with 3/2 degrees of freedom in which simultaneous existence of two resonances of the same order is possible. Analytical conditions of the resonance existence are received. It is shown numerically that the largest n :1 (n = 1, 2, 3) resonances exist, and their energies are equal to theoretical energies in the near integrable case. We provide analytical and numerical evidences for existence of two branches of the two largest n :1 (n = 1, 2) resonances in the region of finite motion.
Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks
Sebastian, Resmi; Sitharam, T. G.
2018-01-01
Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.
Stochastic resonance in overdamped systems with fractional power nonlinearity
Yang, Jianhua; Sanjuán, Miguel A. F.; Chen, Pengpeng; Liu, Houguang
2017-10-01
The stochastic resonance phenomenon in overdamped systems with fractional power nonlinearity is thoroughly investigated. The first kind of nonlinearity is a general fractional power function. The second kind of nonlinearity is a fractional power function with deflection. For the first case, the response is clearly divergent for some fractional exponent values. The curve of the spectral amplification factor versus the fractional exponent presents some discrete regions. For the second case, the response will not be divergent for any fractional exponent value. The spectral amplification factor decreases with the increase in the fractional exponent. For both cases, the nonlinearity is the necessary ingredient to induce stochastic resonance. However, it is not the sufficient cause to amplify the weak signal. On the one hand, the noise cannot induce stochastic resonance in the corresponding linear system. On the other hand, the spectral amplification factor of the nonlinear system is lower than that of the corresponding linear system. Through the analysis carried out in this paper, we are able to find that the system with fractional deflection nonlinearity is a better stochastic resonance system, especially when an appropriate exponent value is chosen. The results in this paper might have a certain reference value for signal processing problems in relation with the stochastic resonance method.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.
Nonlinear Resonance Islands and Modulational Effects in a Proton Synchrotron
Energy Technology Data Exchange (ETDEWEB)
Satogata, Todd Jeffrey [Northwestern Univ., Evanston, IL (United States)
1993-01-01
We examine both one-dimensional and two-dimensional nonlinear resonance islands created in the transverse phase space of a proton synchrotron by nonlinear magnets. We also examine application of the theoretical framework constructed to the phenomenon of modulational diffusion in a collider model of the Fermilab Tevatron. For the one-dimensional resonance island system, we examine the effects of two types of modulational perturbations on the stability of these resonance islands: tune modulation and beta function modulation. Hamiltonian models are presented which predict stability boundaries that depend on only three paramders: the strength and frequency of the modulation and the frequency of small oscillations inside the resonance island. These. models are compared to particle tracking with excellent agreement. The tune modulation model is also successfully tested in experiment, where frequency domain analysis coupled with tune modulation is demonstrated to be useful in measuring the strength of a nonlinear resonance. Nonlinear resonance islands are also examined in two transverse dimensions in the presence of coupling and linearly independent crossing resonances. We present a first-order Hamiltonian model which predicts fixed point locations, but does not reproduce small oscillation frequencies seen in tracking; therefore in this circumstance such a model is inadequate. Particle tracking is presented which shows evidence of two-dimensional persistent signals, and we make suggestions on methods for observing such signals in future experiment.
Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation
Directory of Open Access Journals (Sweden)
Luis Fernando Paullo Muñoz
2017-01-01
Full Text Available The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated.
Nonlinear mechanical resonators for ultra-sensitive mass detection
Energy Technology Data Exchange (ETDEWEB)
Datskos, Panos G [ORNL; Lavrik, Nickolay V [ORNL
2014-01-01
The fundamental sensitivity limit of an appropriately scaled down mechanical resonator can approach one atomic mass unit when only thermal noise is present in the system. However, operation of such nanoscale mechanical resonators is very challenging due to minuteness of their oscillation amplitudes and presence of multiple noise sources in real experimental environments. In order to surmount these challenges, we use microscale cantilever resonators driven to large amplitudes, far beyond their nonlinear instability onset. Our experiments show that such a nonlinear cantilever resonator, described analytically as a Duffing oscillator, has mass sensing performance comparable to that of much smaller resonators operating in a linear regime. We demonstrate femtogram level mass sensing that relies on a bifurcation point tracking that does not require any complex readout means. Our approaches enable straightforward detection of mass changes that are near the fundamental limit imposed by thermo-mechanical fluctuations.
Alfven wave studies on a tokamak
International Nuclear Information System (INIS)
Kortbawi, D.
1987-10-01
The continuum modes of the shear Alfven resonance are studied on the Tokapole II device, a small tokamak operated in a four node poloidal divertor configuration. A variety of antenna designs and the efficiency with which they deliver energy to the resonant layer are discussed. The spatial structure of the driven waves is studied by means of magnetic probes inserted into the current channel. In an attempt to optimize the coupling of energy in to the resonant layer, the angle of antenna currents with respect to the equilibrium field, antenna size, and plasma-to-antenna distance are varied. The usefulness of Faraday shields, particle shields, and local limiters are investigated. Antennas should be well shielded, either a dense Faraday shield or particle shield being satisfactory. The antenna should be large and very near to the plasma. The wave magnetic fields measured show a spatial resonance, the position of which varies with the value of the equilibrium field and mass density. They are polarized perpendicular to the equilibrium field. A wave propagates radially in to the resonant surface where it is converted to the shear Alfven wave. The signal has a short risetime and does not propagate far toroidally. These points are all consistent with a strongly damped shear Alfven wave. Comparisons of this work to theoretical predictions and results from other tokamaks are made
Spiky soliton in circular polarized Alfven wave
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Sanuki, H.; Konno, K.; Wadati, M.
1979-06-01
A new type of nonlinear evolution equation for the Alfven waves, propagating parallel to the magnetic field, is now registered to the completely integrable family of nonlinear evolution equations. In spite of the extensive studies of Kaup and Newell, and of Kawata and Inoue, these analysis have been dealing with solutions for restricted boundary conditions. The present paper presents full account of stationary solitary wave solutions for the plane wave boundary condition. The obtained results exhibit peculiar structure of spiky modulation of amplitude and phase, which arises from the derivative nonlinear coupling term. A nonlinear equation for complex amplitude associated with the carrier wave is shown to be a mixed type of nonlinear Schroedinger equation, having and ordinary cubic nonlinear term and the derivative of cubic nonlinear term. (author)
Nonlinear resonance islands and modulational effects in a proton synchrotron
International Nuclear Information System (INIS)
Satogata, T.J.
1993-01-01
The authors examine one-dimensional and two-dimensional nonlinear resonance islands created in the transverse phase space of a proton synchrotron by nonlinear magnets. The authors examine application of the theoretical framework constructed to the phenomenon of modulational diffusion in a collider model of the Fermilab Tevatron. For the one-dimensional resonance island system, the authors examine the effects of two types of modulational perturbations on the stability of these resonance islands: Tune modulation and beta function modulation. Hamiltonian models are presented which predict stability boundaries that depend on only three parameters: The strength and frequency of the modulation and the frequency of small oscillations inside the resonance island. The tune modulation model is successfully tested in experiment, where frequency domain analysis coupled with tune modulation is demonstrated to be useful in measuring the strength of a nonlinear resonance. Nonlinear resonance islands are examined in two transverse dimensions in the presence of coupling and linearly independent crossing resonances. The authors present a first-order Hamiltonian model which predicts fixed point locations, but does not reproduce small oscillation frequencies seen in tracking. Particle tracking is presented which shows evidence of two-dimensional persistent signals, and the authors make suggestions on methods for observing such signals in future experiment. The authors apply the tune modulation stability diagram to the explicitly two-dimensional phenomenon of modulational diffusion in the Fermilab Tevatron with beam-beam kicks as the source of nonlinearity. The amplitude growth created by this mechanism in simulation is exponential rather than root-time as predicted by modulational diffusion models. The authors comment upon the luminosity and lifetime limitations such a mechanism implies in a proton storage ring
Single particle dynamics and nonlinear resonances in circular accelerators
International Nuclear Information System (INIS)
Ruth, R.D.
1985-11-01
The purpose of this paper is to introduce the reader to single particle dynamics in circular accelerators with an emphasis on nonlinear resonances. We begin with the Hamiltonian and the equations of motion in the neighborhood of the design orbit. In the linear theory this yields linear betatron oscillations about a closed orbit. It is useful then to introduce the action-angle variables of the linear problem. Next we discuss the nonlinear terms which are present in an actual accelerator, and in particular, we motivate the inclusion of sextupoles to cure chromatic effects. To study the effects of the nonlinear terms, we next discuss canonical perturbation theory which leads us to nonlinear resonances. After showing a few examples of perturbation theory, we abandon it when very close to a resonance. This leads to the study of an isolated resonance in one degree of freedom with a 'time'-dependent Hamiltonian. We see the familiar resonance structure in phase space which is simply closed islands when the nonlinear amplitude dependence of the frequency or 'tune' is included. To show the limits of the validity of the isolated resonance approximation, we discuss two criteria for the onset of chaotic motion. Finally, we study an isolated coupling resonance in two degrees of freedom with a 'time'-dependent Hamiltonian and calculate the two invariants in this case. This leads to a surface of section which is a 2-torus in 4-dimensional phase space. However, we show that it remains a 2-torus when projected into particular 3-dimensional subspaces, and thus can be viewed in perspective
Li, Xiao-Fan; Finkbeiner, Joshua; Raman, Ganesh; Daniels, Christopher; Steinetz, Bruce M.
2003-01-01
Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the maximum pressure compression ratio with an acceleration of constant amplitude. The acoustical field was solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects were obtained through an automation scheme based on continuation method. Results are presented for optimizing three types of geometry: a cone, a horn-cone and a half cosine- shape. For each type, different optimized shapes were found when starting with different initial guesses. Further, the one-dimensional model was modified to study the effect of an axisymmetric central blockage on the nonlinear standing wave.
Micromechanical microphone using sideband modulation of nonlinear resonators
Boales, Joseph A.; Mateen, Farrukh; Mohanty, Pritiraj
2017-08-01
We report successful detection of an audio signal via sideband modulation of a nonlinear piezoelectric micromechanical resonator. The 270 × 96-μm resonator was shown to be reliable in audio detection for sound intensity levels as low as ambient room noise and to have an unamplified sensitivity of 23.9 μV/Pa. Such an approach may be adapted in acoustic sensors and microphones for consumer electronics or medical equipment such as hearing aids.
Nonlinear dynamics in micromechanical and nanomechanical resonators and oscillators
Dunn, Tyler
In recent years, the study of nonlinear dynamics in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) has attracted considerable attention, motivated by both fundamental and practical interests. One example is the phenomenon of stochastic resonance. Previous measurements have established the presence of this counterintuitive effect in NEMS, showing that certain amounts of white noise can effectively amplify weak switching signals in nanomechanical memory elements and switches. However, other types of noise, particularly noises with 1/falpha spectra, also bear relevance in these and many other systems. At a more fundamental level, the role which noise color plays in stochastic resonance remains an open question in the field. To these ends, this work presents systematic measurements of stochastic resonance in a nanomechanical resonator using 1/f alpha and Ornstein-Uhlenbeck noise types. All of the studied noise spectra induce stochastic resonance, proving that colored noise can also be beneficial; however, stronger noise correlations suppress the effect, decreasing the maximum signal-to-noise ratio and increasing the optimal noise intensity. Evidence suggests that 1/falpha noise spectra with increasing noise color lead to increasingly asymmetric switching, reducing the achievable amplification. Another manifestly nonlinear effect anticipated in these systems is modal coupling. Measurements presented here demonstrate interactions between various mode types on a wide scale, providing the first reported observations of coupling in bulk longitudinal modes of MEMS. As a result of anharmonic elastic effects, each mode shifts in frequency by an amount proportional to the squared displacement (or energy) of a coupled mode. Since all resonator modes couple in this manner, these effects enable nonlinear measurement of energy and mechanical nonlinear signal processing across a wide range of frequencies. Finally, while these experiments address nonlinear
Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances
Directory of Open Access Journals (Sweden)
Ali H. Nayfeh
1998-01-01
Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.
Jin, Leisheng; Li, Lijie
2017-12-01
In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.
Nonlinear resonance phenomena of a doped fibre laser under cavity ...
Indian Academy of Sciences (India)
- verse mode and multiaxial mode) with an intracavity LiNbO3 electro-optic modulator. (EOM) display the characteristic features of a nonlinear oscillator (e.g., harmonic and period-2 sub-harmonic resonances) when the EOM driver voltage is ...
Nonlinear behavior in a piezoelectric resonator: a method of analysis.
Garcia, J E; Perez, R; Albareda, A; Minguella, E
2000-01-01
Theories used for understanding nonlinear behavior of piezoelectric resonators are usually only valid for a given range of amplitudes. Thus, important discrepancies can sometimes be observed between theory and experiment. In this work, a simplified model of the resonator is assumed in order to extend the analysis of nonlinear behavior to any kind of nonlinear function, without a significant increase of mathematical complexity. Nevertheless, nonlinearities are considered to be weak enough to be taken as perturbations. An asymptotic method is used to obtain the first and second order perturbations of the response to an harmonic excitation applied to the system, and each one is separated into Fourier series. Nonlinearity is described by two functions-Phi, (S,D,S ,D ) and Psi (S,D,S ,D )-that must be added to the constitutive equations that give T and E as functions of S and D. These functions can be split into their symmetrical and antisymmetrical parts, which have different incidence over the perturbation terms. In order to simplify the problem, no mechanical excitation is considered, the electrical one is taken as strictly harmonic, and the current rather than the e.m.f. is taken as initial data. As an application example, this method is applied in order to find the second harmonic generation for a particular kind of nonlinearity.
Parametric resonance in nonlinear vibrations of string under harmonic heating
López-Reyes, L. J.; Kurmyshev, E. V.
2018-02-01
In this paper, vibrations of thin stretched strings carrying an alternating electric current in a non-uniform magnetic field are described by nonlinear equations. Within the frame of a simplified model, we studied the combined effect of geometric nonlinearity and Joule heating acting opposite to each other. An equation including Joule heating only shows unlimited growth in oscillation amplitude near resonant frequencies. Nevertheless, a single mode approximation resulting in Mathieu-Duffing´s equation shows a double resonance with bounded oscillation amplitude. At zero external force, the response frequency of steady-state oscillations is equal to parametric modulation frequency in an interval near the resonant frequency; otherwise, the response frequency equals the natural frequency of the oscillator.
Exploiting nonlinearities of micro-machined resonators for filtering applications
Ilyas, Saad
2017-06-21
We demonstrate the exploitation of the nonlinear behavior of two electrically coupled microbeam resonators to realize a band-pass filter. More specifically, we combine their nonlinear hardening and softening responses to realize a near flat pass band filter with sharp roll-off characteristics. The device is composed of two near identical doubly clamped and electrostatically actuated microbeams made of silicon. One of the resonators is buckled via thermal loading to produce a softening frequency response. It is then further tuned to create the desired overlap with the second resonator response of hardening behavior. This overlapping improves the pass band flatness. Also, the sudden jumps due to the softening and hardening behaviors create sharp roll-off characteristics. This approach can be promising for the future generation of filters with superior characteristics.
Stimulated Brillouin scattering of electromagnetic Alfven waves in a plasma
International Nuclear Information System (INIS)
Sharma, R.R.; Sharma, R.C.; Sharma, O.P.
1981-01-01
The phenomenon of stimulated Brillouin scattering of electromagnetic Alfven waves in a plasma is investigated by employing fluid model approach. The low frequency nonlinearity of ion acoustic wave arises through the ponderomotive force on ions and high frequency nonlinearity arises through the equation of continuity. For a typical isothermal plasma (Tsub(e)/Tsub(i)approx.=10), Alfven wave frequency ω 0 approx.=10 6 rad. sec -1 , the threshold for this instability in a uniform plasma is approx.= milliwatt cm -2 . Above the threshold, the growth rate for forward and back scatterings are approx.=10 -3 rad.sec -1 and approx.=10 -4 rad.sec. -1 , respectively. (author)
DEFF Research Database (Denmark)
Ghasemi, Negareh; Zare, Firuz; Davari, Pooya
2017-01-01
Several factors can affect performance of an ultrasound system such as quality of excitation signal and ultrasound transducer behaviour. Nonlinearity of piezoelectric ultrasound transducers is a key determinant in designing a proper driving power supply. Although, the nonlinearity of piezoelectri...... receiver is a function of a voltage across the resistor in the RLC branches and is related to the resonance frequencies of the ultrasound transducer....
Forced nonlinear resonance in a system of coupled oscillators.
Glebov, Sergei; Kiselev, Oleg; Tarkhanov, Nikolai
2011-06-01
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t∼ɛ(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks.
Directory of Open Access Journals (Sweden)
Franco Mangussi
Full Text Available In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined.
Nonlinear dynamic response of an electrically actuated imperfect microbeam resonator
Ruzziconi, Laura
2013-08-04
We present a study of the dynamic behavior of a MEMS device constituted of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. The nonlinear behavior is highlighted, which includes ranges of multistability, where the non-resonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is capable also to capture the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. Copyright © 2013 by ASME.
Ion temperature in plasmas with intrinsic Alfven waves
International Nuclear Information System (INIS)
Wu, C. S.; Yoon, P. H.; Wang, C. B.
2014-01-01
This Brief Communication clarifies the physics of non-resonant heating of protons by low-frequency Alfvenic turbulence. On the basis of general definition for wave energy density in plasmas, it is shown that the wave magnetic field energy is equivalent to the kinetic energy density of the ions, whose motion is induced by the wave magnetic field, thus providing a self-consistent description of the non-resonant heating by Alfvenic turbulence. Although the study is motivated by the research on the solar corona, the present discussion is only concerned with the plasma physics of the heating process
The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection
Franzen, J.
1994-01-01
The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd
Solitary Alfven wave envelopes and the modulational instability
International Nuclear Information System (INIS)
Kennel, C.F.
1987-06-01
The derivative nonlinear Schroedinger equation describes the modulational instability of circularly polarized dispersive Alfven wave envelopes. It also may be used to determine the properties of finite amplitude localized stationary wave envelopes. Such envelope solitons exist only in conditions of modulational stability. This leaves open the question of whether, and if so, how, the modulational instability produces envelope solitons. 12 refs
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.
Modeling Nonlinear Acoustic Standing Waves in Resonators: Theory and Experiments
Raman, Ganesh; Li, Xiaofan; Finkbeiner, Joshua
2004-01-01
The overall goal of the cooperative research with NASA Glenn is to fundamentally understand, computationally model, and experimentally validate non-linear acoustic waves in enclosures with the ultimate goal of developing a non-contact acoustic seal. The longer term goal is to transition the Glenn acoustic seal innovation to a prototype sealing device. Lucas and coworkers are credited with pioneering work in Resonant Macrosonic Synthesis (RMS). Several Patents and publications have successfully illustrated the concept of Resonant Macrosonic Synthesis. To utilize this concept in practical application one needs to have an understanding of the details of the phenomenon and a predictive tool that can examine the waveforms produced within resonators of complex shapes. With appropriately shaped resonators one can produce un-shocked waveforms of high amplitude that would result in very high pressures in certain regions. Our goal is to control the waveforms and exploit the high pressures to produce an acoustic seal. Note that shock formation critically limits peak-to-peak pressure amplitudes and also causes excessive energy dissipation. Proper shaping of the resonator is thus critical to the use of this innovation.
Resonantly driven nonlinear density waves in protostellar disks
Yuan, Chi; Cassen, Pat
1994-01-01
Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance
The inherent complexity in nonlinear business cycle model in resonance
International Nuclear Information System (INIS)
Ma Junhai; Sun Tao; Liu Lixia
2008-01-01
Based on Abraham C.-L. Chian's research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements' amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future
Shear Alfven waves in tokamaks
International Nuclear Information System (INIS)
Kieras, C.E.
1982-12-01
Shear Alfven waves in an axisymmetric tokamak are examined within the framework of the linearized ideal MHD equations. Properties of the shear Alfven continuous spectrum are studied both analytically and numerically. Implications of these results in regards to low frequency rf heating of toroidally confined plasmas are discussed. The structure of the spatial singularities associated with these waves is determined. A reduced set of ideal MHD equations is derived to describe these waves in a very low beta plasma
Dispersive shock mediated resonant radiations in defocused nonlinear medium
Bose, Surajit; Chattopadhyay, Rik; Bhadra, Shyamal Kumar
2018-04-01
We report the evolution of resonant radiation (RR) in a self-defocused nonlinear medium with two zero dispersion wavelengths. RR is generated from dispersive shock wave (DSW) front when the pump pulse is in non-solitonic regime close to first zero dispersion wavelength (ZDW). DSW is responsible for pulse splitting resulting in the generation of blue solitons when leading edge of the pump pulse hits the first ZDW. DSW also generates a red shifted dispersive wave (DW) in the presence of higher order dispersion coefficients. Further, DSW through cross-phase modulation with red shifted dispersive wave (DW) excites a localized radiation. The presence of zero nonlinearity point in the system restricts red-shift of RR and enhances the red shifting of DW. It also helps in the formation of DSW at shorter distance and squeezes the solitonic region beyond second zero dispersion point. Predicted results indicate that the spectral evolution depends on the product of Kerr nonlinearity and group velocity dispersion.
Compensation of scale factor nonlinearity in resonator fiber optic gyro
Zhi, Yinzhou; Feng, Lishuang; Wang, Junjie; Tang, Yichuang
2014-12-01
Scale factor nonlinearity (SFN) and dynamic range (DR) are the two significant parameters used to evaluate the performance of a resonator fiber optic gyro (RFOG). The inherent SFN of an open-loop RFOG with triangular phase modulation is first analyzed theoretically, and its relationship with the DR is simulated, showing that the DR is significantly constrained by the SFN. For our system, when the SFN is 1%, the DR is less than ±82 deg/s. To decrease the SFN in a certain DR, a real-time compensation method based on a field-programmable gate array is proposed. The compensation model is set up and the compensation scheme is illustrated. With the proposed method, the SFN of the RFOG is decreased from 1.53% to 0.057% with a DR of ±100 deg/s.
A novel nonlinear damage resonance intermodulation effect for structural health monitoring
Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele
2017-04-01
This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.
Winds from Luminous Late-Type Stars: II. Broadband Frequency Distribution of Alfven Waves
Airapetian, V.; Carpenter, K. G.; Ofman, L.
2010-01-01
We present the numerical simulations of winds from evolved giant stars using a fully non-linear, time dependent 2.5-dimensional magnetohydrodynamic (MHD) code. This study extends our previous fully non-linear MHD wind simulations to include a broadband frequency spectrum of Alfven waves that drive winds from red giant stars. We calculated four Alfven wind models that cover the whole range of Alfven wave frequency spectrum to characterize the role of freely propagated and reflected Alfven waves in the gravitationally stratified atmosphere of a late-type giant star. Our simulations demonstrate that, unlike linear Alfven wave-driven wind models, a stellar wind model based on plasma acceleration due to broadband non-linear Alfven waves, can consistently reproduce the wide range of observed radial velocity profiles of the winds, their terminal velocities and the observed mass loss rates. Comparison of the calculated mass loss rates with the empirically determined mass loss rate for alpha Tau suggests an anisotropic and time-dependent nature of stellar winds from evolved giants.
Nonlinear resonance and dynamical chaos in a diatomic molecule driven by a resonant ir field
International Nuclear Information System (INIS)
Berman, G.P.; Bulgakov, E.N.; Holm, D.D.
1995-01-01
We consider the transition from regular motion to dynamical chaos in a classical model of a diatomic molecule which is driven by a circularly polarized resonant ir field. Under the conditions of a nearly two-dimensional case, the Hamiltonian reduces to that for the nonintegrable motion of a charged particle in an electromagnetic wave [A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, City, 1983)]. In the general case, the transition to chaos is connected with the overlapping of vibrational-rotational nonlinear resonances and appears even at rather low radiation field intensity, S approx-gt 1 GW/cm 2 . We also discuss the possibility of experimentally observing this transition
Theory of charged particle heating by low-frequency Alfven waves
International Nuclear Information System (INIS)
Guo Zehua; Crabtree, Chris; Chen, Liu
2008-01-01
The heating of charged particles by a linearly polarized and obliquely propagating shear Alfven wave (SAW) at frequencies a fraction of the charged particle cyclotron frequency is demonstrated both analytically and numerically. Applying Lie perturbation theory, with the wave amplitude as the perturbation parameter, the resonance conditions in the laboratory frame are systematically derived. At the lowest order, one recovers the well-known linear cyclotron resonance condition k parallel v parallel -ω-nΩ=0, where v parallel is the particle velocity parallel to the background magnetic field, k parallel is the parallel wave number, ω is the wave frequency, Ω is the gyrofrequency, and n is any integer. At higher orders, however, one discovers a novel nonlinear cyclotron resonance condition given by k parallel v parallel -ω-nΩ/2=0. Analytical predictions on the locations of fixed points, widths of resonances, and resonance overlapping criteria for global stochasticity are also found to agree with those given by computed Poincare surfaces of section
A nonlinear plasmonic resonator for three-state all-optical switching
Amin, Muhammad
2014-01-01
A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator\\'s metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing. © 2014 Optical Society of America.
Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators
Amin, Muhammad
2013-09-01
A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.
Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance
Directory of Open Access Journals (Sweden)
Ma Ruyun
2007-01-01
Full Text Available We study the existence of solutions of nonlinear discrete boundary value problems , , , where is the first eigenvalue of the linear problem , , , satisfies some asymptotic nonuniform resonance conditions, and for .
Unified Model, and Novel Reverse Recovery Nonlinearities, of the Driven Diode Resonator
de Moraes, Renato Mariz; Anlage, Steven M.
2003-01-01
We study the origins of period doubling and chaos in the driven series resistor-inductor-varactor diode (RLD) nonlinear resonant circuit. We find that resonators driven at frequencies much higher than the diode reverse recovery rate do not show period doubling, and that models of chaos based on the nonlinear capacitance of the varactor diode display a reverse-recovery-like effect, and this effect strongly resembles reverse recovery of real diodes. We find for the first time that in addition t...
E Heebner, John; Boyd, Robert W; Park, Q-Han
2002-03-01
We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which can be described by a generalized nonlinear Schrodinger equation.
Effects of error feedback on a nonlinear bistable system with stochastic resonance
International Nuclear Information System (INIS)
Li Jian-Long; Zhou Hui
2012-01-01
In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing
Photoinduced Nonlinear Mixing of Terahertz Dipole Resonances in Graphene Metadevices.
In, Chihun; Kim, Hyeon-Don; Min, Bumki; Choi, Hyunyong
2016-02-17
The first experimental demonstration of nonlinear terahertz difference-frequency generation in a hybrid graphene metadevice is reported. Decades of research have revealed that terahertz-wave generation is impossible in single-layer graphene. This limitation is overcome and nonlinear terahertz generation by ultra-short optical pulse injection is demonstrated. This device is an essential step toward atomically thin, nonlinear terahertz optoelectronic components. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Lin, Zin; Lončar, Marko; Rodriguez, Alejandro W
2017-07-15
We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ(2) and χ(3) frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes Q≳104, small modal volumes V≳(λ/2n)3, and among the largest nonlinear overlaps (a generalization of phase matching in large-etalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices.
Self-induced light trapping in nonlinear Fabry–Perot resonators
Energy Technology Data Exchange (ETDEWEB)
Pichugin, K.N., E-mail: knp@tnp.krasn.ru; Sadreev, A.F., E-mail: almas@tnp.krasn.ru
2016-10-14
In the framework of the coupled mode theory we consider light trapping between two off-channel resonators which serve as self-adjusted Fano mirrors due to the Kerr effect. By inserting an auxiliary nonlinear resonator between the mirrors we achieve self-tuning of phase shift between the mirrors. That allows for the light trapping for arbitrary distance between the mirrors. - Highlights: • Fabry–Perot resonator traps light in a self-induced way if nonlinear cavity is inserted between mirrors.
International Nuclear Information System (INIS)
Shao, L C; Wong, C L; Palaniapan, M
2008-01-01
This paper presents a comprehensive study of the nonlinearities in micromechanical clamped–clamped beam resonators using a stroboscopic scanning electron microscopy (SEM) technique. Stroboscopic SEM allows direct imaging and measurement of the resonator's momentary displacement, hence eliminating the uncertainties associated with the conventional characterization methods. Five different silicon-on-insulator (SOI) comb-drive clamped–clamped beam resonators with resonant frequencies ranging from 113 kHz to 239 kHz were designed, fabricated and tested to investigate how their nonlinearities are related to the device dimensions. Both the theoretical analysis and experimental results conclusively show that the critical vibration amplitude of the resonator is around 1% of the beam width in a vacuum and is relatively independent of the beam length. Furthermore, it is found that the maximum storable energy of the resonator can be significantly increased by increasing the beam width and/or reducing the beam length if there are no restrictions on these dimensions. On the other hand, if a specific resonant frequency needs to be maintained, the maximum storable energy can be improved by increasing both the beam width and length by the same factor. Such a study not only helps to reveal the intrinsic nonlinear properties of the micromechanical clamped–clamped beam resonators, but also provides useful design guidelines for engineers to optimize the overall device performance
Nonlinear wave damping due to multi-plasmon resonances
Brodin, G.; Ekman, R.; Zamanian, J.
2018-02-01
For short wavelengths, it is well known that the linearized Wigner–Moyal equation predicts wave damping due to wave-particle interaction, where the resonant velocity shifted from the phase velocity by a velocity {v}q={{\\hslash }}k/2m. Here {{\\hslash }} is the reduced Planck constant, k is the wavenumber and m is the electron mass. Going beyond linear theory, we find additional resonances with velocity shifts {{nv}}q,n=2,3, \\ldots , giving rise to a new wave-damping mechanism that we term multi-plasmon damping, as it can be seen as the simultaneous absorption (or emission) of multiple plasmon quanta. Naturally this wave damping is not present in classical plasmas. For a temperature well below the Fermi temperature, if the linear (n = 1) resonant velocity is outside the Fermi sphere, the number of linearly resonant particles is exponentially small, while the multi-plasmon resonances can be located in the bulk of the distribution. We derive sets of evolution equations for the case of two-plasmon and three-plasmon resonances for Langmuir waves in the simplest case of a fully degenerate plasma. By solving these equations numerically for a range of wave-numbers we find the corresponding damping rates, and we compare them to results from linear theory to estimate the applicability. Finally, we discuss the effects due to a finite temperature.
Directory of Open Access Journals (Sweden)
Y. X. Hao
2010-01-01
Full Text Available The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle. Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm. The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.
SURFACE ALFVEN WAVES IN SOLAR FLUX TUBES
Energy Technology Data Exchange (ETDEWEB)
Goossens, M.; Andries, J.; Soler, R.; Van Doorsselaere, T. [Centre for Plasma Astrophysics, Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven (Belgium); Arregui, I.; Terradas, J., E-mail: marcel.goossens@wis.kuleuven.be [Solar Physics Group, Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain)
2012-07-10
Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. Alfven waves and magneto-sonic waves are particular classes of MHD waves. These wave modes are clearly different and have pure properties in uniform plasmas of infinite extent only. Due to plasma non-uniformity, MHD waves have mixed properties and cannot be classified as pure Alfven or magneto-sonic waves. However, vorticity is a quantity unequivocally related to Alfven waves as compression is for magneto-sonic waves. Here, we investigate MHD waves superimposed on a one-dimensional non-uniform straight cylinder with constant magnetic field. For a piecewise constant density profile, we find that the fundamental radial modes of the non-axisymmetric waves have the same properties as surface Alfven waves at a true discontinuity in density. Contrary to the classic Alfven waves in a uniform plasma of infinite extent, vorticity is zero everywhere except at the cylinder boundary. If the discontinuity in density is replaced with a continuous variation of density, vorticity is spread out over the whole interval with non-uniform density. The fundamental radial modes of the non-axisymmetric waves do not need compression to exist unlike the radial overtones. In thin magnetic cylinders, the fundamental radial modes of the non-axisymmetric waves with phase velocities between the internal and the external Alfven velocities can be considered as surface Alfven waves. On the contrary, the radial overtones can be related to fast-like magneto-sonic modes.
Unified model and reverse recovery nonlinearities of the driven diode resonator.
de Moraes, Renato Mariz; Anlage, Steven M
2003-08-01
We study the origins of period doubling and chaos in the driven series resistor-inductor-varactor diode (RLD) nonlinear resonant circuit. We find that resonators driven at frequencies much higher than the diode reverse recovery rate do not show period doubling. Models of chaos based on the nonlinear capacitance of the varactor diode display a reverse-recovery-like effect, and this effect strongly resembles reverse recovery of real diodes. We find for the first time that in addition to the known dependence of the reverse recovery time on past current maxima, there are also important nonlinear dependencies on pulse frequency, duty cycle, and dc voltage bias. Similar nonlinearities are present in the nonlinear capacitance models of these diodes. We conclude that a history-dependent and nonlinear reverse-recovery time is an essential ingredient for chaotic behavior of this circuit, and demonstrate for the first time that all major competing models have this effect, either explicitly or implicitly. Besides unifying the two major models of RLD chaos, our work reveals that the nonlinearities of the reverse-recovery time must be included for a complete understanding of period doubling and chaos in this circuit.
Suppression of two-photon resonantly enhanced nonlinear processes in extended media
International Nuclear Information System (INIS)
Garrett, W.R.; Moore, M.A.; Payne, M.G.; Wunderlich, R.K.
1988-11-01
On the basis of combined experimental and theoretical studies of nonlinear processes associated with two-photon excitations near 3d and 4d states in Na, we show how resonantly enhanced stimulated hyper-Raman emission, parametric four-wave mixing processes and total resonant two-photon absorption can become severely suppressed through the actions of internally generated fields on the total atomic response in extended media. 7 refs., 3 figs
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
Directory of Open Access Journals (Sweden)
Ciprian G. Gal
2017-01-01
Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.
The stationary Alfven wave in laboratory and space regimes
Finnegan, S. M.
In this thesis, a non-linear, collisional, two-fluid model of uniform plasma convection across field-aligned current (FAC) sheets, describing stationary Alfven (StA) waves is developed in support of laboratory experiments performed to test the hypothesis that a stationary inertial Alfven wave pattern forms within a channel of parallel electron current across which plasma is convected. In a previous work, Knudsen (D. J. Knudsen, J. Geophys. Res. 101, 10,761 (1996)) showed that, for cold, collisionless plasma, stationary inertial Alfven (StIA) waves can accelerate electrons parallel to a background magnetic field and cause large, time-independent plasma-density variations having spatial periodicity in the direction of the convective flow over a broad range of spatial scales and energies. Here, Knudsen's model has been generalized for warm, collisional, anisotropic plasma. The inclusion of parallel electron thermal pressure introduces dispersive effects which extend the model to the kinetic (beta > me/mi) regime. The effects of both ion-neutral and electron-ion collisional resistivity on StIA and stationary kinetic Alfven (StKA) wave solutions is studied. Conditions for both periodic and solitary wave solutions are identified. In the small amplitude limit, it is shown that the StA wave equation reduces to the differential equation describing the behavior of a forced harmonic oscillator. Analytical solutions are obtained for both a step and impulse, of finite width, forcing functions. Plasma rotation experiments in the West Virginia University Q-machine (WVUQ) demonstrate that an electron-emitting spiral electrode produces controllable, parabolic radial profile of floating potential, while the space potential showed no such structure. Laser-induced fluorescence measurements confirmed that the azimuthal ion drift velocity is inconsistent with a drift due to a gradient in the space potential. Experiments designed to produce StIA wave signatures were performed in the
International Nuclear Information System (INIS)
Chambrier, A. de; Heym, A.; Hofmann, F.; Joye, B.; Keller, R.; Lietti, A.; Lister, J.B.; Pochelon, A.; Simm, W.
1983-01-01
The aim of the TCA project is to investigate the heating effects of resonant absorption of Alfven waves in a Tokamak plasma. In TCA, the ion temperature increases linearly with the heating. Depending on the conditions, the ion temperature rises from 150 eV to 225 eV. (Auth./G.T.H.)
Nonlinear resonances in a multi-stage free-electron laser amplifier
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, S. [Graduate Univ. for Advanced Studies, Ibaraki-ken (Japan); Takayama, K. [National Lab. for High Energy Physics, Ibaraki-ken (Japan)
1995-12-31
A two-beam accelerator (TBA) is a possible candidate of future linear colliders, in which the demanded rf power is provided by a multi-stage free-electron laser (MFEL). After if amplification in each stage, a driving beam is re-accelerated by an induction unit and propagates into the next stage. Recently it has been recognized that the multi-stage character of the MFEL causes resonances between its periodicity and the synchrotron motion in an rf bucket. Since the synchrotron oscillation is strongly modulated by the resonance and at the worst a large fraction of particles is trapped in the resonance islands, the nonlinear resonances in the FEL longitudinal beam dynamics can lead to notable degradation of the MFEL performance, such as output fluctuation and phase modulation which have been big concerns in the accelerator society. The overall efficiency of the MFEL and the quality of the amplified microwave power are key issues for realizing the TBA/FEL Particularly the rf phase and amplitude errors must be maintained within tolerance. One of significant obstacles is an amplification of undesired modes. If a small-size waveguide is employed, the FEL resonance energies for undesired higher order modes shift very far from that for a fundamental mode; so it is possible to prevent higher order modes from evolving. Such a small-size waveguide, however, gives a high power density in the FEL. Simulation results have demonstrated that the nonlinear resonances occur in die FEL longitudinal motion when the power density exceeds some threshold. An analytical method for studying the nonlinear resonance in the TBA/FEL is developed based on the macroparticle model which can describe analytically the drastic behaviors in the evolutions of the phase and amplitude. In the theory the basic 1D-FEL equations are reduced to a nonlinear pendulum equation with respect to the ponderomotive phase.
Large resonant third-order optical nonlinearity of thin film containing ...
Indian Academy of Sciences (India)
2011-11-08
Nov 8, 2011 ... (J-band) red-shifted in the absorption spectrum with respect to the monomer absorption. Because of the resonant .... rise to orientation nonlinearity. The rise and fall times for this orientational .... aggregates, energy transfer from site to site within the J-like aggregates gives rise to the shortening of the S1.
Linear and nonlinear resonance features of an erbium-doped fibre ...
Indian Academy of Sciences (India)
2014-07-01
Jul 1, 2014 ... 147–159. Linear and nonlinear resonance features of an erbium-doped fibre ring laser under cavity-loss modulation. ADITI GHOSH1 and R VIJAYA2,∗. 1Fibre Optics and Photonics Division, Central Glass and Ceramic Research Institute,. Council of Scientific and Industrial Research, Kolkata 700 032, India.
Performance of SOI Bragg Grating Ring Resonator for Nonlinear Sensing Applications
Directory of Open Access Journals (Sweden)
Francesco De Leonardis
2014-08-01
Full Text Available In this paper, a spectroscopic sensor formed by a silicon-on-insulator waveguiding Bragg grating ring resonator working in linear and non-linear regime is proposed. In linear regime, the device shows a spectral response characterized by a photonic band gap (PBG. Very close to the band gap edges, the resonant structure exhibits split modes having a splitting magnitude equal to the PBG spectral extension, whose characteristics can be exploited to obtain a RI optical sensor almost insensitive to the fabrication tolerances and environmental perturbations. When the device operates in nonlinear regime, exactly in the spectral region showing the split resonant modes, the RI sensing performance is strongly improved with respect to the linear regime. This improvement, demonstrated by taking into account all the non-linear effects excited in the integrated silicon structure (i.e., Two Photon Absorption (TPA, TPA-induced Free Carrier Absorption, plasma dispersion, Self-Phase-Modulation and Cross-Phase-Modulation effects as induced by Kerr nonlinearity as well as the deleterious thermal and stress effects, allows enhancing the performance of the RI split mode resonant sensors, while achieving good immunity to the fabrication tolerances and environmental perturbations. The improvement in terms of sensor resolution can be at least one order of magnitude, still without using optimal parameters.
Diffusion rate for the emittance growth due to periodic crossings of nonlinear coupled resonances
Energy Technology Data Exchange (ETDEWEB)
Shi, J. (Texas Univ., Houston, TX (United States). Dept. of Physics); Gluckstern, R.L.; Ohnuma, S. (Brookhaven National Lab., Upton, NY (United States))
1992-01-01
Assuming that many betatron oscillations occur between crossings so that the betatron phase is uncorrelated from one crossing to the next, we estimate the diffusion rate for the emittance growth due to periodic crossing of coupled nonlinear resonances. It was shown that the diffusion rate is more or less independent of the frequency, but it is inversely proportional to the modulation amplitude.
Diffusion rate for the emittance growth due to periodic crossings of nonlinear coupled resonances
Energy Technology Data Exchange (ETDEWEB)
Shi, J. [Texas Univ., Houston, TX (United States). Dept. of Physics; Gluckstern, R.L.; Ohnuma, S. [Brookhaven National Lab., Upton, NY (United States)
1992-06-01
Assuming that many betatron oscillations occur between crossings so that the betatron phase is uncorrelated from one crossing to the next, we estimate the diffusion rate for the emittance growth due to periodic crossing of coupled nonlinear resonances. It was shown that the diffusion rate is more or less independent of the frequency, but it is inversely proportional to the modulation amplitude.
The mixed BVP for second order nonlinear ordinary differential equation at resonance
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan
2017-01-01
Roč. 290, 2-3 (2017), s. 393-400 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : mixed problem at resonance * nonlinear ordinary differencial equation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.742, year: 2016
Linear and nonlinear resonance features of an erbium-doped fibre ...
Indian Academy of Sciences (India)
2014-07-01
Jul 1, 2014 ... Abstract. The continuous-wave output of a single-mode erbium-doped fibre ring laser when sub- jected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the ...
Peter, Simon; Leine, Remco I.
2017-11-01
Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.
Weak-periodic stochastic resonance in a parallel array of static nonlinearities.
Directory of Open Access Journals (Sweden)
Yumei Ma
Full Text Available This paper studies the output-input signal-to-noise ratio (SNR gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.
Discrete Alfven waves in the TORTUS tokamak
International Nuclear Information System (INIS)
Amagishi, Y.; Ballico, M.J.; Cross, R.C.; Donnely, I.J.
1989-01-01
Discrete Alfven Waves (DAWs) have been observed as antenna resistance peaks and as enhanced edge fields in the TORTUS tokamak during Alfven wave heating experiments. A kinetic theory code has been used to calculate the antenna loading and the structure of the DAW fields for a range of plasma current and density profiles. There is fair agreement between the measured and predicted amplitude of the DAW fields in the plasma edge when both are normalized to the same antenna power
Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.
2015-03-01
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.
Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.
2015-01-01
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes. PMID:25762243
Effects of compressional magnetic perturbation on kinetic Alfven waves
Dong, Ge; Bhattacharjee, Amitava; Lin, Zhihong
2016-10-01
Kinetic Alfven waves play a very important role in the dynamics of fusion as well as space and astrophysical plasmas. The compressional magnetic perturbation δB|| can play important role in kinetic Alfven waves (KAW) and various instabilities at large plasma β. It could affect the nonlinear behavior of these modes significantly even at small β. In this study, we have implemented δB|| in gyrokinetic toroidal code (GTC). The perpendicular Ampere's law is solved as a force balance equation. Double gyroaveraging is incorporated in the code to treat the finite Larmor radius effects related to δB|| terms. KAW is studied in slab geometry as a benchmark case. A scan in β for the KAW dispersion relation shows that as β approaches 1 (>0.3), the effects of δB|| becomes important. Connections are made with other existing studies of KAWs in the fusion and space plasma literature. This new capability of including δB|| in GTC could be applied to nonlinear simulations of modes such as kinetic ballooning and tearing modes. This research is supported by DOE Contract No. DE-AC02-09CH11466.
Directory of Open Access Journals (Sweden)
A. Franchi
2009-01-01
Full Text Available The multiturn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order n, n+1 beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in n parts. Islands are generated by nonlinear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.
Nonlinear Parameter Identification of a Resonant Electrostatic MEMS Actuator.
Al-Ghamdi, Majed S; Alneamy, Ayman M; Park, Sangtak; Li, Beichen; Khater, Mahmoud E; Abdel-Rahman, Eihab M; Heppler, Glenn R; Yavuz, Mustafa
2017-05-13
We experimentally investigate the primary superharmonic of order two and subharmonic of order one-half resonances of an electrostatic MEMS actuator under direct excitation. We identify the parameters of a one degree of freedom (1-DOF) generalized Duffing oscillator model representing it. The experiments were conducted in soft vacuum to reduce squeeze-film damping, and the actuator response was measured optically using a laser vibrometer. The predictions of the identified model were found to be in close agreement with the experimental results. We also identified the noise spectral density of process (actuation voltage) and measurement noise.
Nonlinear interactions of focused resonance cone fields with plasmas
International Nuclear Information System (INIS)
Stenzel, R.L.; Gekelman, W.
1977-01-01
A simple yet novel rf exciter structure has been developed for generating remotely intense rf fields in a magnetoplasma. It is a circular line source of radius R in a plane perpendicularB 0 driven with an rf signal at ω 0 E/sub rf/ 2 /nkT/sub e/>0.2, a strong density depression in the focal region (deltan/n>40%) is observed. The density perturbation modifies the cone angle and field distribution. This nonlinear interaction leads to a rapid growth of ion acoustic wave turbulence and a corresponding random rf field distribution in a broadened focal region. The development of the interaction is mapped in space and time
Basic mode of nonlinear spin-wave resonance in normally magnetized ferrite films
International Nuclear Information System (INIS)
Gulyaev, Yu.V.; Zil'berman, P.E.; Timiryazev, A.G.; Tikhomirova, M.P.
2000-01-01
Modes of nonlinear and spin-wave resonance (SWR) in the normally magnetized ferrite films were studied both theoretically and experimentally. The particular emphasis was placed on the basic mode of SWR. One showed theoretically that with the growth of the precession amplitude the profile of the basic mode changed. The nonlinear shift of the resonance field depends on the parameters of fixing of the surface spins. Films of ferroyttrium garnet (FYG) with strong gradient of the single-axis anisotropy field along the film thickness, as well as, FYG films of the submicron thickness where investigated experimentally. With the intensification of Uhf-power one observed the sublinear shift of the basic mode resonance field following by the superlinear growth of the absorbed power. That kind of behaviour is explained by variation of the profile of the varying magnetization space distribution [ru
Multiple nonlinear dielectric resonance of ultra-long silver trimolybdate nanowires
International Nuclear Information System (INIS)
Wang, Guang-Sheng; Wen, Bo; He, Shuai; Guo, Lin; Cao, Mao-Sheng
2013-01-01
The silver molybdate nanowires (NWs) have been synthesized and characterized. The multiple dielectric resonant peaks of the nanocomposites filled with silver molybdate nanowires have been studied from 2 to 18 GHz. The as-established equivalent circuit model of the silver molybdate nanowires were employed to explain the nonlinear dielectric resonant behavior. - Graphical abstract: The untralong silver trimolybdate nanowires were synthesized and the dielectric peoperties of the products were studied from 2 to 18 GHz. The as-established equivalent circuit model of the silver molybdate nanowires were employed to explain the nonlinear dielectric resonant behavior. Highlights: ► The silver molybdate nanowires have been synthesized and characterized. ► The dielectric properties of the silver molybdate/ paraffin nanocomposites have been studied. ► Higher concentration of silver trimolybdate enhances the dielectric properties of composite. ► The dielectric behaviors were explained based on the as-established equivalent circuit mode
Large enhancement of third-order nonlinear effects with a resonant all-dielectric metasurface
Directory of Open Access Journals (Sweden)
Samad Jafar-Zanjani
2016-11-01
Full Text Available A novel low-profile nonlinear metasurface, consisting of a single-layer of all-dielectric material, is proposed and numerically investigated by a nonlinear full-wave finite-difference time-domain (FDTD method. The proposed metasurface is transparent for low, and opaque for high values of incident light intensity. The metasurface design is broadly applicable to enhancement of intrinsic nonlinearities of any material with a sufficiently high refractive index contrast. We illustrate the ability of this design to enhance intrinsic nonlinear absorption of a transition metal oxide, vanadium pentoxide (V2O5, with resonant metasurface elements. The complex third-order nonlinear susceptibility (χ(3 for V2O5, representing both nonlinear refraction and absorption is considered in FDTD simulations. Our design achieves high initial transparency (>90% for low incident light intensity. An order of magnitude decrease in the required input light intensity threshold for nonlinear response of the metasurface is observed in comparison with an unpatterend film. The proposed all-dielectric metasurface in this work is ultrathin and easy to fabricate. We envision a number of applications of this design for thin film coatings that offer protection against high-power laser radiation.
Control of the symmetry breaking in double-well potentials by the resonant nonlinearity management
International Nuclear Information System (INIS)
Nistazakis, H. E.; Frantzeskakis, D. J.; Malomed, B. A.; Kevrekidis, P. G.
2011-01-01
We introduce a one-dimensional model of Bose-Einstein condensates (BECs), combining the double-well potential, which is a usual setting for the onset of spontaneous-symmetry-breaking (SSB) effects, and time-periodic modulation of the nonlinearity, which may be implemented by means of the Feshbach-resonance-management (FRM) technique. Both cases of the nonlinearity that is repulsive or attractive on the average are considered. In the former case, the main effect produced by the application of the FRM is spontaneous self-trapping of the condensate in either of the two potential wells in parameter regimes where it would remain untrapped in the absence of the management. In the weakly nonlinear regime, the frequency of intrinsic oscillations in the FRM-induced trapped state is very close to half the FRM frequency, suggesting that the effect is accounted for by a parametric resonance. In the case of the attractive nonlinearity, the FRM-induced effect is the opposite, i.e., enforced detrapping of a state which is self-trapped in its unmanaged form. In the latter case, the frequency of oscillations of the untrapped mode is close to a quarter of the driving frequency, suggesting that a higher-order parametric resonance may account for this effect.
International Nuclear Information System (INIS)
Chen, Jia Nen; Liu, Jun; Zhang, Wei; Yao, Ming Hui; Sun, Min
2016-01-01
Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy's third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude
Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance
Directory of Open Access Journals (Sweden)
Liu-Yang Xiong
2014-01-01
Full Text Available Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time. For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance. The ordinary differential equations of the two mode shapes are established using the Galerkin method. The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities. The multiple scales method is applied to derive the modulation-phase equations. Steady-state solutions of the system as well as their stability are examined. The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction. The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance. The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method. The unstable regions in the internal resonance are explored via numerical simulations.
Nonlinear properties of double and triple barrier resonant tunneling structures in the sub-THz range
International Nuclear Information System (INIS)
Karuzskij, A.L.; Perestoronin, A.V.; Volchkov, N.A.
2012-01-01
The high-frequency nonlinear properties of GaAs/AlAs resonant tunneling diode (RTD) nanostructures and perspectives of implementation of the quantum regime of amplification in such structures, which is especially efficient in the range of sub-THz and THz ranges, are investigated. It is shown that in a triple barrier RTD the symmetry between the processes of amplification and dissipation can be avoided because of the interaction of an electromagnetic wave with both of resonant states in two quantum wells, that results in the significant growth of an RTD efficiency [ru
Noise-induced transitions and resonant effects in nonlinear systems
Zaikin, Alexei
2003-02-01
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences. Unsere alltägliche Erfahrung ist mit verschiedenen akustischen Einfluessen wie Lärm, aber auch Musik verbunden. Jeder weiss, wie Lärm stören kann und Kommunikation behindert oder gar unterbindet. Ähnliche optische Effekte sind bekannt: starkes Schneetreiben oder Regengüsse verschlechtern die Sicht und lassen uns Umrisse nur noch schemenhaft erkennen. Jedoch koennen ähnliche Stimuli auch sehr positive Auswirkungen haben: Autofahrer fahren bei leiser Musik konzentrierter -- die Behauptung von Schulkindern, nur bei dröhnenden Bässen die Mathehausaufgaben richtig rechnen zu können, ist allerdings nicht wissenschaftlich
Excitation of Alfvenic instabilities in spherical tokamaks
International Nuclear Information System (INIS)
McClements, K.G.; Appel, L.C.; Hole, M.J.; Thyagaraja, A.
2003-01-01
Understanding energetic particle confinement in spherical tokamak (STs) is important for optimising the design of ST power plants, and provides a testbed for theoretical modelling under conditions of strong toroidicity and shaping, and high beta. MHD analysis of some recent beam-heated discharges in the MAST ST indicates that high frequency modes observed in these discharges can be identified as toroidal Alfven Eigenmodes (TAEs) and elliptical Alfven Eigenmodes (EAEs). It is possible that such modes could strongly enhance fusion alpha-particle transport in an ST power plant. Computations of TAE growth rates for one particular MAST discharge, made using the HAGIS guiding centre code and benchmarked against analytical estimates, indicate strong drive by sub-Alfvenic neutral beam ions. HAGIS computations using higher mode amplitudes than those observed indicate that whereas co-passing beam ions provide the bulk of he TAE drive, counter-passing ions provide the dominant component of TAE-induced particle losses. Axisymmetric Alfvenic mode activity has been detected during ohmic discharges in MAST. These observations are shown by computational modelling to be consistent with the excitation of global Alfven Eigenmodes (GAEs) with n=0 and low m, driven impulsively by low frequency MHD. (author)
Directory of Open Access Journals (Sweden)
Souayeh Saoussen
2014-01-01
Full Text Available The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while taking into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretization coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.
Sub-Alfvenic reduced equations in a tokamak
Sengupta, Wrick
Magnetized fusion experiments generally perform under conditions where ideal Alfvenic modes are stable. It is therefore desirable to develop a reduced formalism which would order out Alfvenic frequencies. This is challenging because sub-Alfvenic phenomena are sensitive to magnetic geometries. In this work an attempt has been made to develop a formalism to study plasma phenomena on time scales much longer than the Alfvenic time scales. (Abstract shortened by ProQuest.).
Yang, Tao; Cao, Qingjie
2018-03-01
This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.
Förner, K.; Polifke, W.
2017-10-01
The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.
Dispersive MHD Shock Properties and Interactions with Alfven Solitons
Hamilton, R.; Toll, K.; Ellis, C.
2017-12-01
The weakly nonlinear, weakly dispersive limit of Hall MHD with resistivity for 1D waves travelling nearly parallel to the ambient magnetic field reduces to the derivative nonlinear Schrödinger-Burgers (DNLSB) equation. This model equation describes the coupling between the Alfvenic and magnetosonic modes for a low b plasma. Without dissipation this model equation reduces to the DNLS which can be solved as an initial value problem using the Inverse Scattering Transformation through which the nonlinear component of the magnetic field profile can be represented as a combination of one-parameter bright and dark solitons as well as two-parameter solitons. The one-parameter solitons are constrained to travel at speeds ranging between the Alfvenic and magnetosonic characteristic speeds of the ambient field. We have found that these one-parameter solitons are effectively bound to a 1-2 Fast Shock and will pass back and forth across the shock until they are damped away with no apparent effect on the Fast Shock. A similar mechanism is expected for a sufficiently compressive Intermediate Shock as it arises simply from two effects: damping of a one-parameter soliton causes it to speed up and, if it does not damp away, it will eventually overtake the shock; passing forwards through a compressive shock the decrease of the field strength leads to a slowing of the soliton. We also discuss an extension of results [C. F. Kennel, R. D. Blandford, C. C. Wu, Phys. Fluids B 2(2), 1990] related to the time dependence of Intermediate Shocks in the presence of dispersion.
Linear and Nonlinear Acoustic Measurements of Buried Landmines: Detection Schemes Near Resonance
Sabatier, James M.
2003-03-01
Measurements of the acoustic impedance of an anti-personnel and anti-tank plastic, blast-hardened landmines reveal resonances in the frequency range between 100 and 1000 Hz. The top surface resonances are due to its complicated mechanical structure vibrating in air. The lowest mode results from the blast hardened design of the landmine. Typically, a portion or cavity of the landmine is designed to absorb the shock from an explosion that is intended to detonate the landmine but still allow the landmine to trigger its explosive device when a slow steady pressure is applied. The mechanical design of the blast hardened aspects results in a high Q simple harmonic oscillator resonance of the top surface. At higher frequencies the top surface behaves like thin circular plate acoustic modes. When these landmines are buried in soils, the modes are mass loaded. Resonances from measurements of the normal component of the acoustically induced soil surface particle velocity are used for detection schemes. Since the interface between the top plate and the soil responds to pressure fluctuations nonlinearly, characteristics of landmines, the soil, and the interface are rich in nonlinear physics and allow for new methods of landmine detection not previously exploited.
Current generation by the Kinetic Alfven wave
International Nuclear Information System (INIS)
Assis, A.S.
1987-01-01
The current generated and the efficiency of the shear Kinetic Alfven wave are obtained using a self-consistent quasilinear formulation. Also, the current generation by the monochromatic shear Kinetic Alfven wave introduced by Hasegawa is re-examined taking into account the nonresonant electrons. To obtain the RF current density at the level of the ohmic heating current density in a tokamak, the required external magnetic field is smaller than 0.1% of the DC magnetic field, and the parallel electric field (E 2 ), using the Lausanne-TCA-Tokamak parameters is of the order of 0.01 V cm -1 . (author) [pt
Nonlinear Dynamics of Z-Shaped Folding Wings with 1:1 Inner Resonance
Guo, Xiangying; Zhang, Yang; Zhang, Wei; Sun, Lin; Chen, Shuping
Predicting the nonlinear vibration responses of a Z-shaped folding wing during the morphing process is a prerequisite for structural design analysis. Therefore, the present study focuses on the nonlinear dynamical characteristics of a Z-shaped folding wing. The folding wing is divided into three carbon fiber composite plates connected by rigid hinges. The nonlinear dynamic equations of the system are derived using Hamilton’s principle based on the von Kármán equations and classical laminate plate theory. The mode shape functions of the system are then obtained using finite element analysis. Galerkin’s approach is employed to discretize the partial differential governing equations into a two-degree-of-freedom nonlinear system. The case of 1:1 inner resonance is considered. The method of multiple scales is employed to obtain the averaged equations of the system. Finally, numerical simulation is performed to investigate the nonlinear dynamical characteristics of the system. Bifurcation diagrams and wave-form diagrams illustrate the different motions of the Z-shaped folding wing, including periodic and chaotic motions under given conditions. The influence of transverse excitations on the bifurcations and chaotic motion of the Z-shaped folding wing is investigated numerically.
Nonlinear theory of wakefield excitation in a rectangular multizone dielectric resonator
Directory of Open Access Journals (Sweden)
K. V. Galaydych
2011-01-01
Full Text Available A nonlinear self-consistent theory has been constructed and used to investigate numerically the wakefield excitation in multilayered dielectric resonators by relativistic electron bunches. Analytical expressions for solenoidal and potential components of an excited electromagnetic field have been derived. The excitation of a five-zone dielectric resonator by relativistic electron bunches was numerically investigated and comparison was made between the longitudinal distribution of an axial electric field and the results obtained previously for a corresponding problem in the waveguide formulation. The necessity of optimizing geometrical parameters of the resonator to reduce mode amplitudes nonresonant with a bunch, and to obtain a symmetric distribution of the longitudinal electric field component in the drive and accelerating channels, has been demonstrated.
Third-order resonance effects and the nonlinear stability of drop oscillations
Natarajan, Ramesh; Brown, Robert A.
1987-01-01
The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small nonaxisymmetric perturbations, as is demonstrated here for the three- and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, nonaxisymmetric traveling-wave solutions are also obtained and their stability is investigated. A nongeneric cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions.
Excitation of beta Alfven eigenmodes in Tore-Supra
International Nuclear Information System (INIS)
Nguyen, C; Garbet, X; Sabot, R; Goniche, M; Maget, P; Basiuk, V; Decker, J; Elbeze, D; Huysmans, G T A; Macor, A; Segui, J-L; Schneider, M; Eriksson, L-G
2009-01-01
Modes oscillating at the acoustic frequency and identified as beta Alfven eigenmodes (BAEs) have been observed in Tore-Supra under ion cyclotron resonant heating. In this paper, the linear excitation threshold of these modes, thought to be driven by suprathermal ions, is calculated and compared with Tore-Supra observations. Similar studies of the linear excitation threshold of energetic particles driven modes were carried out previously for toroidal Alfven eigenmodes or fishbones. In the case of BAEs, the main point is to understand whether the energetic particle drive is able to exceed ion Landau damping, which is expected to be important in the acoustic frequency range. For this, the BAE dispersion relation is computed and simplified in order to derive a tractable excitation criterion suitable for comparison with experiments. The observation of BAEs in Tore-Supra is found to be in agreement with the calculated criterion and confirms the possibility to trigger these modes in the presence of ion Landau damping. Moreover, the conducted analysis clearly puts forward the role of the global tunable parameters which play a role in the BAE excitation (the magnetic field, the density etc), as well as the role of some plasma profiles. In particular, the outcome of a modification of the shear or of the heating localization is found to be non-negligible and it is discussed in the paper.
Schwartz, Sylvain; Gutty, François; Feugnet, Gilles; Bouyer, Philippe; Pocholle, Jean-Paul
2008-05-09
We report fine-tuning of nonlinear interactions in a solid-state ring laser gyroscope by vibrating the gain medium along the cavity axis. We demonstrate both experimentally and theoretically that nonlinear interactions vanish for some values of the vibration parameters, leading to quasi-ideal rotation sensing. We eventually point out that our conclusions can be mapped onto other subfields of physics such as ring-shaped superfluid configurations, where nonlinear interactions could be tuned by using Feshbach resonance.
Schwartz, Sylvain; Gutty, François; Feugnet, Gilles; Bouyer, Philippe; Pocholle, Jean-Paul
2008-01-01
International audience; We study the suppression of nonlinear interactions in resonant macroscopic quantum devices in the case of the solid-state ring laser gyroscope. These nonlinear interactions are tuned by vibrating the gain medium along the cavity axis. Beat note occurrence under rotation provides a precise measurement of the strength of nonlinear interactions, which turn out to vanish for some discrete values of the amplitude of vibration. Our theoretical description, in very good agree...
Warm-ion drift Alfven turbulence and the L-H transition
International Nuclear Information System (INIS)
Scott, B.
1998-01-01
Computations of fluid drift turbulence treating ions and electrons on equal footing, including both temperatures, are conducted in a model toroidal geometry. The resulting 'ion mixing mode' turbulence bears features of both electron drift-Alfven and ion temperature gradient turbulence, and nonlinear sensitivity to the relative strengths of the density and temperature gradients provides a possible route to the bifurcation needed for the L-H transition. (author)
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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.
Ruzziconi, Laura
2013-06-10
We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.
International Nuclear Information System (INIS)
Das, Priyam; Panigrahi, Prasanta K
2015-01-01
We study Bose–Einstein condensate in the combined presence of time modulated optical lattice and harmonic trap in the mean-field approach. Through the self-similar method, we show the existence of sinusoidal lattice modes in this inhomogeneous system, commensurate with the lattice potential. A significant advantage of this system is wide tunability of the parameters through chirp management. The combined effect of the interaction, harmonic trap and lattice potential leads to the generation of nonlinear resonances, exactly where the matter wave changes its direction. When the harmonic trap is switched off, the BEC undergoes a nonlinear compression for the static optical lattice potential. For better understanding of chirp management and the nature of the sinusoidal excitation, we investigate the energy spectrum of the condensate, which clearly reveals the generation of nonlinear resonances in the appropriate regime. We have also identified a classical dynamical phase transition occurring in the system, where loss of superfluidity takes the superfluid phase to an insulating state. (paper)
Przekwas, A. J.; Yang, H. Q.
1989-01-01
The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.
Design of triply-resonant microphotonic parametric oscillators based on Kerr nonlinearity.
Zeng, Xiaoge; Popović, Miloš A
2014-06-30
We propose optimal designs for triply-resonant optical parametric oscillators (OPOs) based on degenerate four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling to pump and signal/idler resonances. We provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength-and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in silicon at the wavelengths 1.55 μm (with TPA) and 2.3 μm (no TPA) as well as in silicon nitride (Si(3)N(4)) at 1.55 μm. For typical microcavity quality factor of 10(6), we show that the oscillation threshold in excitation bus can be well into the sub-mW regime for silicon microrings and a few mW for silicon nitride microrings. The conversion efficiency can be a few percent when pumped at 10 times of the threshold. Next, based on our results, we suggest a family of synthetic "photonic molecule"-like, coupled-cavity systems to implement optimum FWM, where structure design for control of resonant wavelengths can be separated from that of optimizing nonlinear conversion efficiency, and where furthermore pump, signal, and idler coupling to bus waveguides can be controlled independently, using interferometric cavity supermode coupling as an example. Finally, consideration of these complex geometries calls for a generalization of the nonlinear
The spectrum of axisymmetric torsional Alfven waves
International Nuclear Information System (INIS)
Sy, W.N.
1977-03-01
The spectrum of axisymmetric torsional Alfven waves propagating in a cylindrical, non-uniform, resistive plasma waveguide has been analysed by a method of singular perturbations. A simple condition has been derived which predicts whether the spectrum is continuous or discrete under given physical conditions. Application of this result to resolve an apparent discrepancy in experimental observations is briefly discussed. (Author)
Polunin, Pavel M.
In this work we consider several nonlinearity-based and/or noise-related phenomena that have been recently observed in micro-electromechanical vibratory systems. The main goals are to closely examine these phenomena, develop an understanding of their underlying physics, derive techniques for characterizing parameters in relevant mathematical models, and determine ways to improve the performance of specific classes of micro-electromechanical systems (MEMS) used in applications. The general perspective of this work is based on the fact that nonlinearity and noise represent integral parts of the models needed to describe the response of these systems, and the focus is on situations where these generally undesirable features can be utilized or accounted for in design. We consider three different, but related, topics in this general area. The first topic uses the slowly varying states in a rotating frame of reference where we analyze the stationary probability distribution of a nonlinear parametrically-driven resonator subjected to Poisson pulses and thermal noise. We show that Poisson pulses with low pulse rates, as compared with the resonator decay rate, cause a power-law divergence of the probability density at the resonator equilibrium in both the underdamped (overdamped) regimes, in which the response does (does not) spiral in the rotating frame. We have also found that the shape of the probability distribution away from the equilibrium position is qualitatively different for the overdamped and underdamped cases. In particular, in the overdamped regime, the form of the secondary singularity in the probability distribution depends strongly on the reference phase of the resonator response and the pulse modulation phase, while in the underdamped regime several singular peaks occur in the distribution, and their locations are determined by the resonator frequency and decay rate in the rotating frame. Finally, we show that even weak Gaussian noise smoothens out the
Magnetic resonance imaging with nonlinear gradient fields signal encoding and image reconstruction
Schultz, Gerrit
2013-01-01
Within the past few decades magnetic resonance imaging has become one of the most important imaging modalities in medicine. For a reliable diagnosis of pathologies further technological improvements are of primary importance. This text deals with a radically new approach of image encoding: The fundamental principle of gradient linearity is challenged by investigating the possibilities of acquiring anatomical images with the help of nonlinear gradient fields. Besides a thorough theoretical analysis with a focus on signal encoding and image reconstruction, initial hardware implementations are tested using phantom as well as in-vivo measurements. Several applications are presented that give an impression about the implications that this technological advancement may have for future medical diagnostics. Contents n Image Reconstruction in MRI n Nonlinear Gradient Encoding: PatLoc Imaging n Presentation of Initial Hardware Designs n Basics of Signal Encoding and Image Reconstruction in PatLoc Imaging n ...
Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet
Energy Technology Data Exchange (ETDEWEB)
Cunha, R. O. [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Centro Interdisciplinar de Ciências da Natureza, Universidade Federal da Integração Latino-Americana, 85867-970 Foz do Iguaçu, PR (Brazil); Holanda, J.; Azevedo, A.; Rezende, S. M., E-mail: rezende@df.ufpe.br [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Vilela-Leão, L. H. [Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil); Centro Acadêmico do Agreste, Universidade Federal de Pernambuco, 55002-970 Caruaru, PE (Brazil); Rodríguez-Suárez, R. L. [Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago (Chile)
2015-05-11
We report an investigation of the dynamics of the three-magnon splitting process associated with the ferromagnetic resonance (FMR) in films of the insulating ferrimagnet yttrium iron garnet (YIG). The experiments are performed with a 6 μm thick YIG film close to a microstrip line fed by a microwave generator operating in the 2–6 GHz range. The magnetization precession is driven by the microwave rf magnetic field perpendicular to the static magnetic field, and its dynamics is observed by monitoring the amplitude of the FMR absorption peak. The time evolution of the amplitude reveals that if the frequency is lowered below a critical value of 3.3 GHz, the FMR mode pumps two magnons with opposite wave vectors that react back on the FMR, resulting in a nonlinear dynamics of the magnetization. The results are explained by a model with coupled nonlinear equations describing the time evolution of the magnon modes.
Resonant Tunneling Diodes-Based Cellular Nonlinear Networks with Fault Tolerance Analysis
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Shukai Duan
2013-01-01
Full Text Available The resonant tunneling diodes (RTD have found numerous applications in high-speed digital and analog circuits owing to its folded-back negative differential resistance (NDR in current-voltage (I-V characteristics and nanometer size. On account of the replacement of the state resistor in standard cell by an RTD, an RTD-based cellular neural/nonlinear network (RTD-CNN can be obtained, in which the cell requires neither self-feedback nor a nonlinear output, thereby being more compact and versatile. This paper addresses the structure of RTD-CNN in detail and investigates its fault-tolerant properties in image processing taking horizontal line detection and edge extraction, for examples. A series of computer simulations demonstrates the promising fault-tolerant abilities of the RTD-CNN.
Directory of Open Access Journals (Sweden)
Rossikhin Yury A.
2018-01-01
Full Text Available Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance, resulting in modal interaction, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential equations of the second order are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the combinational internal resonance. A good agreement in results is declared.
International Nuclear Information System (INIS)
Hernandez-Tenorio, C.; Belyaeva, T.L.; Serkin, V.N.
2007-01-01
The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered
International Nuclear Information System (INIS)
Poterasu, V.F.
1984-01-01
It is presented a method and the phase resonance for damping characteristic identification of non-linear soil-structural interaction. The algorithm can be applied in case of any, not necessarily, damping characteristic of the system examined. For the identification, the system is harmonically excited and are considered the super-harmonic amplitudes for odd and even powers of the x. The response of shear beam system for different levels of base excitation and for different locations of the load is considered. (Author) [pt
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
International Nuclear Information System (INIS)
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-01-01
In this paper, the efficiency of electron acceleration by a short, powerful laser pulse propagating across an external magnetic field is investigated. Conditions for the decay of a laser pulse with frequency close to the upper hybrid resonance frequency are analyzed. It is also shown that a laser pulse propagating as an extraordinary wave in cold, magnetized, low-density plasma takes the form of a nonlinear wave with the modulated amplitude (envelope soliton). Finally, simulation results on the interaction of an electromagnetic pulse with a semi-infinite plasma, obtained with the help of an electromagnetic relativistic PIC code, are discussed and a comparison with the obtained theoretical results is presented
All-electrical nonlinear fano resonance in coupled quantum point contacts
Xiao, Shiran
This thesis is motivated by recent interest in the Fano resonance (FR). As a wave-interference phenomenon, this resonance is of increasing importance in optics, plasmon-ics, and metamaterials, where its ability to cause rapid signal modulations under variation of some suitable parameter makes it desirable for a variety of applications. In this thesis, I focus on a novel manifestation of this resonance in systems of coupled quantum point contacts (QPCs). The major finding of this work is that the FR in this system may be ma-nipulated by applying a nonlinear DC bias to the system. Under such conditions, we are able to induce significant distortions of resonance lineshape, providing a pathway to all-electrical manipulation of the FR. To interpret this behavior we apply a recently-developed model for a three-path FR, involving an additional "intruder" continuum. We have previously used this model to account for the magnetic-field induced distortions of the FR observed in coupled QPCs, and show here that this model also provides a frame-work for understanding the observed nonlinear behavior. Our work therefore reveals a new manifestation of the FR that can be sensitively tailored by external control, a finding that may eventually allow the application of this feature to nanoelectronics. Since the in-terference scheme involves in this thesis is a completely general one, it should be broadly applicable across a variety of different wave-based systems, including those in both pho-tonics and electronics and opening up the possibility of new applications in areas such as chemical and biological sensing and secure communications.
The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfven Eigenmodes
International Nuclear Information System (INIS)
Lesur, M.
2010-01-01
The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of alpha particles, which are high-energy ions produced by the fusion reaction. Such particles can excite instabilities in the frequency range of Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. In order to develop diagnostics and control schemes, a better understanding of linear and nonlinear features of resonant interactions between plasma waves and high-energy particles, which is the aim of this thesis, is required. In the case of an isolated single resonance, the description of AE destabilization by high-energy ions is homothetic to the so-called Berk-Breizman (BB) problem, which is an extension of the classic bump-on-tail electrostatic problem, including external damping to a thermal plasma, and collisions. A semi-Lagrangian simulation code, COBBLES, is developed to solve the initial-value BB problem in both perturbative (δ f) and self-consistent (full-f) approaches. Two collision models are considered, namely a Krook model, and a model that includes dynamical friction (drag) and velocity-space diffusion. The nonlinear behavior of instabilities in experimentally-relevant conditions is categorized into steady-state, periodic, chaotic, and frequency-sweeping (chirping) regimes, depending on external damping rate and collision frequency. The chaotic regime is shown to extend into a linearly stable region, and a mechanism that solves the paradox formed by the existence of such subcritical instabilities is proposed. Analytic and semi-empirical laws for nonlinear chirping characteristics, such as sweeping-rate, lifetime, and asymmetry, are developed and validated. Long-time simulations demonstrate the existence of a quasi-periodic chirping regime. Although the existence of such regime stands for both collision models, drag and diffusion are essential to reproduce the alternation between
Nonlinear dynamics of spring softening and hardening in folded-mems comb drive resonators
Elshurafa, Amro M.
2011-08-01
This paper studies analytically and numerically the spring softening and hardening phenomena that occur in electrostatically actuated microelectromechanical systems comb drive resonators utilizing folded suspension beams. An analytical expression for the electrostatic force generated between the combs of the rotor and the stator is derived and takes into account both the transverse and longitudinal capacitances present. After formulating the problem, the resulting stiff differential equations are solved analytically using the method of multiple scales, and a closed-form solution is obtained. Furthermore, the nonlinear boundary value problem that describes the dynamics of inextensional spring beams is solved using straightforward perturbation to obtain the linear and nonlinear spring constants of the beam. The analytical solution is verified numerically using a Matlab/Simulink environment, and the results from both analyses exhibit excellent agreement. Stability analysis based on phase plane trajectory is also presented and fully explains previously reported empirical results that lacked sufficient theoretical description. Finally, the proposed solutions are, once again, verified with previously published measurement results. The closed-form solutions provided are easy to apply and enable predicting the actual behavior of resonators and gyroscopes with similar structures. © 2011 IEEE.
On the Nonlinear Dynamics of a Doubly Clamped Microbeam near Primary Resonance
Jaber, Nizar
2017-04-07
This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.
Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study
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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.
Nonlinear simulation of ELM dynamics in the presence of resonant magnetic perturbations
Chandra, D.; Thyagaraja, A.; Sen, A.; Kaw, P.
2017-07-01
We report on nonlinear simulation studies on the dynamical behaviour of ELMs under the influence of resonant magnetic perturbations (RMPs) using a two-fluid initial value electromagnetic nonlinear global code (CUTIE). To simulate ELMs we introduce a particle source in the confinement region and a particle sink in the edge region. To study ELM control using RMPs we have applied an n = 2 static external magnetic perturbation at the edge and made detailed parametric studies under varying conditions for the machine and plasma parameters typical of COMPASS-D. Our results show that ELM mitigation is possible for RMP powers beyond a specific threshold. The results also provide valuable insights into the RMP induced modifications of the complex nonlinear dynamics of the ELMs, in particular on the redistribution of mode energy and the cascading of energy to shorter scale lengths. We also observe a hysteresis in states as we increase the amplitude of RMPs and then decrease it to the same value.
Interplanetary Alfvenic fluctuations: A stochastic model
International Nuclear Information System (INIS)
Barnes, A.
1981-01-01
The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfvenic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfvenic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested
Low-n shear Alfven spectra in axisymmetric toroidal plasmas
Energy Technology Data Exchange (ETDEWEB)
Cheng, C.Z.; Chance, M.S.
1985-11-01
In toroidal plasmas, the toroidal magnetic field is nonuniform over a magnetic surface and causes coupling of different poloidal harmonics. It is shown both analytically and numerically that the toroidicity not only breaks up the shear Alfven continuous spectrum, but also creates new, discrete, toroidicity-induced shear Alfven eigenmodes with frequencies inside the continuum gaps. Potential applications of the low-n toroidicity-induced shear Alfven eigenmodes on plasma heating and instabilities are addressed. 17 refs., 4 figs.
Low-n shear Alfven spectra in axisymmetric toroidal plasmas
International Nuclear Information System (INIS)
Cheng, C.Z.; Chance, M.S.
1985-11-01
In toroidal plasmas, the toroidal magnetic field is nonuniform over a magnetic surface and causes coupling of different poloidal harmonics. It is shown both analytically and numerically that the toroidicity not only breaks up the shear Alfven continuous spectrum, but also creates new, discrete, toroidicity-induced shear Alfven eigenmodes with frequencies inside the continuum gaps. Potential applications of the low-n toroidicity-induced shear Alfven eigenmodes on plasma heating and instabilities are addressed. 17 refs., 4 figs
Enhancement of current diffusion in the presence of a kink mode or an Alfven wave
International Nuclear Information System (INIS)
Beklemishev, A.D.
1991-08-01
Many characteristic features of Alfven waves and related instabilities are strongly dependent on the inhomogeneity of the background density and the magnetic field. On the other hand, these waves also have an influence on the inhomogeneity, which is caused by the enhancement of the cross-field transport through wave- distortion of flux surfaces. This problem is addressed here within the framework of the single-fluid reduced MHD model and generalized Lagrangian representation of motion. The new effect of transport enhancement is identified as a consequence of the local squeezing of adjacent flux surfaces, which results in increased radial gradients and cross-field fluxes. This effect is found to be proportional to the second power of the ratio of the magnetic field perturbation to the normal field component. The result is applied to several problems related to m = 1 equilibrium relaxation and Alfven resonance broadening. 10 refs., 1 fig
Improved model of quasi-particle turbulence (with applications to Alfven and drift wave turbulence)
International Nuclear Information System (INIS)
Mendonca, J. T.; Hizanidis, K.
2011-01-01
We consider the classical problem of wave stability and dispersion in a turbulent plasma background. We adopt a kinetic description for the quasi-particle turbulence. We describe an improved theoretical approach, which goes beyond the geometric optics approximation and retains the recoil effects associated with the emission and absorption of low frequency waves by nearly resonant quasi-particles. We illustrate the present approach by considering two particular examples. One is the excitation of zonal flows by drift wave turbulence or driftons. The other is the coupling between ion acoustic waves and Alfven wave turbulence, eventually leading to saturation of Alfven wave growth. Both examples are relevant to anomalous transport in magnetic fusion devices. Connection with previous results is established. We show that these results are recovered in the geometric optics approximation.
International Nuclear Information System (INIS)
Chowdhury, A.; Yeo, I.; Tsvirkun, V.; Beaudoin, G.; Sagnes, I.; Raj, R.; Robert-Philip, I.; Raineri, F.; Braive, R.
2016-01-01
We investigate the non-linear mechanical dynamics of a nano-optomechanical mirror formed by a suspended membrane pierced by a photonic crystal. By applying to the mirror a periodic electrostatic force induced by interdigitated electrodes integrated below the membrane, we evidence superharmonic resonances of our nano-electro-mechanical system; the constant phase shift of the oscillator across the resonance tongues is observed on the onset of principal harmonic and subharmonic excitation regimes.
International Nuclear Information System (INIS)
Remillard, S K; Kirkendall, D; Ghigo, G; Gerbaldo, R; Gozzelino, L; Laviano, F; Yang, Z; Mendelsohn, N A; Ghamsari, B G; Friedman, B; Jung, P; Anlage, S M
2014-01-01
Micro-channels of nanosized columnar tracks were planted by heavy-ion irradiation into superconducting microwave microstrip resonators that were patterned from YBa 2 Cu 3 O 7 − x thin films on LaAlO 3 substrates. Three different ion fluences were used, producing different column densities, with each fluence having a successively greater impact on the microwave nonlinearity of the device, as compared to a control sample. Photoresponse (PR) images made with a 638 nm rastered laser beam revealed that the channel is a location of enhanced PR and a hot spot for the generation of intermodulation distortion. The microwave PR technique was also advanced in this work by investigating the role of coupling strength on the distribution of PR between inductive and resistive components. (paper)
Remillard, S. K.; Kirkendall, D.; Ghigo, G.; Gerbaldo, R.; Gozzelino, L.; Laviano, F.; Yang, Z.; Mendelsohn, N. A.; Ghamsari, B. G.; Friedman, B.; Jung, P.; Anlage, S. M.
2014-09-01
Micro-channels of nanosized columnar tracks were planted by heavy-ion irradiation into superconducting microwave microstrip resonators that were patterned from YBa2Cu3O7 - x thin films on LaAlO3 substrates. Three different ion fluences were used, producing different column densities, with each fluence having a successively greater impact on the microwave nonlinearity of the device, as compared to a control sample. Photoresponse (PR) images made with a 638 nm rastered laser beam revealed that the channel is a location of enhanced PR and a hot spot for the generation of intermodulation distortion. The microwave PR technique was also advanced in this work by investigating the role of coupling strength on the distribution of PR between inductive and resistive components.
Nonlinear Container Ship Model for the Study of Parametric Roll Resonance
DEFF Research Database (Denmark)
Holden, Christian; Galeazzi, Roberto; Rodríguez, Claudio
2007-01-01
Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to 40, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head...... seas. A Matlab/Simulinkr parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007). The benchmark implements a 3rd-order nonlinear model where the dynamics of roll...... is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic...
Role of 3D-Dispersive Alfven Waves in Coronal Heating and Solar Wind
Sharma, R. P.; Yadav, N.
2013-03-01
Dispersive Alfven waves (DAWs) play a very important role in the acceleration and heating of plasma particles in space as well in laboratory plasmas. DAWs may be Kinetic Alfven waves (KAW) or Inertial Alfven waves (IAW) depending upon the plasma beta (here beta is ratio of the plasma thermal pressure and magnetic pressure). Using two-fluid model of plasma DAWs have been studied extensively in literature but to explain the dynamics of Alfvén vortices one has to study the three dimensional (3D) propagation of these waves rather than 2D- propagation. 3D- DAW itself propagates in magnetized plasma in the form of a vortex beam which is manifestation of orbital angular momentum. These magnetic flux ropes or Alfvén vortices trap charged plasma particles and energize and transport them from one place to another. Thus these Alfvén vortices can also be an alternative mechanism to explain the energy transport in space plasmas. Coronal heating is one of the unresolved problems in solar physics. A number of theories have been given to explain the mystery behind coronal heating but no satisfactory solution has been found yet. We propose to study the nonlinear interaction between 3D-DAW and Ion acoustic wave as a mechanism in solar environment to generate the 3D- DAW localized structures. In the absence of ponderomotive non-linearity we get Laguerre Gauss (LG) polynomials as solutions of paraxial wave equation governing propagation of 3D-KAW. These LG modes are characterized by spiral phase front and concentric rings as intensity pattern. The relevance of this nonlinear process to coronal heating and solar wind turbulence has been pointed out. For this we have developed a (numerical) code based on pseudo-spectral technique and simulate this nonlinear interaction.
Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality
Paraz, Florine; Schouveiler, Lionel; Eloy, Christophe
2016-01-01
Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.
Driving Perpendicular Decay by the Parametric Instabilities of Parallel Propagating Alfven Waves
Comisel, H.; Nariyuki, Y.; Narita, Y.; Motschmann, U. M.
2017-12-01
The decay of monochromatic Alfven waves is studied by means of 2-D and 3-D hybrid simulations. The goal of the work is to follow up the long-time nonlinear development of theparametric decays after the saturation process in a multi-spatial dimension for coherent Alfven waves with three different polarizations: left-handed circularly polarized -, right-handed circularly polarized - and linearly polarized - Alfven pump waves. The analyzing is restricted for the parallel propagation with respect to the direction of the mean magnetic field in low beta plasmas. Numerical results suggest that the parametric instabilities can lead to broadband decays along the perpendicular direction, in which the magnetic field spectrum is extended towards the perpendicular direction.Perpendicular propagating daughter waves are observed atfinite perpendicular wave numbers as well as direct incompressible energy cascades driven by plasma turbulence.The density power spectrum shows inverse compressible cascades at smallerperpendicular wave numbers and direct cascades at larger wave numbers. The one-dimensional reduced spectra of the magnetic field and densities show correlations for a significant large range of perpendicular wave numbers beforedissipation. The time evolution of the anisotropy index is also determined for all the three analyzed setups.
Experimental Investigation of 2:1 and 3:1 Internal Resonances in Nonlinear MEMS Arch Resonators
Ramini, Abdallah
2016-12-05
We demonstrate experimentally internal resonances in MEMS resonators. The investigation is conducted on in-plane MEMS arch resonators fabricated with a highly doped silicon. The resonators are actuated electrostatically and their stiffness are tuned by electrothermal loading by passing an electrical current though the microstructures. We show that through this tuning, the ratio of the various resonance frequencies can be varied and set at certain ratios. Particularly, we adjust the resonance frequencies of two different vibrational modes to 2:1 and 3:1. Finally, we validate the internal resonances at these ratios through frequency-response curves and FFTs.
Wu, R. Q.; Zhang, W.; Yao, M. H.
2018-02-01
In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.
Alfven wave experiments on the TORTUS tokamak
International Nuclear Information System (INIS)
Ballico, M.J.; Bowden, M.; Brand, G.F.; Brennan, M.H.; Cross, R.C.; Fekete, P.; James, B.W.
1989-01-01
Results are presented on the first observations of the Discrete Alfven Wave (DAW) and the first measurements of laser scattering off the kinetic Alfven wave in the TORTUS tokamak. TORTUS is a relatively small device, with major radius R=0.44m, minor radius 0.1m and has previously been operated routinely with B Φ =0.7T, I p =20 kA and n e ∼ 1x10 19 m -3 . Under these conditions, and over a wide frequency range (1-14 MHz), there has been no evidence of the DAW modes observed on TCA. Recently, a minor upgrade of TORTUS has permitted routine operation at B Φ =1.0 T, I p =39 kA, q(a)∼5 and n e ∼1-4 x 10 19 m -3 . At the operating frequency, 3.2 MHz, chosen for this study, DAW modes are observed clearly at both low and high densities. The appearance of DAW modes appears to be due to a steeper current profile at the higher plasma currents now generated in TORTUS. The general behaviour of DAW modes is in fact quite sensitive to the density and current profiles, indicating that DAW modes should provide a useful current profile diagnostic. (author) 6 refs., 2 figs
Investigation of global Alfven instabilities in TFTR
International Nuclear Information System (INIS)
Wong, K.L.; Paul, S.F.; Fredrickson, E.D.; Nazikian, R.; Park, H.K.; Bell, M.; Bretz, N.L.; Budny, R.; Cheng, C.Z.; Cohen, S.; Hammett, G.W.; Jobes, F.C.; Johnson, L.; Meade, D.M.; Medley, S.S.; Mueller, D.; Nagayama, Y.; Owens, D.K.; Synakowski, E.J.; Roberts, D.R.; Sabbagh, S.
1992-01-01
Toroidal Alfven Eigenmodes (TAE) were excited by the energetic neutral beam ions tangentially injected into TFTR plasmas at low magnetic field such that the injection velocities were comparable to the Alfven speed. The modes were identified by measurements from Mirnov coils and beam emission spectroscopy (BES). TAE modes appear in bursts whose repetition rate increases with beam power. The neutron emission rate exhibits sawtooth-like behavior and the crashes always coincide with TAE bursts. This indicates ejection of fast ions from the plasma until these modes are stabilized. The dynamics of growth and stabilization was investigated at various plasma current and magnetic field. The results indicate that the instability can effectively clamp the number of energetic ions in the plasma. The observed instability threshold is discussed in the light of recent theories. In addition to these TAE modes, intermittent oscillations at three times the fundamental TAE frequency were observed by Mirnov coils, but no corresponding signal was found in BES. It appears that these high frequency oscillations do not have direct effect on the plasma neutron source strength
Djomo Mbong, T. L. M.; Siewe Siewe, M.; Tchawoua, C.
2018-01-01
In this study, the effect of a controllable parametric excitation on both linear and nonlinear vibrational resonances on the dynamic of a buckled beam excited by a combination of uncontrollable low- and high-frequency periodic forces are investigated. First of all, the beam dynamic is assumed to be constrained by two periodic and independent ambient solicitations, such as wind and earthquake. An axial load of the beam represented by a periodic and parametric excitation is used to control the vibrational resonance phenomenon, induced by the presence of the two external excitations. Approximate analytical expressions for the linear response and the high-frequency force amplitude at which linear vibrational resonance occurs are obtained. An analytical expression of the amplitude of the nonlinear response at the superharmonic equal to the double of the low-frequency, is obtained. For all these expressions, we show the effect of the parametric excitation. We compare all the obtained results with the ones of the case where, the parametric force is absent. It is shown that, the presence of the parametric excitation permit the suppression of both linear and nonlinear vibrational resonances. Moreover, the vibration amplitudes of the buckled beam are significantly reduced, around certain threshold values for the amplitude and the frequency of the parametric excitation.
The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfven Eigenmodes
International Nuclear Information System (INIS)
Lesur, M.
2010-01-01
The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of alpha particles. Such particles can excite instabilities in the frequency range of Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. In the case of an isolated single resonance, the description of AE destabilization by high-energy ions is homothetic to the so-called Berk-Breizman (BB) problem. A semi-Lagrangian simulation code, COBBLES, is developed to solve the initial-value BB problem in both perturbative (δf) and self-consistent (full-f) approaches. Two collision models are considered, namely a Krook model, and a model that includes dynamical friction (drag) and velocity-space diffusion. The nonlinear behavior of instabilities in experimentally-relevant conditions is categorized into steady-state, periodic, chaotic, and frequency-sweeping (chirping) regimes, depending on external damping rate and collision frequency. The chaotic regime is shown to extend into a linearly stable region, and a mechanism that solves the paradox formed by the existence of such subcritical instabilities is proposed. Analytic and semi-empirical laws for nonlinear chirping characteristics, such as sweeping-rate, lifetime, and asymmetry, are developed and validated. Long-time simulations demonstrate the existence of a quasi-periodic chirping regime. Although the existence of such regime stands for both collision models, drag and diffusion are essential to reproduce the alternation between major chirping events and quiescent phases, which is observed in experiments. A new method for analyzing fundamental kinetic plasma parameters, such as linear drive and external damping rate, is developed. The method, which consists of fitting procedures between COBBLES simulations and quasi-periodic chirping AE experiments, does not require any internal diagnostics. This approach is applied to Toroidicity-induced AEs
International Nuclear Information System (INIS)
Vasconcellos, J.I.C.
1982-01-01
The nonlinear real index of refraction variations of a gas medium due to a strong monochromatic radiation causing saturation effects is calculated. The gas is supposed to be composed of two-level molecules with which the external field is nearly resonant. It is assumed homogeneous (hard collisions, spontaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms acting on the real index of refraction of the medium. The nonlinear dispersion of the medium is studied as a function of the detuning frequencies, saturation conditions and for various ratios between the homogeneous and inhomogeneous linewidths. In particular, the modification of the index of refraction due to saturation effects are emphasized. (Author) [pt
Heating of solar coronal holes by reflected Alfven waves
Moore, R. L.; Musielak, Z. E.; Suess, S. T.; An, C.-H.
1992-01-01
As a continuation of the work of Moore et al. (1991), who found evidence that coronal holes are heated by Alfven waves that are reflected back down within the coronal holes, this paper shows that to demonstrate this evidence, it is only necessary to consider a subset of the Moore et al. models, namely, those having radial magnetic field. Using these models, it is shown that the Alfven velocity is not constant in the atmosphere of coronal holes, but changes with height (or radius), causing downward reflection of all upward Alfven waves of sufficiently long wavelength (or period).
Nonlinear Container Ship Model for the Study of Parametric Roll Resonance
Directory of Open Access Journals (Sweden)
Christian Holden
2007-10-01
Full Text Available Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to +-40 degrees, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head seas. A Matlab/Simulink parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007. The benchmark implements a 3rd-order nonlinear model where the dynamics of roll is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic results which are in good agreement with the model tank experiments.
Directory of Open Access Journals (Sweden)
Sebastian Schaetz
2017-01-01
Full Text Available Purpose. To develop generic optimization strategies for image reconstruction using graphical processing units (GPUs in magnetic resonance imaging (MRI and to exemplarily report on our experience with a highly accelerated implementation of the nonlinear inversion (NLINV algorithm for dynamic MRI with high frame rates. Methods. The NLINV algorithm is optimized and ported to run on a multi-GPU single-node server. The algorithm is mapped to multiple GPUs by decomposing the data domain along the channel dimension. Furthermore, the algorithm is decomposed along the temporal domain by relaxing a temporal regularization constraint, allowing the algorithm to work on multiple frames in parallel. Finally, an autotuning method is presented that is capable of combining different decomposition variants to achieve optimal algorithm performance in different imaging scenarios. Results. The algorithm is successfully ported to a multi-GPU system and allows online image reconstruction with high frame rates. Real-time reconstruction with low latency and frame rates up to 30 frames per second is demonstrated. Conclusion. Novel parallel decomposition methods are presented which are applicable to many iterative algorithms for dynamic MRI. Using these methods to parallelize the NLINV algorithm on multiple GPUs, it is possible to achieve online image reconstruction with high frame rates.
Finite orbit energetic particle linear response to toroidal Alfven eigenmodes
International Nuclear Information System (INIS)
Berk, H.L.; Ye Huanchun; Breizman, B.N.
1992-01-01
The linear response of energetic particles of the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width; when the banana width Δ b is much larger than the mode thickness Δ m , we obtain a new compact expression for the linear power transfer. When Δ m /Δ b m /Δ b from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balanced-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (vertical strokev parallel vertical stroke=v A ) is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (vertical strokev parallel vertical stroke=v A /(2l-1) with l≥2) is substantially reduced. (orig.)
Fu, X.; Li, H.; Guo, F.; Li, X.; Roytershteyn, V.
2017-12-01
The solar wind is a turbulent magnetized plasma extending from the upper atmosphere of the sun to the edge of the heliosphere. It carries charged particles and magnetic fields originated from the Sun, which have great impact on the geomagnetic environment and human activities in space. In such a magnetized plasma, Alfven waves play a crucial role in carrying energy from the surface of the Sun, injecting into the solar wind and establishing power-law spectra through turbulent energy cascades. On the other hand, in compressible plasmas large amplitude Alfven waves are subject to a parametric decay instability (PDI) which converts an Alfven wave to another counter-propagating Alfven wave and an ion acoustic wave (slow mode). The counter-propagating Alfven wave provides an important ingredient for turbulent cascade, and the slow-mode wave provides a channel for solar wind heating in a spatial scale much larger than ion kinetic scales. Growth and saturation of PDI in quiet plasma have been intensively studied using linear theory and nonlinear simulations in the past. Here using 3D hybrid simulations, we show that PDI is still effective in turbulent low-beta plasmas, generating slow modes and causing ion heating. Selected events in WIND data are analyzed to identify slow modes in the solar wind and the role of PDI, and compared with our simulation results. We also investigate the validity of linear Vlasov theory regarding PDI growth and slow mode damping in turbulent plasmas. Since PDI favors low plasma beta, we expect to see more evidence of PDI in the solar wind close to the Sun, especially from the upcoming NASA's Parker Solar Probe mission which will provide unprecedented wave and plasma data as close as 8.5 solar radii from the Sun.
Sahmani, S.; Aghdam, M. M.
2018-03-01
A wide range of biological applications such as drug delivery, biosensors and hemodialysis can be provided by nanoporous biomaterials due to their uniform pore size as well as considerable pore density. In the current study, the size dependency in the nonlinear primary resonance of micro/nano-beams made of nanoporous biomaterials is anticipated. To accomplish this end, a refined truncated cube is introduced to model the lattice structure of nanoporous biomaterial. Accordingly, analytical expressions for the mechanical properties of material are derived as functions of pore size. After that, based upon a nonlocal strain gradient beam model, the size-dependent nonlinear Duffing type equation of motion is constructed. The Galerkin technique together with the multiple time-scales method is employed to obtain the nonlocal strain gradient frequency-response and amplitude-response related to the nonlinear primary resonance of a micro/nano-beam made of the nanoporous biomaterial with different pore sizes. It is indicated that the nonlocality causes to decrease the response amplitudes associated with the both bifurcation points of the jump phenomenon, while the strain gradient size dependency causes to increase them. Also, it is found that increasing the pore size leads to enhance the nonlinearity, so the maximum deflection of response occurs at higher excitation frequency.
Central mass feedback control using the discrete Alfven wave spectrum
International Nuclear Information System (INIS)
Dudok de Wit, Th.; Lister, J.B.; Duval, B.P.; Joye, B.; Marmillod, Ph.
1990-04-01
The dispersion relation of the shear Alfven wave depends on several internal plasma parameters, including the central effective mass. By frequency tracking a Discrete Alfven Wave during the plasma current flat-top, we obtained a real-time estimate of the central effective mass. Using the measured mass, we have been able to feedback control both the effective mass and the electron density of the plasma, using separately controllable hydrogen and deuterium filling valves. (author) 5 refs., 6 figs
Theory of semicollisional kinetic Alfven modes in sheared magnetic fields
International Nuclear Information System (INIS)
Hahm, T.S.; Chen, L.
1985-02-01
The spectra of the semicollisional kinetic Alfven modes in a sheared slab geometry are investigated, including the effects of finite ion Larmor radius and diamagnetic drift frequencies. The eigenfrequencies of the damped modes are derived analytically via asymptotic analyses. In particular, as one reduces the resistivity, we find that, due to finite ion Larmor radius effects, the damped mode frequencies asymptotically approach finite real values corresponding to the end points of the kinetic Alfven continuum
Confinement relevant Alfven instabilities in Wendelstein 7-AS
International Nuclear Information System (INIS)
Yakovenko, Yu.V.; Kolesnichenko, Ya.I.; Lutsenko, V.V.; Weller, A.; Werner, A.; Zegenhagen, S.; Geiger, J.
2005-01-01
Bursting Alfvenic activity accompanied by strong thermal crashes and frequency chirping in a W7-AS shot is studied. A theory explaining the experimental observations is developed. A novel mechanism of anomalous electron thermal conductivity is found. In addition, a general consideration of the influence of the gap crossing on the Alfven continuum in stellarators is carried out and a phenomenon of gap annihilation is predicted. (author)
International Nuclear Information System (INIS)
Zhou, Hao-Miao; Li, Chao; Xuan, Li-Ming; Zhao, Ji-Xiang; Wei, Jing
2011-01-01
This paper analyzes the magnetoelectric (ME) response around the resonance frequency in the magnetostrictive/piezoelectric/magnetostrictive (MPM) magnetoelectric laminate composites. Following the equivalent circuit method and considering the mechanical loss, we select the nonlinear magnetostrictive constitutive model to present a novel explicit nonlinear expression for the resonant magnetoelectric (ME) coefficient of the magnetoelectric laminate composites. Compared with the experimental results, the predicted resonant ME coefficient of the explicit expression shows a good agreement both qualitatively and quantitatively. Also, when the electromechanical coupling factor of the piezoelectric material, k 31 p , is small, this explicit expression can be reduced to the existing model. On this basis, this paper considers and predicts the magnetoelectric conversion characteristics of the magnetoelectric laminate composites, calculates and analyzes the influences of the thickness ratio of magnetostrictive layer and piezoelectric material, bias magnetic field, and saturation magnetostrictive coefficient on the resonant ME coefficient. This research can provide a theoretical basis for the preparation of magnetoelectric devices with good magnetoelectric conversion characteristics, such as magnetoelectric sensors, energy harvesting transducers, microwave devices etc
Nonlinear Oscillations and Flow of Gas Within Closed and Open Conical Resonators
Daniels, Christopher; Finkbeiner, Joshua; Steinetz, Bruce; Li, Xiaofan; Raman, Ganesh
2004-01-01
A dissonant acoustic resonator with a conical shaped cavity was tested in four configurations: (A) baseline resonator with closed ends and no blockage; (B) closed resonator with internal blockage; (C) ventilated resonator with no blockage; and (D) ventilated resonator with an applied pressure differential. These tests were conducted to investigate the effects of blockage and ventilation holes on dynamic pressurization. Additionally, the investigation was to determine the ability of acoustic pressurization to impede flow through the resonator. In each of the configurations studied, the entire resonator was oscillated at the gas resonant frequency while dynamic pressure, static pressure, and temperature of the fluid were measured. In the final configuration, flow through the resonator was recorded for three oscillation conditions. Ambient condition air was used as the working fluid. The baseline results showed a marked reduction in the amplitude of the dynamic pressure waveforms over previously published studies due to the use of air instead of refrigerant as the working fluid. A change in the resonant frequency was recorded when blockages of differing geometries were used in the closed resonator, while acoustic pressure amplitudes were reduced from baseline measurements. A sharp reduction in the amplitude of the acoustic pressure waves was expected and recorded when ventilation ports were added. With elevated pressure applied to one end of the resonator, flow was reduced by oscillating the cavity at the fluid fundamental resonant frequency compared to cases without oscillation and oscillation off-resonance.
Eslami, M.; Mirzazadeh, M.; Biswas, Anjan
2013-11-01
In this paper, the resonant nonlinear Schrödinger's equation is studied with four forms of nonlinearity. This equation is also considered with time-dependent coefficients. The simplest equation method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.
Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators.
Nourmohammadi, Zahra; Joshi, Surabhi; Vengallatore, Srikar
2016-01-01
The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.
Cao, Jingming; Xiaver, Jolly
2017-10-01
We manipulated the simulation and apparatus to generate the entangled quantum photons by the enhanced higher quality factor in waveguide of whispering gallery mode resonator in silica microsphere. As the several nonlinear optics effects have been validated in micro-disk (lithium niobate materials based), others micro-cavity (microfiber and micro ring on the chip) and second harmonic generation (SHG) on the surface of silica microsphere because of the characterization of enhanced higher quality factor Q and smaller volume mode in these resonator. However until now for the second third nonlinearity of spontaneous parametric down conversion (SPDC), third order nonlinearity of spontaneous parametric down conversion (TOSPDC) and spontaneous four wave mixing (SFWM) in whispering gallery mode (WGM) resonator of silica microsphere rarely have not been fully investigated and verified to generate the triple and pair entangled photons where are widely applied on the applications of biosensor, quantum communications and spectroscopy, respectively. Specially, the features of silica microsphere have attracted many applications due to the simple fabrication, simplified materials melted by silica fiber. The work we demonstrated in this paper based on the breaking of the dispersion rules to make perfect phase matching in normal dispersion in silica microsphere depending on the blue laser spectrum in visible spectrum, then manipulated the modified size of microsphere to detune the pump laser of free spectral range (FSR) and both shift the geometrical dispersion are characterized in the variation of FSR given by (see PDF for equation), where n is refractive index, R is the microspheres radius and m is mode numbers in resonator, to compensate the materials dispersion given by (see PDF for equation), where c is the speed of light and λ is pump laser wavelength to fulfill the perfect phase matching in parametric down conversion regimes and the modeling fabrication coupling results also
Advanced antenna system for Alfven wave plasma heating and current drive in TCABR tokamak
International Nuclear Information System (INIS)
Ruchko, L.F.; Ozono, E.; Galvao, R.M.O.; Nascimento, I.C.; Degasperi, F.T.; Lerche, E.
1998-01-01
An advanced antenna system that has been developed for investigation of Alfven wave plasma heating and current drive in the TCABR tokamak is described. The main goal was the development of such a system that could insure the excitation of travelling single helicity modes with predefined wave mode numbers M and N. The system consists of four similar modules with poloidal windings. The required spatial spectrum is formed by proper phasing of the RF feeding currents. The impedance matching of the antenna with the four-phase oscillator is accomplished by resonant circuits which form one assembly unit with the RF feeders. The characteristics of the antenna system design with respect to the antenna-plasma coupling and plasma wave excitation, for different phasing of the feeding currents, are summarised. The antenna complex impedance Z=Z R +Z I is calculated taking into account both the plasma response to resonant excitation of fast Alfven waves and the nonresonant excitation of vacuum magnetic fields in conducting shell. The matching of the RF generator with the antenna system during plasma heating is simulated numerically, modelling the plasma response with mutually coupled effective inductances with corresponding active Z R and reactive Z I impedances. The results of the numerical simulation of the RF system performance, including both the RF magnetic field spectrum analysis and the modeling of the RF generator operation with plasma load, are presented. (orig.)
Resonant tunneling and nonlinear current in heterobarrier with complex dispersion of carriers
Kim, C S; Shtenberg, V B
2002-01-01
The study of novel effects in resonant tunneling of electrons in GaAs/Al sub x Ga sub 1 sub - sub x As/GaAs single-barrier structures under an applied electric bias is carried out. GAMMA-X mixing of electron states at the interfaces is responsible for Fano resonance in the barrier transmittance. A motion of Fano resonances and the interaction between Fano and Breit-Wigner resonances in electric field have been investigated. The current-voltage characteristic of the heterobarrier is calculated. It is shown that the differential conductivity presents a way to get the Fano resonance profile and its parameters
Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing
DEFF Research Database (Denmark)
Karamehmedovic, Emir; Pedersen, Christian; Jensen, Ole Bjarlin
2009-01-01
We investigate the possibility of improving the beam quality and obtaining high conversion efficiency in nonlinear sum-frequency generation. A 765 nm beam from an external cavity tapered diode laser is single-passed through a nonlinear crystal situated in the high intracavity field of a 1342 nm N...
Directory of Open Access Journals (Sweden)
Merboldt Klaus-Dietmar
2010-07-01
Full Text Available Abstract Background Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR commonly rely on (i electrocardiographic (ECG gating yielding pseudo real-time cine representations, (ii balanced gradient-echo sequences referred to as steady-state free precession (SSFP, and (iii breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts, and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. Methods The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Results Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle with an opposed-phase or in-phase condition for water and fat signals (depending on echo time. They completely avoid (i susceptibility-induced artefacts due to the very short echo times, (ii radiofrequency power limitations due to excitations with flip angles of 10° or less, and (iii the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Conclusions Though awaiting thorough clinical evaluation, this work describes a robust and
An Experimental Study of Nonlinear Standing Waves in Resonators with Numerical Comparison
Finkbeiner, Joshua R.; Raman, Ganesh; Li, Xiaofan; Steinetz, Bruce M.; Daniels, Christopher; Huff, Dennis (Technical Monitor)
2002-01-01
Lawrenson et. al. [Journal of the Acoustic Society of America, Nov. 1998] described the generation of shock-free high-amplitude pressure waves in closed cavities using large equipment and resonators to produce the reported effects. An attempt is made to generate shock-free high-amplitude pressure waves using relatively small resonators. Ambient air is used as the working fluid. A small cylindrical resonator is tested resulting in the lack of a shocked waveform while a larger model of the same shape produces shock waves. A small conical resonator produces shock-free pressure waves at resonance, but the amplitude of these waves is small. A larger cone resonator model produces shock-free pressure waves of higher amplitude. A large horn-cone resonator also produces shock-free high amplitude pressure waves, A numerical model is used to compare the experimental results to theoretical results. The effects of structural resonances on the production of shock-free high-amplitude pressure waves are discussed, especially concerning difficulties encountered when these resonances were in the frequency ranges of interest. Identifying features of a structural resonance are presented.
Oscillations in sunspot umbras due to trapped Alfven waves excited by overstability
International Nuclear Information System (INIS)
Uchida, Yutaka; Sakurai, Takashi.
1975-01-01
Oscillations observed in sunspot umbras are interpreted as a vertical motion in the atmosphere induced by a standing Alfven wave trapped in the region between the overstable layer under the photosphere and the chromosphere-corona transition layer. The Alfven wave motion is considered to be excited by the overstable convection occurring at the bottom of the abovementioned oscillating layer, and waves with special frequencies are selected as eigen-mode waves standing in the ''cavity,'' while other waves which are out of phase with themselves after reflections will disappear. It is shown by solving the eigen-value problem that the fundamental eigen frequency falls in a range around 0.04 rad s -1 (corresponding to 140-180 s) for the condition in the umbra of a typical spot, and also that the eigen frequencies do not depend greatly on the circumstantial physical or geometric parameters of the model atmosphere, such as the temperature in the layer, or the height of the transition layer, etc. The eigen frequencies, however, depend on the Alfven velocity at the base of the oscillating layer (or at the top of the overstable layer), but the latter quantity, which represents the stiffness of the magnetic tube of force against the overturning motion, takes roughly a common value for different sunspots according to SAVAGE's (1969) stability analysis of the umbral atmosphere against thermal convection, and thus gives a comparatively narrow range of resonant frequencies. In addition to the selection mechanism for oscillations of 140-180-s period, some other aspects of the oscillation, such as the relation to the running penumbral waves, are discussed. (auth.)
International Nuclear Information System (INIS)
Klofai, Yerima; Essimbi, B Z; Jaeger, D
2011-01-01
Pulse propagation on high-frequency dissipative nonlinear transmission lines (NLTLs)/resonant tunneling diode line cascaded maps is investigated for long-distance propagation of short pulses. Applying perturbative analysis, we show that the dynamics of each line is reduced to an expanded Korteweg-de Vries-Burgers equation. Moreover, it is found by computer experiments that the soliton developed in NLTLs experiences an exponential amplitude decay on the one hand and an exponential amplitude growth on the other. As a result, the behavior of a pulse in special electrical networks made of concatenated pieces of lines is closely similar to the transmission of information in optical/electrical communication systems.
Alabastri, A.
2013-10-25
In this paper, we review the principal theoretical models through which the dielectric function of metals can be described. Starting from the Drude assumptions for intraband transitions, we show how this model can be improved by including interband absorption and temperature effect in the damping coefficients. Electronic scattering processes are described and included in the dielectric function, showing their role in determining plasmon lifetime at resonance. Relationships among permittivity, electric conductivity and refractive index are examined. Finally, a temperature dependent permittivity model is presented and is employed to predict temperature and non-linear field intensity dependence on commonly used plasmonic geometries, such as nanospheres. 2013 by the authors; licensee MDPI, Basel, Switzerland.
International Nuclear Information System (INIS)
Chai, Zhen; Hu, Xiaoyong; Gong, Qihuang
2013-01-01
A low-power all-optical switching is presented based on the all-optical tunable Fano-like resonance in a two-dimensional nonlinear ferroelectric photonic crystal made of polycrystalline lithium niobate. An asymmetric Fano-like line shape is achieved in the transmission spectrum by using two cascaded and uncoupled photonic crystal microcavities. The physical mechanism underlying the all-optical switching is attributed to the dynamic shift of the Fano-like resonance peak caused by variations in the dispersion relations of the photonic crystal structure induced by pump light. A large switching efficiency of 61% is reached under excitation of a weak pump light with an intensity as low as 1 MW cm −2 . (paper)
Directory of Open Access Journals (Sweden)
El Aroudi A.
2014-01-01
Full Text Available In this paper, the model of a two-degree-of-freedom (2-DOF spring resonator with end stopper for an energy harvesting application is presented. Then we characterize its nonlinear dynamical behavior by numerical simulations when some suitable parameters are varied. The system is formed by two resonators subject to external vibrational excitation and with an end stopper. We present the continuous time dynamical model of the system in the form of a switched fourth order differential equation. Harmonic vibrations are considered as the main ambient energy source for the system and its frequency response representing the RMS value of the displacement is first computed. The dynamical behavior is unveiled by computing state-space trajectories, timedomain series and FFT spectra and frequency response as the excitation amplitude is varied.
Signatures of mode conversion and kinetic Alfven waves at the magnetopause
International Nuclear Information System (INIS)
Johnson, Jay R.; Cheng, C. Z.
2000-01-01
It has been suggested that resonant mode conversion of compressional MHD waves into kinetic Alfven waves at the magnetopause can explain the abrupt transition in wave polarization from compressional to transverse commonly observed during magnetopause crossings. The authors analyze magnetic field data for magnetopause crossings as a function of magnetic shear angle (defined as the angle between the magnetic fields in the magnetosheath and magnetosphere) and compare with the theory of resonant mode conversion. The data suggest that amplification in the transverse magnetic field component at the magnetopause is not significant up to a threshold magnetic shear angle. Above the threshold angle significant amplification results, but with weak dependence on magnetic shear angle. Waves with higher frequency are less amplified and have a higher threshold angle. These observations are qualitatively consistent with theoretical results obtained from the kinetic-fluid wave equations
Comments on the Alfven wave spectrum as measured on the TCA tokamak
International Nuclear Information System (INIS)
Puri, S.
1986-06-01
The heating in the TCA tokamak is ascribed to a combination of compressional Alfven wave heating (CAW) and discrete Alfven wave (DAW) heating. In this communication we invoke an alternative plasma heating mechanism by the direct excitation of torsional Alfven waves (TAW) to account for the observed features of the TCA experiment. (orig./GG)
Neutrino induced vorticity, Alfven waves and the normal modes
Energy Technology Data Exchange (ETDEWEB)
Bhatt, Jitesh R. [Theory Division, Physical Research Laboratory, Ahmedabad (India); George, Manu [Theory Division, Physical Research Laboratory, Ahmedabad (India); Indian Institute of Technology, Department of Physics, Ahmedabad (India)
2017-08-15
We consider a plasma consisting of electrons and ions in the presence of a background neutrino gas and develop the magnetohydrodynamic equations for the system. We show that the electron neutrino interaction can induce vorticity in the plasma even in the absence of any electromagnetic perturbations if the background neutrino density is left-right asymmetric. This induced vorticity supports a new kind of Alfven wave whose velocity depends on both the external magnetic field and on the neutrino asymmetry. The normal mode analysis show that in the presence of neutrino background the Alfven waves can have different velocities. We also discuss our results in the context of dense astrophysical plasma such as magnetars and show that the difference in the Alfven velocities can be used to explain the observed pulsar kick. We discuss also the relativistic generalisation of the electron fluid in presence of an asymmetric neutrino background. (orig.)
Excitation of global Alfven Eigenmodes by RF heating in JET
Energy Technology Data Exchange (ETDEWEB)
Kerner, W.; Borba, D.; Gormezano, C.; Huysmans, G.; Porcelli, F.; Start, D. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking; Fasoli, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP); Sharapov, S. [Kurchatov Institute, Moscow (Russian Federation)
1994-07-01
The alpha-particle confinement of future D-T experiments at JET can be severely degraded by Global Alfven Eigenmodes (AE). Scenarios for the excitation of Alfven Eigenmodes in usual (e.g. D-D) plasmas are proposed, which provide a MHD diagnostic and allow the study of the transport of super-Alfvenic ions. Active studies with separate control of TAE amplitude and energetic particle destabilization, measuring the plasma response, give more information than passive studies, in particular concerning the damping mechanisms. The TAE excitation can be achieved by means of the saddle coil and the ICRH antenna. The experimental method is introduced together with a theoretical model for RF excitation. (authors). 6 refs., 3 figs.
Direct measurement of the damping of toroidicity induced Alfven eigenmodes
International Nuclear Information System (INIS)
Fasoli, A.; Lister, J.B.; Moret, J.M.; Lavanchy, P.; Marmillod, P.; Sharapov, S.; Borba, D.; Bosia, G.; Campbell, D.J.; Dobbing, J.A.; Gormezano, C.; Jacquinot, J.; Santagiustina, A.
1995-01-01
This paper presents the first direct experimental measurements of the damping of toroidicity induced Alfven eigenmodes (TAE), carried out in the JET tokamak. These measurements were obtained during the first experiments to drive these modes with antennas external to a tokamak plasma. Different regimes corresponding to different dominant TAE absorption mechanisms with a wide range of damping rates, 10 -3 ≤γ/ω≤10 -1 , have been identified in ohmically heated plasma discharges using this new active diagnostic for Alfven eigenmodes. (author) 5 figs., tabs., 25 refs
High and low frequency Alfven modes in tokamaks
International Nuclear Information System (INIS)
Briguglio, S.; Fogaccia, G.; Vlad, G.; Zonca, F.; Chen, L.; Dong, J.Q.; Santoro, R.A.
2001-01-01
We present an analysis of the typical features of shear Alfven waves in tokamak plasmas in a frequency domain ranging from the ''high'' frequencies (ω ≅ ν A /2qR 0 ; ν A being the Alfven speed and qR 0 the tokamak connection length) of the toroidal gap to the ''low'' frequencies, comparable with the thermal ion diamagnetic frequency, ω *pi and/or the thermal ion transit frequency ω ti = ν ti /qR 0 (ν ti being the ion thermal speed). (author)
Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics
International Nuclear Information System (INIS)
Passot, T.; Sulem, P. L.
2005-01-01
In may astrophysical plasmas such as the solar wind, the terrestrial magnetosphere, or in the interstellar medium at small enough scales, collisions are negligible. When interested in the large-scale dynamics, a hydrodynamic approach is advantageous not only because its numerical simulations is easier than of the full Vlasov-Maxwell equations, but also because it provides a deep understanding of cross-scale nonlinear couplings. It is thus of great interest to construct fluid models that extended the classical magnetohydrodynamic (MHD) equations to collisionless situations. Two ingredients need to be included in such a model to capture the main kinetic effects: finite Larmor radius (FLR) corrections and Landau damping, the only fluid-particle resonance that can affect large scales and can be modeled in a relatively simple way. The Modelization of Landau damping in a fluid formalism is hardly possible in the framework of a systematic asymptotic expansion and was addressed mainly by means of parameter fitting in a linearized setting. We introduced a similar Landau fluid model but, that has the advantage of taking dispersive effects into account. This model properly describes dispersive MHD waves in quasi-parallel propagation. Since, by construction, the system correctly reproduces their linear dynamics, appropriate tests should address the nonlinear regime. In a first case, we show analytically that the weakly nonlinear modulational dynamics of quasi-parallel propagating Alfven waves is well captured. As a second test we consider the parametric decay instability of parallel Alfven waves and show that numerical simulations of the dispersive Landau fluid model lead to results that closely match the outcome of hybrid simulations. (Author)
International Nuclear Information System (INIS)
Letokhov, V.S.; Minogin, V.G.
1976-01-01
The possibilities of obtaining narrow resonances without the Doppler broadening for transition between the fine structure levels of the ground and first excited states of a positronium atom are considered. An analysis is carried out of the conditions required for observation of the narrow resonances of saturation of single quantum absorption in the 1S-2P transitions and observation of narrow two-photon absorption resonances in the 1S-2S transitions. It is shown that narrow 2γ annihilation radiation lines of a positronium atom may be obtained with a width much smaller than the Doppler one
Kinetic Alfven waves and electron physics. II. Oblique slow shocks
International Nuclear Information System (INIS)
Yin, L.; Winske, D.; Daughton, W.
2007-01-01
One-dimensional (1D) particle-in-cell (PIC; kinetic ions and electrons) and hybrid (kinetic ions; adiabatic and massless fluid electrons) simulations of highly oblique slow shocks (θ Bn =84 deg. and β=0.1) [Yin et al., J. Geophys. Res., 110, A09217 (2005)] have shown that the dissipation from the ions is too weak to form a shock and that kinetic electron physics is required. The PIC simulations also showed that the downstream electron temperature becomes anisotropic (T e parallel )>T e perpendicular ), as observed in slow shocks in space. The electron anisotropy results, in part, from the electron acceleration/heating by parallel electric fields of obliquely propagating kinetic Alfven waves (KAWs) excited by ion-ion streaming, which cannot be modeled accurately in hybrid simulations. In the shock ramp, spiky structures occur in density and electron parallel temperature, where the ion parallel temperature decreases due to the reduction of the ion backstreaming speed. In this paper, KAW and electron physics in oblique slow shocks are further examined under lower electron beta conditions. It is found that as the electron beta is reduced, the resonant interaction between electrons and the wave parallel electric fields shifts to the tail of the electron velocity distribution, providing more efficient parallel heating. As a consequence, for β e =0.02, the electron physics is shown to influence the formation of a θ Bn =75 deg. shock. Electron effects are further enhanced at a more oblique shock angle (θ Bn =84 deg.) when both the growth rate and the range of unstable modes on the KAW branch increase. Small-scale electron and ion phase-space vortices in the shock ramp formed by electron-KAW interactions and the reduction of the ion backstreaming speed, respectively, are observed in the simulations and confirmed in homogeneous geometries in one and two spatial dimensions in the accompanying paper [Yin et al., Phys. Plasmas 14, 062104 (2007)]. Results from this study
Directory of Open Access Journals (Sweden)
A. Karami Mohammadi
2015-07-01
Full Text Available : In this paper, a nonlinear model of clamped-clamped microbeam actuated by electrostatic load with stretching and thermoelastic effects is presented. Free vibration frequency is calculated by discretization based on DQ method. Frequency is a complex value due to the thermoelastic effect that dissipates the energy. By separating the real and imaginary parts of frequency, quality factor of thermoelastic damping is calculated. Both stretching and thermoelastic effects are validated against the results of the reference papers. The variations of thermoelastic damping versus elasticity modulus, coefficient of thermal expansion and geometrical parameters such as thickness, gap distance, and length are investigated and these results are compared in the linear and nonlinear models for high values of voltage. Also, this paper shows that since for high values of electrostatic voltage the linear model reveals a large error for calculating the thermoelastic damping, the nonlinear model should be used for this purpose.
Nonlinear saturation of non-resonant internal instabilities in a straight spheromak
International Nuclear Information System (INIS)
Park, W.; Jardin, S.C.
1982-04-01
An initial value numerical solution of the time dependent nonlinear ideal magnetohydrodynamic equations demonstrates that spheromak equilibria which are linearly unstable to nonresonant helical internal perturbations saturate at low amplitude without developing singularities. These instabilities thus represent the transition from an axisymmetric to a non-axisymmetric equilibrium state, caused by a peaking of the current density
Stefszky, Michael; Mow-Lowry, Conor M.; McKenzie, Kirk; Chua, Sheon; Buchler, Ben C.; Symul, Thomas; McClelland, David E.; Lam, Ping Koy
2011-01-01
A squeezed light source requires properties such as high squeezing amplitude, high bandwidth and stability over time, ideally using as few resources, such as laser power, as possible. We compare three nonlinear materials, two of which have not been well characterized for squeezed state production,
Reflection of Alfven waves at an open magnetopause
International Nuclear Information System (INIS)
Cao, F.; Kan, J.R.
1990-01-01
Reflection of an Alfven wave incident on an open magnetopause form the magnetospheric side is examined. An open magnetopause, whose structure is different from the standard rotational discontinuity, is assumed to be a parameterized discontinuity with a nonzero normal field component. When an Alfven wave is incident on the open magnetopause, reflected and transmitted waves are generated. The emanating waves can be analyzed using linearized MHD conservation relations across the magnetopause, together with Snell's law. Under the assumption that the magnetic fields on the two sides of the open magnetopause are coplanar with the normal direction of the magnetopause, the governing equations are solved numerically. The results show that the electric fields of emanating Alfven waves depend mainly on the number density and the magnetic field jumps across the magnetopause. Under conditions representing the open magnetopause, it turns out that the open magnetopause behaves like a near perfect reflector. The corresponding reflection coefficient for the wave electric field can be approximated by R E = E r /E i ∼ -1 as has been deduced by Kan and Sun (1985) based on physical arguments. In other words, the solar wind flow is more or less unchanged by the loading effect of the Alfven wave incident on the magnetopause from the magnetospheric side. Therefore, under the assumptions of the model, the open magnetopause can be viewed as a constant voltage source
ALFVEN WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
Energy Technology Data Exchange (ETDEWEB)
Soler, R.; Ballester, J. L.; Terradas, J. [Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Carbonell, M., E-mail: roberto.soler@uib.es, E-mail: joseluis.ballester@uib.es, E-mail: jaume.terradas@uib.es, E-mail: marc.carbonell@uib.es [Departament de Matematiques i Informatica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain)
2013-04-20
Alfven waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfven waves is affected by the interaction between ionized and neutral species. Here we study Alfven waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible, we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cutoff values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mode approach and solve the initial-value problem in order to study the time-dependent evolution of the wave perturbations in the two fluids. An application to Alfven waves in the low solar atmospheric plasma is performed and the implication of partial ionization for the energy flux is discussed.
Current drive by Alfven waves in elongated cross section tokamak
Energy Technology Data Exchange (ETDEWEB)
Tsypin, V.S.; Elfimov, A.G.; Nekrasov, F.M.; Azevedo, C.A. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica; Assis, A.S. de [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica
1997-12-31
Full text. The problem of the noninductive current drive in cylindrical plasma model and in circular cross-section tokamaks had been already discussed intensively. At the beginning of the study of this problem it have been clear that there are significant difficulties in using of the current-drive in toroidal magnetic traps, especially in a tokamak reactor. Thus, in the case of the lower-hybrid current-drive the efficiency of this current-drive drops strongly as the plasma density increases. For the Alfven waves, there is an opinion that the efficiency of the current-drive drops as a result of waves absorption by the trapped particles 1,2. Okhawa proposed that the current in a magnetized plasma can be maintained also by means of forces, depending on the radiofrequency (rf) field amplitude gradients (the helicity injection). This idea was developed later, some new hopes appeared, connected with the possibility of the current-drive efficiency increasing. It was shown that for the cylindrical plasmas the local efficiency of Alfev wave current drive can be increased by one order of magnitude due to gradient forces, for the kinetic Alfven waves (KAW) and the global Alfven waves (GAW) at some range of the phase velocity. For tokamaks, this additional nonresonant current drive does not depend on the trapped particle effects, which reduce strongly the Alfven current drive efficiency in tokamaks, as it is supposed. Now, the theory development of the Alfven wave (AW) current drive is very important in the cource of the future experiments on the TCA/BR tokamak (Brazil). In this paper, an attempt is made to clarify some general aspects of this problems for magnetic traps. For large aspects ratio tokamaks, with an elongated cross-section, some general formulas concerning the untrapped and trapped particles dynamics and their input to the Landau damping of the Alfven waves, are presented. They are supposed to be used for the further development of the Alfven current drive theory
Muriano, Alejandro; Salvador, J.-Pablo; Galve, Roger; Marco, M.-Pilar; Thayil K. N., Anisha; Loza-Alvarez, Pablo; Soria, Silvia
2011-01-01
We report the non linear fluorescence real-time detection of methylboldenone, an androgenic anabolic steroid used illegally as growth promoter based on a resonant sensing chip: a double grating waveguide structure. The limit of detection of this synthetic steroid is two orders of magnitude lower than the Minimum Required Performance Limit required by the World Anti-Doping Agency. The immunoreagents have been have been immobilized onto the surface of the resonant sensor after being activated with phosphonohexanoic acid spacers. The developed immunosensor presents great potential as a robust sensing device for fast and early detection of illegal dopants and food contaminants.
Directory of Open Access Journals (Sweden)
Thimo Hugger
Full Text Available In this article we aim at improving the performance of whole brain functional imaging at very high temporal resolution (100 ms or less. This is achieved by utilizing a nonlinear regularized parallel image reconstruction scheme, where the penalty term of the cost function is set to the L(1-norm measured in some transform domain. This type of image reconstruction has gained much attention recently due to its application in compressed sensing and has proven to yield superior spatial resolution and image quality over e.g. Tikhonov regularized image reconstruction. We demonstrate that by using nonlinear regularization it is possible to more accurately localize brain activation from highly undersampled k-space data at the expense of an increase in computation time.
Double-resonant processes in x.sup.20.sup. nonlinear periodic media
Czech Academy of Sciences Publication Activity Database
Konotop, V. V.; Kuzmiak, Vladimír
2000-01-01
Roč. 17, č. 11 (2000), s. 1874-1883 ISSN 0740-3224 Grant - others:Fundo European de Desenvolvimento Regional and Program PRAXIS XXI(PT) PRAXIS/2/2.1/FIS/176/94 Institutional research plan: CEZ:AV0Z2067918 Keywords : nonlinear media * electromagnetic wave propagation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.943, year: 2000
DEFF Research Database (Denmark)
Bache, Morten; Lodahl, Peter; Mamaev, Alexander V.
2002-01-01
We predict and experimentally observe temporal self-pulsing in singly resonant intracavity second-harmonic generation under conditions of simultaneous parametric oscillation. The threshold for self-pulsing as a function of cavity tuning and phase mismatch are found from analysis of a three-compon...
Amplitude calibration of 2D mechanical resonators by nonlinear optical transduction
Dolleman, R.J.; Davidovikj, D.; van der Zant, H.S.J.; Steeneken, P.G.
2017-01-01
Contactless characterization of mechanical resonances using Fabry-Perot interferometry is a powerful tool to study the mechanical and dynamical properties of atomically thin membranes. However, amplitude calibration is often not performed or only possible by making assumptions on the device
Rojan, Katharina; Léger, Yoan; Morigi, Giovanna; Richard, Maxime; Minguzzi, Anna
2017-09-01
Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the terahertz (THz) frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic media, the transition between both polaritonic states is dipole forbidden. In this work, we show that, in cadmium telluride microcavities, the Rabi-oscillation-driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states and leads to a giant enhancement of the second-order nonlinearity.
Electric-field induced nonlinear ferromagnetic resonance in a CoFeB/MgO magnetic tunnel junction
Hirayama, E.; Kanai, S.; Ohe, J.; Sato, H.; Matsukura, F.; Ohno, H.
2015-09-01
We investigate the rf power dependence of homodyne-detected ferromagnetic resonance (FMR) spectra of a nanoscale CoFeB/MgO magnetic tunnel junction, in which the FMR is induced by the electric-field modulation of the magnetic anisotropy. The increase of the rf power changes the spectral lineshape and decreases characteristic frequency, at which drastic change in spectrum is observed. The behavior is consistent with nonlinear magnetization precession with a large precessional angle at high powers. From the rf power dependence of FMR spectra, we determine electric-field modulation ratio of magnetic anisotropy energy density to be 78 fJ/Vm, which is in agreement with the reported values.
Nurmohammadi, Tofiq; Abbasian, Karim; Yadipour, Reza
2018-03-01
In this paper, an all-optical plasmonic switch based on metal-insulator-metal (MIM) nanoplasmonic waveguide with a Kerr nonlinear ring resonator is introduced and studied. Two-dimensional simulations utilizing the finite-difference time-domain algorithm are used to demonstrate an apparent optical bistability and significant switching mechanisms (in enabled-low condition: T(ON/OFF) =21.9 and in enabled-high condition: T(ON/OFF) =24.9) of the signal light arisen by altering the pump-light intensity. The proposed all-optical switching demonstrates femtosecond-scale feedback time (90 fs) and then ultra-fast switching can be achieved. The offered all-optical switch may recognize potential significant applications in integrated optical circuits.
Nonlinear State Estimation and Control for Chaos Suppression in MEMS Resonator
Directory of Open Access Journals (Sweden)
Angelo Marcelo Tusset
2013-01-01
Full Text Available During the last decade the chaotic behavior in MEMS resonators have been reported in a number of works. Here, the chaotic behavior of a micro-mechanical resonator is suppressed. The aim is to control the system forcing it to an orbit of the analytical solution obtained by the multiple scales method. The State Dependent Riccati Equation (SDRE and the Optimal Linear Feedback Control (OLFC strategies are used for controlling the trajectory of the system. Additionally, the SDRE technique is used in the state estimator design. The state estimation and the control techniques proved to be effective in controlling the trajectory of the system. Additionally, the robustness of the control strategies are tested considering parametric errors and measurement noise in the control loop.
Scaccabarozzi, Luigi; Fejer, M M; Huo, Yijie; Fan, Shanhui; Yu, Xiaojun; Harris, James S
2006-11-15
We report the design, fabrication and characterization of novel dichroic mirrors embedded in a tightly confining AlGaAs/Al(x)O(y) waveguide. Reflection at the first-harmonic wavelength as high as 93% is achieved, while high transmission is maintained at the second-harmonic wavelength. The measured cavity spectrum is in excellent agreement with finite-difference time-domain simulations. Such a mirror is essential for achieving resonant enhancement of second-harmonic generation.
Wei, Liu; Yuanyuan, Han; Yanping, Cai; Jiaojiao, Jin; Guohua, Hui
2015-01-01
In this paper, Penaeus orientolis prawn freshness rapid determination method using electronic nose (e-nose) and non-linear data processing technique is studied. E-nose responses to prawns stored at 4 °C are measured. Meanwhile, physical/chemical indexes (firmness, pH, total volatile basic nitrogen (TVB-N), total viable count (TVC), and human sensory evaluation) are examined to provide freshness references for e-nose analysis. E-nose measurement data is analyzed by principal component analysis (PCA), stochastic resonance (SR), and double-layered cascaded serial stochastic resonance (DCSSR). PCA partially discriminates prawns under different storage time. SR and DCSSR signal-to-noise ratio (SNR) spectrum eigen values discriminate prawns successfully. Multi-variables regressions (MVR) are conducted between physical/chemical indexes and SR/DCSSR output SNR minimal (SNR-Min) values. Results indicate that SNR-Min values present more significant linearity relation with physical/chemical indexes. Prawn freshness forecasting model is developed via Harris fitting regression on DCSSR SNR-Min values. Validating experiments demonstrate that forecasting accuracy of this model is 94.29%.
Filamentation instability of large-amplitude Alfven waves
International Nuclear Information System (INIS)
Kuo, S.P.; Whang, M.H.; Lee, M.C.
1988-01-01
An instability that leads to the filamentation of large-amplitude Alfven waves and gives rise to purely growing density and magnetic field fluctuations is studied. The dispersion relation of the instability is derived, from which the threshold conditions and the growth rates of the instability are analyzed quantitatively for applications to the solar wind plasma. We have examined their dependence on the filamentation spectrum, the plasma β, and the pump frequency and intensity for both right-hand and left-hand circularly polarized Alfven waves. The excitation of filamentation instability for certain cases of interest is discussed and compared with that of the parametric decay and modulation instability. The relevance of the proposed instability with some observations is discussed. copyright American Geophysical Union 1988
Kinetic global analysis of Alfven eigenmodes in toroidal plasmas
International Nuclear Information System (INIS)
Fukuyama, A.
2002-01-01
Systematic study on low to medium n (toroidal mode number) Alfven eigenmodes (AE) in tokamaks and helical systems is presented. Linear stability of AE in the presence of energetic ions was studied using the kinetic full-wave code TASK/WM.We have reproduced the destabilizing effect of toroidal co-rotation on TAE for JT-60U parameters. We have found the existence of reversed-shear-induced Alfven eigenmode (RSAE) which localizes near the q minimum in a reversed magnetic shear configuration. Two kinds of mode structures are identified for energetic particle mode (EPM) below the TAE frequency gap. The coupling to lower-frequency modes such as drift waves and MHD modes as well as the effect of trapped particles are also taken into account. For a helical plasma, the existence of GAE in the central region and TAE in the off-axis region was confirmed. (author)
Alfven frequency modes at the edge of TFTR plasmas
Energy Technology Data Exchange (ETDEWEB)
Chang, Z.; Fredrickson, E.D.; Zweben, S.J. [and others
1995-07-01
An Alfven frequency mode (AFM) is very often seen in TFTR neutral beam heated plasmas as well as ohmic plasmas. This quasi-coherent mode is so far only seen on the magnetic fluctuation diagnostics (Mirnov coils). A close correlation between the plasma edge density and the mode activity (frequency and amplitude) has been observed, which indicates that the AFM is an edge localized mode with r/a > 0.85. No direct impact of this mode on the plasma global performance or fast ion loss (e.g., the {alpha}-particles in DT experiments) has been observed. This mode is apparently not the conventional TAE (toroidicity-induced Alfven eigenmodes). The present TAE theory cannot explain the observation. Other possible explanations are discussed.
Nonlinear magnetohydrodynamics of footpoint-driven coronal loops
Poedts, S.; Boynton, G. C.
1996-01-01
Results are presented from magnetohydrodynamic (MHD) simulations of the phase-mixing and resonant absorption of standing torsional Alfven waves generated by motion at the footpoint of a line-tied coronal loop with axial symmetry. The high wave amplitudes that develop in the resonant layer cause
Detection of Parametric Roll Resonance on Ships from Indication of Nonlinear Energy Flow
DEFF Research Database (Denmark)
Galeazzi, Roberto; Blanke, Mogens; Poulsen, Niels Kjølstad
2009-01-01
The detection of the onset of parametric roll resonance on ships is of a central importance in order to activate specific control strategies able to counteract the large roll motion. One of the main priorities is to have detectors with a small detection time, such that warnings can be issued when...... the roll oscillations are about 5◦. This paper proposes two different detection approaches: the first one based on sinusoidal detection in white gaussian noise; the second one utilizes an energy flow indicator in order to catch the onset of parametric roll based upon the transfer of energy from heave...... and pitch to roll. Both detectors have been validated against experimental data of a scale model of a container vessel excited with both regular and irregular waves. The detector based on the energy flow indicator proved to be very robust to different scenarios (regular/irregular waves) since it does...
Energy Technology Data Exchange (ETDEWEB)
Nishimura, Seiya, E-mail: n-seiya@kobe-kosen.ac.jp [Kobe City College of Technology, Kobe, Hyogo 651-2194 (Japan)
2014-12-15
Resonant magnetic perturbations (RMPs) produce magnetic islands in toroidal plasmas. Self-healing (annihilation) of RMP-induced magnetic islands has been observed in helical systems, where a possible mechanism of the self-healing is shielding of RMP penetration by plasma flows, which is well known in tokamaks. Thus, fundamental physics of RMP shielding is commonly investigated in both tokamaks and helical systems. In order to check this mechanism, detailed informations of magnetic island phases are necessary. In experiments, measurement of radial magnetic responses is relatively easy. In this study, based on a theoretical model of rotating magnetic islands, behavior of radial magnetic fields during the self-healing is investigated. It is confirmed that flips of radial magnetic fields are typically observed during the self-healing. Such behavior of radial magnetic responses is also observed in LHD experiments.
Simulation of the interaction between Alfven waves and fast particles
Energy Technology Data Exchange (ETDEWEB)
Feher, Tamas Bela
2014-02-18
There is a wide variety of Alfven waves in tokamak and stellarator plasmas. While most of them are damped, some of the global eigenmodes can be driven unstable when they interact with energetic particles. By coupling the MHD code CKA with the gyrokinetic code EUTERPE, a hybrid kinetic-MHD model is created to describe this wave-particle interaction in stellarator geometry. In this thesis, the CKA-EUTERPE code package is presented. This numerical tool can be used for linear perturbative stability analysis of Alfven waves in the presence of energetic particles. The equations for the hybrid model are based on the gyrokinetic equations. The fast particles are described with linearized gyrokinetic equations. The reduced MHD equations are derived by taking velocity moments of the gyrokinetic equations. An equation for describing the Alfven waves is derived by combining the reduced MHD equations. The Alfven wave equation can retain kinetic corrections. Considering the energy transfer between the particles and the waves, the stability of the waves can be calculated. Numerically, the Alfven waves are calculated using the CKA code. The equations are solved as an eigenvalue problem to determine the frequency spectrum and the mode structure of the waves. The results of the MHD model are in good agreement with other sophisticated MHD codes. CKA results are shown for a JET and a W7-AS example. The linear version of the EUTERPE code is used to study the motion of energetic particles in the wavefield with fixed spatial structure, and harmonic oscillations in time. In EUTERPE, the gyrokinetic equations are discretized with a PIC scheme using the delta-f method, and both full orbit width and finite Larmor radius effects are included. The code is modified to be able to use the wavefield calculated externally by CKA. Different slowing-down distribution functions are also implemented. The work done by the electric field on the particles is measured to calculate the energy transfer
Liu, Xiaole; Liu, Houguang; Yang, Jianhua; Litak, Grzegorz; Cheng, Gang; Han, Shuai
2017-11-01
It is a challenging task to detect the weak character signal in the noisy background. The stochastic resonance (SR) method has been wildly adopted recently because it can not only reduce the noise, but also enhance the weak feature information simultaneously. However, the traditional bistable model for SR is not perfect. So, this paper presents a new model with periodic potential to induce the adaptive SR. In the new model, based on the adaptive SR theory, the system parameters are simultaneously optimized by the improved artificial fish swarm algorithm. Meanwhile, the improved signal-to-noise ratio (ISNR) is set as the evaluation index. When the ISNR reaches a maximum, the output is optimal. In order to eliminate interference to obtain more useful information, the signals are preprocessed by Hilbert transform and High-pass filter before being input to the adaptive SR system. To verify the effectiveness of the proposed method, both numerical simulation and the vibration signal of the rolling element bearing from the lab experimental are adopted. Both of the results indicate that the adaptive SR model proposed shows better performance in weak character signals detection than the traditional adaptive SR in the bistable model. Meanwhile, the experimental signals with different working conditions are also processed by the new method. The results show that the method proposed could be more widely applied.
Nonlinear Microwave Optomechanics
Shevchuk, O.
2017-01-01
The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure
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.
DEFF Research Database (Denmark)
Petersen, Nils Holger
2014-01-01
A chapter in a book about terminology within the field of medievalism: the chapter discusses the resonance of medieval music and ritual in modern (classical) music culture and liturgical practice.......A chapter in a book about terminology within the field of medievalism: the chapter discusses the resonance of medieval music and ritual in modern (classical) music culture and liturgical practice....
Peculiarities of destabilization of Alfven modes by energetic ions in stellarators
International Nuclear Information System (INIS)
Lutsenko, V.V.; Kolesnichenko, Ya.I.; Yakovenko, Yu.V.; Fesenyuk, O.P.; Weller, A.; Werner, A.; Wobig, H.
2003-01-01
Alfven Eigenmodes (AE) associated with the breaking of the axial symmetry in stellarators are considered. Specific calculations are carried out for the Helias reactor HSR4/18. An explanation of the temporal evolution of Alfvenic activity observed in experiments on W7-AS is suggested. (author)
Non-axial-symmetric Alfven waves in cylindrical, radial inhomogeneous plasmas
International Nuclear Information System (INIS)
Raeuchle, E.
1978-08-01
The propagation of nonaxialsymmetric Alfven waves is investigated theoretically. Eigenfunctions and dispersion relations are calculated numerically for radial inhomogeneous cylindrical plasmas. In the MHD treatment resistivity, neutral particle loading and ion cyclotron effects are included. The investigations are of importance for plasma heating by Alfven waves. (orig.) [de
Destabilization of Alfven eigenmodes by fast particles in W7-AS
Energy Technology Data Exchange (ETDEWEB)
Zegenhagen, S.
2006-02-15
In the present thesis, a systematic study of beam driven Alfven eigenmodes in high-density and low-temperature plasmas of the W7-AS stellarator is performed. The goal of this thesis is twofold: (I) identification and description of fast particle driven Alfven instabilities in W7-AS, and (II) study of energetic particle losses induced by Alfven instabilities. A total of 133 different Alfven eigenmodes is studied in discharges from different experimental campaigns. The discharges are characterized by high density, n{sub e}=5 x 1019 m{sup -3} to 2.5 x 1020 m{sup -3} at relatively low temperatures of T{sub e}=T{sub i}=150..600 eV. Additional 13 events are found to have frequencies inside the EAE gap and could possibly be EAEs. Evidence for high-frequency Alfven eigenmodes (mirror- and helicity-induced Alfven eigenmodes) is seen, but can not be proven rigorously due to uncertain mode numbers and the complexity of the Alfven continuum. The remaining 41 Alfven eigenmodes can not be classified to be one of the above cases. (orig.)
Dvoretskiy, Dmitriy A.; Sazonkin, Stanislav G.; Kudelin, Igor S.; Orekhov, Ilya O.; Pnev, Alexey B.; Karasik, Valeriy E.; Denisov, Lev K.
2017-12-01
Today ultrashort pulse (USP) fiber lasers are in great demand in a frequency metrology field, THz pulse spectroscopy, optical communication, quantum optics application, etc. Therefore mode-locked (ML) fiber lasers have been extensively investigated over the last decade due the number of scientific, medical and industrial applications. It should be noted, that USP fiber lasers can be treated as an ideal platform to expand future applications due to the complex ML nonlinear dynamics in a laser resonator. Up to now a series of novel ML regimes have been investigated e.g. self-similar pulses, noise-like pulses, multi-bound solitons and soliton rain generation. Recently, we have used a highly nonlinear germanosilicate fiber (with germanium oxides concentration in the core 50 mol. %) inside the resonator for more reliable and robust launching of passive mode-locking based on the nonlinear polarization evolution effect in fibers. In this work we have measured promising and stable ML regimes such as stretched pulses, soliton rain and multi-bound solitons formed in a highly-nonlinear ring laser and obtained by intracavity group velocity dispersion (GVD) variation in slightly negative region. As a result, we have obtained the low noise ultrashort pulse generation with duration 59 dB) and relative intensity noise <-101 dBc / Hz.
On the stability of shear-Alfven vortices
International Nuclear Information System (INIS)
Jovanovic, D.; Horton, W.
1993-08-01
Linear stability of shear-Alfven vortices is studied analytically using the Lyapunov method. Instability is demonstrated for vortices belonging to the drift mode, which is a generalization of the standard Hasegawa-Mima vortex to the case of large parallel phase velocities. In the case of the convective-cell mode, short perpendicular-wavelength perturbations are stable for a broad class of vortices. Eventually, instability of convective-cell vortices may occur on the perpendicular scale comparable with the vortex size, but it is followed by a simultaneous excitation of coherent structures with better localization than the original vortex
DEFF Research Database (Denmark)
an impetus or drive to that account: change, innovation, rupture, or discontinuity. Resonances: Historical Essays on Continuity and Change explores the historiographical question of the modes of interrelation between these motifs in historical narratives. The essays in the collection attempt to realize...... theoretical consciousness through historical narrative ‘in practice’, by discussing selected historical topics from Western cultural history, within the disciplines of history, literature, visual arts, musicology, archaeology, philosophy, and theology. The title Resonances indicates the overall perspective...... of the book: how connotations of past meanings may resonate through time, in new contexts, assuming new meanings without surrendering the old....
The Interaction of Coronal Mass Ejections with Alfvenic Turbulence
Manchester, W.; van der Holst, B.
2017-12-01
We provide a first attempt to understand the interaction between Alfven wave turbulence, kinetic instabilities and temperature anisotropies in the environment of a fast coronal mass ejection (CME). The impact of a fast CME on the solar corona causes turbulent energy, thermal energy and dissipative heating to increase by orders of magnitude, and produces conditions suitable for a host of kinetic instabilities. We study these CME-induced effects with the recently developed Alfven Wave Solar Model, with which we are able to self-consistently simulate the turbulent energy transport and dissipation as well as isotropic electron heating and anisotropic proton heating. Furthermore, the model also offers the capability to address the effects of firehose, mirror mode, and cyclotron kinetic instabilities on proton energy partitioning, all in a global-scale numerical simulation. We find turbulent energy greatly enhanced in the CME sheath, strong wave reflection at the shock, which leads to wave dissipation rates increasing by more than a factor of 100. In contrast, wave energy is greatly diminished by adiabatic expansion in the flux rope. Finally, we find proton temperature anisotropies are limited by kinetic instabilities to a level consistent with solar wind observations.
Coronal heating by Alfven waves dissipation in compressible nonuniform media
International Nuclear Information System (INIS)
Malara, Francesco; Primavera, Leonardo; Veltri, Pierluigi
1996-01-01
The possibility to produce small scales and then to efficiently dissipate energy has been studied by Malara et al. [1992b] in the case of MHD disturbances propagating in an weakly dissipative incompressible and inhomogeneous medium, for a strictly 2D geometry. We extend this work to include both compressibility and the third component for vector quantities. Numerical simulations show that, when an Alfven wave propagates in a compressible nonuniform medium, the two dynamical effects responsible for the small scales formation in the incompressible case are still at work: energy pinching and phase-mixing. These effects give rise to the formation of compressible perturbations (fast and slow waves or a static entropy wave). Some of these compressive fluctuations are subject to the steepening of the wave front and become shock waves, which are extremely efficient in dissipating their energy, their dissipation being independent of the Reynolds number. Rough estimates of the typical times the various dynamical processes take to produce small scales show that these times are consistent with those required to dissipate inside the solar corona the energy of Alfven waves of photospheric origin
Crossing a Nonlinear Resonance
Indian Academy of Sciences (India)
IAS Admin
quadratic function of q and kinetic energy is a quadratic function of dq/dt. Both q2 and (dq/dt). 2 are squares of sinusoidal functions, respectively square of cosine and sine according to the above solution. The integrals of both, kinetic and potential energies, over a single period of a harmonic oscillator are equal, and they ...
Crossing a Nonlinear Resonance
Indian Academy of Sciences (India)
IAS Admin
transformation two independent variables must go over to two other independent variables. Calling θ as the angle vaiable, and J as action, we have a new set of variables. We see that the transformed Hamiltonian, H is independent of the angle variable. With this Hamil- tonian as a function of θ, J, the equations of motion are.
Indian Academy of Sciences (India)
maceutical, paper, food, dyes, petrochemi- cals, pigments, etc., to identify molecules, to monitor reaction products and so on. One of the most spectacular contributions of NMR has been in the development of magnetic resonance imaging (MRI), a method that has today revolutionized diagnosis and treatment of diseases in ...
Alfven Waves Underlying Ionospheric Destabilization: Ground-Based Observations
Hirsch, Michael
During geomagnetic storms, terawatts of power in the million mile-per-hour solar wind pierce the Earth's magnetosphere. Geomagnetic storms and substorms create transverse magnetic waves known as Alfven waves. In the auroral acceleration region, Alfven waves accelerate electrons up to one-tenth the speed of light via wave-particle interactions. These inertial Alfven wave (IAW) accelerated electrons are imbued with sub-100 meter structure perpendicular to geomagnetic field B. The IAW electric field parallel to B accelerates electrons up to about 10 keV along B. The IAW dispersion relation quantifies the precipitating electron striation observed with high-speed cameras as spatiotemporally dynamic fine structured aurora. A network of tightly synchronized tomographic auroral observatories using model based iterative reconstruction (MBIR) techniques were developed in this dissertation. The TRANSCAR electron penetration model creates a basis set of monoenergetic electron beam eigenprofiles of auroral volume emission rate for the given location and ionospheric conditions. Each eigenprofile consists of nearly 200 broadband line spectra modulated by atmospheric attenuation, bandstop filter and imager quantum efficiency. The L-BFGS-B minimization routine combined with sub-pixel registered electron multiplying CCD video stream at order 10 ms cadence yields estimates of electron differential number flux at the top of the ionosphere. Our automatic data curation algorithm reduces one terabyte/camera/day into accurate MBIR-processed estimates of IAW-driven electron precipitation microstructure. This computer vision structured auroral discrimination algorithm was developed using a multiscale dual-camera system observing a 175 km and 14 km swath of sky simultaneously. This collective behavior algorithm exploits the "swarm" behavior of aurora, detectable even as video SNR approaches zero. A modified version of the algorithm is applied to topside ionospheric radar at Mars and
Tiwari, Pallavi; Rosen, Mark; Madabhushi, Anant
2009-01-01
Magnetic resonance spectroscopy (MRS) has been shown to have great clinical potential as a supplement to magnetic resonance imaging in the detection of prostate cancer (CaP). MRS provides functional information in the form of changes in the relative concentration of specific metabolites including choline, creatine, and citrate which can be used to identify potential areas of CaP. With a view to assisting radiologists in interpretation and analysis of MRS data, some researchers have begun to develop computer-aided detection (CAD) schemes for CaP identification from spectroscopy. Most of these schemes have been centered on identifying and integrating the area under metabolite peaks which is then used to compute relative metabolite ratios. However, manual identification of metabolite peaks on the MR spectra, and especially via CAD, is a challenging problem due to low signal-to-noise ratio, baseline irregularity, peak overlap, and peak distortion. In this article the authors present a novel CAD scheme that integrates nonlinear dimensionality reduction (NLDR) with an unsupervised hierarchical clustering algorithm to automatically identify suspicious regions on the prostate using MRS and hence avoids the need to explicitly identify metabolite peaks. The methodology comprises two stages. In stage 1, a hierarchical spectral clustering algorithm is used to distinguish between extracapsular and prostatic spectra in order to localize the region of interest (ROI) corresponding to the prostate. Once the prostate ROI is localized, in stage 2, a NLDR scheme, in conjunction with a replicated clustering algorithm, is used to automatically discriminate between three classes of spectra (normal appearing, suspicious appearing, and indeterminate). The methodology was quantitatively and qualitatively evaluated on a total of 18 1.5 T in vivo prostate T2-weighted (w) and MRS studies obtained from the multisite, multi-institutional American College of Radiology (ACRIN) trial. In the
Tiwari, Pallavi; Rosen, Mark; Madabhushi, Anant
2009-09-01
Magnetic resonance spectroscopy (MRS) has been shown to have great clinical potential as a supplement to magnetic resonance imaging in the detection of prostate cancer (CaP). MRS provides functional information in the form of changes in the relative concentration of specific metabolites including choline, creatine, and citrate which can be used to identify potential areas of CaP. With a view to assisting radiologists in interpretation and analysis of MRS data, some researchers have begun to develop computer-aided detection (CAD) schemes for CaP identification from spectroscopy. Most of these schemes have been centered on identifying and integrating the area under metabolite peaks which is then used to compute relative metabolite ratios. However, manual identification of metabolite peaks on the MR spectra, and especially via CAD, is a challenging problem due to low signal-to-noise ratio, baseline irregularity, peak overlap, and peak distortion. In this article the authors present a novel CAD scheme that integrates nonlinear dimensionality reduction (NLDR) with an unsupervised hierarchical clustering algorithm to automatically identify suspicious regions on the prostate using MRS and hence avoids the need to explicitly identify metabolite peaks. The methodology comprises two stages. In stage 1, a hierarchical spectral clustering algorithm is used to distinguish between extracapsular and prostatic spectra in order to localize the region of interest (ROI) corresponding to the prostate. Once the prostate ROI is localized, in stage 2, a NLDR scheme, in conjunction with a replicated clustering algorithm, is used to automatically discriminate between three classes of spectra (normal appearing, suspicious appearing, and indeterminate). The methodology was quantitatively and qualitatively evaluated on a total of 18 1.5 T in vivo prostate T2-weighted (w) and MRS studies obtained from the multisite, multi-institutional American College of Radiology (ACRIN) trial. In the
Fokker-Planck simulation study of Alfven eigenmode burst
International Nuclear Information System (INIS)
Todo, Y.; Watanabe, T.; Park, Hyoung-Bin; Sato, T.
2001-01-01
Recurrent bursts of toroidicity-induced Alfven eigenmodes (TAEs) are reproduced with a Fokker-Planck-magnetohydrodynamic simulation where a fast-ion source and slowing down are incorporated self-consistently. The bursts take place at regular time intervals and the behaviors of all the TAEs are synchronized. The fast-ion transport due to TAE activity spatially broadens the classical fast-ion distribution and significantly reduces its peak value. Only a small change of the distribution takes place with each burst, leading to loss of a small fraction of the fast ions. The system stays close to the marginal stability state established through the interplay of the fast-ion source, slowing down, and TAE activity. (author)
High-n helicity-induced shear Alfven eigenmodes
International Nuclear Information System (INIS)
Nakajima, N.; Cheng, C.Z.; Okamoto, M.
1992-05-01
The high-n Helicity-induced shear Alfven Eigenmodes (HAE) are considered both analytically and numerically for the straight helical magnetic system, where n is the toroidal mode number. The eigenmode equation for the high-n HAE modes is derived along the field line and with the aid of the averaging method is shown to reduce to the Mathieu equation asymptotically. The discrete HAE modes are shown to exist inside the continuum spectrum gaps. The continuous spectrum gaps appear around ω 2 = ω A 2 [N(lι-m)/2] 2 for N = 1,2,.., where ω A is the toroidal Alfven transit frequency, and l, m, and ι are the polarity of helical coils, the toroidal pitch number of helical coils, and the rotational transform, respectively. For the same ω A and ι, the frequency of the helical continuum gap is larger than that of the continuum gap in tokamak plasmas by |l-ι -1 m|. The polarity of helical coils l plays a crucial role in determining the spectrum gaps and the properties of the high-n HAE modes. The spectrum gaps near the magnetic axis are created by the helical ripple with circular flux surfaces for l = 1, and ≥ 3 helicals. For l = 2 helical systems, the spectrum gaps are created by the ellipticity of the flux surfaces. These analytical results for the continuum gaps and the existence of the high-n HAE modes in the continuum gaps are confirmed numerically for the l = 2 case, and we find that the HAE modes exist for mode structures with the even and the odd parities. (author)
Alfven wave stability in D-III-D
International Nuclear Information System (INIS)
Campbell, R.B.; Samec, T.K.
1989-09-01
Within the framework of the global Alfven eigenmode theory in a cylindrical background plasma, I examine the excitation of global Alfven eigenmodes by intense neutral beam injection in the D III-D tokamak operating at General Atomics. I have considered two separate sets of experimental conditions, a ''low power'' set of cases using 10MW of hydrogen beams, and a ''high power'' shot of 20MW of deuterium beams. My results are particularly sensitive to the background density profile. For parabolic background density profiles, n 0 x (1 - (r/a) 2 ), I have determined that the plasma is stable to all toroidal and poloidal mode numbers for both high and low power cases. For density profiles which are of the form n 0 x (1 - (r/a) 2 ) 1/2 , for the same n 0 , my calculation indicates that the m = -1, l = 0 mode is unstable in each case. The high power case has a considerably higher growth rate at the baseline conditions, which motivated me to study this case more extensively. The results are also sensitive to the beam source radial scalelength, L s , and the electron temperature T e . By narrowing the source from the baseline 36 cm to 20 cm, the growth rate of the (0,-1) actually decreases, but the (0,-2) mode appears with a substantial growth rate. If the source could be made even narrower, L s ∼ 10 cm, the (1,-1) mode would appear, also with a large growth rate. 12 refs., 16 figs., 6 tabs
Anisotropic Alfven-ballooning modes in the Earth's magnetosphere
International Nuclear Information System (INIS)
Chan, A.A.; Xia, Mengfen; Chen, Liu
1993-05-01
We have carried out a theoretical analysis of the stability and parallel structure of coupled shear-Alfven and slow-magnetosonic waves in the Earth's inner magnetosphere including effects of finite anisotropic plasma pressure. Multiscale perturbation analysis of the anisotropic Grad-Shafranov equation yields an approximate self-consistent magnetohydrodynamic (MHD) equilibrium. This MHD equilibrium is used in the numerical solution of a set of eigenmode equations which describe the field line eigenfrequency, linear stability, and parallel eigenmode structure. We call these modes anisotropic Alfven-ballooning modes. The main results are: The field line eigenfrequency can be significantly lowered by finite pressure effects. The parallel mode structure of the transverse wave components is fairly insensitive to changes in the plasma pressure but the compressional magnetic component can become highly peaked near the magnetic equator due to increased pressure, especially when P perpendicular > P parallel. For the isotropic case ballooning instability can occur when the ratio of the plasma pressure to the magnetic pressure, exceeds a critical value β o B ∼ 3.5 at the equator. Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field-line-bending stabilization when P parallel > P perpendicular, or due to increased ballooning-mirror destabilization when P perpendicular > P parallel. We use a ''β-6 stability diagram'' to display the regions of instability with respect to the equatorial values of the parameters bar β and δ, where bar β = (1/3)(β parallel + 2 β perpendicular) is an average beta value and δ = 1 - P parallel/P perpendicular is a measure of the plasma anisotropy
Ion and relativistic electron acceleration by Alfven and whistler turbulence in solar flares
Miller, James A.; Ramaty, Reuven
1987-01-01
A model is proposed in which turbulent Alfven and whistler waves simultaneously produce the proton and electron spectra implied by the gamma-ray observations noted during the impulsive phase of the June 3, 1982 flare. The results demonstrate that protons can be accelerated to several GeV in less than about 10 sec by Alfven turbulence whose energy density is greater than a few erg/cu cm. It is also found that electrons may be accelerated to tens of MeV on similar time scales by whistler and Alfven turbulence. A lower limit on the energy density of the Alfven turbulence is obtained which is small compared to the total magnetic energy density.
Alfven. Symphony No 5 in A minor, Op. 54 / Robert Layton
Layton, Robert
1994-01-01
Uuest heliplaadist "Alfven. Symphony No 5 in A minor, Op. 54. The Mountain King - Suite, Gustav II Adolf, Op. 49 - Elegy. Royal Stockholm Philarmonic Orchestra / Neeme Järvi. BIS CD 585 (68 minutes) Recorded in association with Trygg Hansa"
Convective cell excitation by inertial Alfven waves in a low density plasma
International Nuclear Information System (INIS)
Pokhotelov, O.A.; Onishchenko, O.G.; Sagdeev, R.Z.; Srenflo, L.; Balikhin, M.A.
2005-01-01
The parametric interaction of inertial Alfven waves with large-scale convective cells in a low-density plasma is investigated. It is shown that, in plasmas where the Alfven velocity is comparable to or exceeds the speed of light, the parametric interaction is substantially suppressed. A compact expression for the optimal scale and instability growth rate of the fastest growing mode is obtained [ru
Alfven wave trapping, network microflaring, and heating in solar coronal holes
Moore, R. L.; Suess, S. T.; Musielak, Z. E.; An, C.-H.
1991-01-01
Fresh evidence that much of the heating in coronal holes is provided by Alfven waves is presented. This evidence comes from examining the reflection of Alfven waves in an isothermal hydrostatic model coronal hole with an open magnetic field. Reflection occurs if the wavelength is as long as the order of the scale height of the Alfven velocity. For Alfven waves with periods of about 5 min, and for realistic density, magnetic field strength, and magnetic field spreading in the model, the waves are reflected back down within the model hole if the coronal temperature is only slightly less than 1.0 x 10 to the 6th K, but are not reflected and escape out the top of the model if the coronal temperature is only slightly greater than 1.0 x 10 to the 6th K. Because the spectrum of Alfven waves in real coronal holes is expected to peak around 5 min and the temperature is observed to be close to 1.0 x 10 to the 6th K, the sensitive temperature dependence of the trapping suggests that the temperature in coronal holes is regulated by heating by the trapped Alfven waves.
DEFF Research Database (Denmark)
Liu, Chuan; Berg, Rolf W.
2013-01-01
The relation between Raman scattering, resonance Raman scattering and absorption is reviewed to see to what extent quantitative analysis can be applied in Resonance Raman spectroscopy. In addition to this it is demonstrated experimentally that normal Raman spectra can be dramatically inhibited...... of the compounds and deviate due to absorption resonance effects. An approximated mathematical model is developed to demonstrate that the intensities of the normal Raman scattering bands are suppressed. An inhibition coefficient Ki is introduced to describe the situation and determine the penetration depth. Most...
Ananthakrishnan, Palaniswamy
2012-11-01
The problem is of practical relevance in determining the motion response of multi-hull and air-cushion vehicles in high seas and in littoral waters. The linear inviscid problem without surface pressure has been well studied in the past. In the present work, the nonlinear wave-body interaction problem is solved using finite-difference methods based on boundary-fitted coordinates. The inviscid nonlinear problem is tackled using the mixed Eulerian-Lagrangian formulation and the solution of the incompressible Navier-Stokes equations governing the viscous problem using a fractional-step method. The pressure variation in the air cushion is modeled using the isentropic gas equation pVγ = Constant. Results show that viscosity and free-surface nonlinearity significantly affect the hydrodynamic force and the wave motion at the resonant Helmholtz frequency (at which the primary wave motion is the vertical oscillation of the mean surface in between the bodies). Air compressibility suppresses the Helmholtz oscillation and enhances the wave radiation. Work supported by the ONR under the grant N00014-98-1-0151.
International Nuclear Information System (INIS)
Ji, J.C.; Zhang, N.
2009-01-01
Non-resonant bifurcations of codimension two may appear in the controlled van der Pol-Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation.
Fahleson, Tobias; Norman, Patrick
2017-10-14
The second-order nonlinear (or cubic) response function is derived from the Ehrenfest theorem with inclusion made of the finite lifetimes of the excited states, representing the extension of the derivation of the quadratic response function in the same framework [P. Norman et al., J. Chem. Phys. 123, 194103 (2005)]. The resulting damped response functions are physically sound and converging also in near-resonance and resonance regions of the spectrum. Being an accurate approximation for small complex frequencies (defined as the sum of an optical frequency and an imaginary damping parameter), the polynomial expansion of the complex cubic response function in terms of the said frequencies is presented and used to validate the program implementation. In terms of approximate state theory, the computationally tractable expressions of the damped cubic response function are derived and implemented at the levels of Hartree-Fock and Kohn-Sham density functional theory. Numerical examples are provided in terms of studies of the intensity-dependent refractive index of para-nitroaniline and the two-photon absorption cross section of neon. For the latter property, a numerical comparison is made against calculations of the square of two-photon matrix elements that are identified from a residue analysis of the resonance-divergent quadratic response function.
Particle energization by inertial Alfven wave in auroral ionosphere
Kumar, S.
2017-12-01
The role of inertial Alfven wave in auroral acceleration region and in the inertial regime to energize the plasma particles is an interesting field and widely discussed observationally as well as theoretically in recent years. In this work, we present the density perturbations by inertial Alfvén wave (AW) in the auroral ionosphere. We obtain dynamical equations for inertial AW and fast mode of AW using two-fluid model and then solve them numerically in order to analyze the localized structures and cavity formation. The ponderomotive force due to the high frequency inertial AW changes the background density and is believed to be responsible for the wave localization or for the formation of density cavities in auroral ionosphere. These density cavities are believed to be the sites for particle energization. This perturbed density channel grow with time until the modulation instability acquires steady state. We find that the density cavities are accompanied by the high amplitude magnetic fields. The amplitude of the strongest density cavity is estimated as ˜ 0.26n0 (n0 is unperturbed plasma number density). The results presented here are found consistent with the observational studies using FAST spacecraft.
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
-, - (2018), , , --- ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : nonlinear dynamics * generalized van der Pol system * quasiperiodic response * synchronization effects * stability of auto-oscillation Subject RIV: JM - Building Engineering OBOR OECD: Mechanical engineering Impact factor: 2.847, year: 2016 http://www. science direct.com/ science /article/pii/S004579491730278X
Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma
Vasquez, Bernard J.
1993-01-01
The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.
Directory of Open Access Journals (Sweden)
R. M. Arkhipov
2016-11-01
Full Text Available We study theoretically the possibility of few-cycle short bipolar optical pulse compression and their transformation to unipolar pulses due to coherent interaction with resonance absorbing medium. It is shown that single-cycle pulse compression occurs when each half-wave starts to behave as an independent unipolar soliton. These solitons are attracted to each other under certain conditions, that leads to the emergence of single-cycle pulse of shorter duration. Numerical simulations revealed 3-5 times reduction of the pulse duration. The substantial absence of light loss in this scheme gives the possibility to create a multistage passive system of three resonance absorbers and results in a 125-time reduction of the pulse duration. Generation of unipolar pulses occurs when two powerful extremely short bipolar pulses propagate and collide in a dense resonant medium. In this case, as shown by numerical calculations, the mutual influence of oncoming solitons leads to the fact that some part of them is destroyed and another part is not. A high power unipolar soliton and low intensity bipolar optical ringing are observed in the medium output.
Experiments and Observations on Intense Alfven Waves in the Laboratory and in Space
International Nuclear Information System (INIS)
Gekelman, W.; VanZeeland, M.; Vincena, S.; Pribyl, P.
2003-01-01
There are many situations, which occur in space (coronal mass ejections, supernovas), or are man-made (upper atmospheric detonations) in which a dense plasma expands into a background magnetized plasma that can support Alfven waves. The LArge Plasma Device (LAPD) is a machine, at UCLA, in which Alfven wave propagation in homogeneous and inhomogeneous plasmas has been studied. These will be briefly reviewed. A new class of experiments which involve the expansion of a dense (initially, δn/no>>1) laser-produced plasma into an ambient highly magnetized background plasma capable of supporting Alfven waves will be presented. Measurements are used to estimate the coupling efficiency of the laser energy and kinetic energy of the dense plasma into wave energy. The wave generation mechanism is due to field aligned return currents, coupled to the initial electron current, which replace fast electrons escaping the initial blast
Khoa, Doan Quoc; Phuong, Le Thi Thu; Hoi, Bui Dinh
2017-03-01
A quantum kinetic equation for electrons interacting with confined phonons is used to investigate the nonlinear absorption of an intense electromagnetic wave by electrons in cylindrical GaAs/AlAs quantum wires. The analytic expression for absorption coefficient is calculated for three models of confined optical phonons: the dielectric continuum (DC), hydrodynamic continuum (HC), and Huang-Zhu (HZ) models. The absorption coefficient depends on the square of the electromagnetic wave amplitude. The electrophonon resonance and optically detected electrophonon resonance (ODEPR) are observed through the absorption spectrum. The full width at half maximum (the line-width) of the ODEPR peaks is obtained by a computational method. The line-width is found to increase with increasing temperature and decrease with increasing the quantum wire radius. In particular, numerical results show that the DC and HZ models lead to a similar behaviour of electron - confined phonon interaction whereas the HC model results in a quite different one, especially at small quantum wire radius. For large quantum wire radii, above mentioned phonon models have equivalent contributions to the ODEPR line-width.
Alfven-wave particle interaction in finite-dimensional self-consistent field model
International Nuclear Information System (INIS)
Padhye, N.; Horton, W.
1998-01-01
A low-dimensional Hamiltonian model is derived for the acceleration of ions in finite amplitude Alfven waves in a finite pressure plasma sheet. The reduced low-dimensional wave-particle Hamiltonian is useful for describing the reaction of the accelerated ions on the wave amplitudes and phases through the self-consistent fields within the envelope approximation. As an example, the authors show for a single Alfven wave in the central plasma sheet of the Earth's geotail, modeled by the linear pinch geometry called the Harris sheet, the time variation of the wave amplitude during the acceleration of fast protons
Beta-Suppression of Alfven Cascade Modes in the National Spherical Torus Experiment
International Nuclear Information System (INIS)
Fredrickson, E.D.; N.A. Crocker; N.N. Gorelenkov; W.W. Heidbrink; S. Kubota; F.M. Levinton; H. Yuh; J.E. Menard; Bell, R.E.
2007-01-01
The coupling of Alfven Cascade (AC) modes or reversed-shear Alfven eigenmodes (rsAE) to Geodesic Acoustic Modes (GAM) implies that the range of the AC frequency sweep is reduced as the electron β is increased. This model provides an explanation for the otherwise surprising absence of AC modes in reverse shear NSTX plasmas, given the rich spectrum of beam-driven instabilities typically seen in NSTX. In experiments done at very low β to investigate this prediction, AC modes were seen, and as the β e was increased from shot to shot, the range of the AC frequency sweep was reduced, in agreement with this theoretical prediction.
Energy Technology Data Exchange (ETDEWEB)
Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)
2001-02-01
In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.
International Nuclear Information System (INIS)
Bruma, C; Cuperman, S; Komoshvili, K
2003-01-01
In an effort to optimize the internal transport barriers (ITBs) generated by externally launched mode-converted fast waves (FWs) in pre-heated spherical tokamaks (STs), we have carried out a systematic parametric investigation with respect to the rf waves and antenna characteristics; as a study case, a START-like device has been considered. Within the framework of a plasma model including both kinetic effects (collisionless Landau damping on passing electrons) and collisional damping on both trapped and passing electrons and ions, and starting with the solution of the full wave equation for a ST-plasma, we show that optimized ITBs, suitable for the stabilization of plasma turbulence (e.g. overpassing the maximum growth rate of the ITG-instability, γ ITG ) in STs can be generated by the aid of externally launched FW and mode-converted to kinetic Alfven waves. This result holds in spite of the limiting trapped-particles associated squeezing factor S present in the non-linear equation for E r (via the viscosity coefficient μ θi ∝|S| 3/2 , S = S(dE r /dr))
Alfven waves in the auroral ionosphere: A numerical model compared with measurements
International Nuclear Information System (INIS)
Knudsen, D.J.; Kelley, M.C.; Vickrey, J.F.
1992-01-01
The authors solve a linear numerical model of Alfven waves reflecting from the high-latitude ionosphere, both to better understanding the role of the ionosphere in the magnetosphere/ionosphere coupling process and to compare model results with in situ measurements. They use the model to compute the frequency-dependent amplitude and phase relations between the meridional electric and the zonal magnetic fields due to Alfven waves. These relations are compared with measurements taken by an auroral sounding rocket flow in the morningside oval and by the HILAT satellite traversing the oval at local noon. The sounding rocket's trajectory was mostly parallel to the auroral oval, and is measured enhanced fluctuating field energy in regions of electron precipitation. The rocket-measured phase data are in excellent agreement with the Alfven wave model, and the relation between the modeled and the measured by HILAT are related by the height-integrated Pedersen conductivity Σ p , indicating that the measured field fluctuations were due mainly to structured field-aligned current systems. A reason for the relative lack of Alfven wave energy in the HILAT measurements could be the fact that the satellite traveled mostly perpendicular to the oval and therefore quickly traversed narrow regions of electron precipitation and associated wave activity
Influence of the Alfven wave spectrum on the scrape-off layer of the TCA tokamak
International Nuclear Information System (INIS)
Martin, Y.; Hollenstein, Ch.
1988-01-01
The study of the Scrape-Off Layer (SOL) during Alfven wave heating may lead to a better understanding of the antenna-plasma interaction. The SOL of the TCA tokamak has been widely investigated by means of Langmuir probes. The aim of the present work is to present in detail the influence of the Alfven wave spectrum on the SOL. The experiments have shown that the plasma boundary layer is strongly affected by the RF, in particular the ion density, the electron temperature and the floating potential. In TCA, as the spectrum evolves due to a density rise, the passage of the Alfven continua and their associated eigenmodes (DAW) induces a strong depletion in the edge density of up to 70% during the continuum part and a density increase during the crossing of an eigenmode. The floating potential becomes negative during the continua and even more negative crossing the eigenmodes. This behaviour changes as a function of the power transmitted to the plasma through the antennae, especially we have found with MHD modes a change around 100 kW. The profiles of the basic parameters are modified, depending on the wave spectrum. MHD mode activity which can occur during the RF phase considerably alters the behaviour mentioned above. Finally, the modulation of the RF power allows us to characterize the difference in coupling, for the continua and the eigenmodes, between the Alfven wave field and the scrape-off layer. (author) 5 figs., 6 refs
Influence of the Alfven wave spectrum on the scrape-off layer of the TCA tokamak
International Nuclear Information System (INIS)
Martin, Y.; Hollenstein, C.
1989-01-01
The study of the scrape-off layer (SOL) during Alfven wave heating may lead to a better understanding of the antenna-plasma interaction. The scrape-off layer of the TCA tokamak has been widely investigated by means of Langmuir probes. The aim of this work is to present measurements on the influence of the Alfven wave spectrum on the scrape-off layer. These experiments have shown that the plasma boundary layer is strongly affected by the wave field, in particular the ion saturation current and the floating potential. In TCA, as the spectrum evolves due to a density rise, the passage of the Alfven continua and their associated eigenmodes, the Discrete Alfven Wave (DAW) induces a strong depletion in the edge density of up to 70% during the continuum part and a density increase during the crossing of an eigenmode. The floating potential becomes negative during the continua and even more negative crossing the eigenmodes. In case of MHD mode activity, this behaviour changes for power exceeding 100 kW. The profiles of basic parameters are modified, depending on the wave spectrum. MHD mode activity which can occur during the RF (radio frequency) phase considerably alters the behaviour mentioned above. Finally, the modulation of the RF power allows us to characterize the coupling between RF power and typical edge parameters. (orig.)
Energy balance in the TCA tokamak plasma with Alfven wave heating
International Nuclear Information System (INIS)
Ding Ning; Qu Wenxiao; Huang Li; Long Yongxing; Qiu Xiaoming
1993-01-01
The energy balance in TCA tokamak plasma with Alfven wave heating is studied, in which the equivalent electron thermal conductivity is determined by using the profile consistency principle. The results are in good agreement with experiments. It is shown that this method is applicable to various devices and other heating methods
Energy Technology Data Exchange (ETDEWEB)
Nishi-Kawa, K.I.
1978-12-01
Collisional drift eigenmode, coupled to shear Alfven mode, is studied numerically in a current-carrying slab with finite magnetic shear. It is shown that, due to finite-beta effects, in the presence of current, a drift mode becomes unstable.
The effect of toroidal plasma rotation on low-frequency reversed shear Alfven eigenmodes in tokamaks
Haverkort, J. W.
2012-01-01
The influence of toroidal plasma rotation on the existence of reversed shear Alfven eigenmodes (RSAEs) near their minimum frequency is investigated analytically. An existence condition is derived showing that a radially decreasing kinetic energy density is unfavourable for the existence of RSAEs.
Electromagnetic transport components and sheared flows in drift-Alfven turbulence
DEFF Research Database (Denmark)
Naulin, V.
2003-01-01
Results from three-dimensional numerical simulations of drift-Alfven turbulence in a toroidal geometry with sheared magnetic field are presented. The simulations show a relation between self-generated poloidal shear flows and magnetic field perturbations. For large values of the plasma beta we...
Heating and current-drive with high phase velocity compressional Alfven waves
International Nuclear Information System (INIS)
Li, Y.M.; Mahajan, S.M.; Ross, D.W.
1986-12-01
It is shown that high phase velocity compressional Alfven waves have the desirable features needed for efficient current drive in fusion-reactor-like conditions; the energy deposition is low on the α-particles, and high on the hot electrons in the plasma interior
Alfven, Hugo. Die drei Schwedischen Rhapsodien op. 19, 24 und 47 / Andreas Meyer
Meyer, Andreas
1995-01-01
Uuest heliplaadist "Alfven, Hugo. Die drei Schwedischen Rhapsodien op. 19, 24 und 47, En skärgardssägen op. 20, Suite aus Der Berkönig. Königliche Stockholmer Philharmoniker, Neeme Järvi". AD: 1987-1992. BIS?Disco-Center CD 725 (WD: 77'00")
Stability of Global Alfven Waves (Tae, Eae) in Jet Tritium Discharges
Kerner, W.; Borba, D.; Huysmans, G. T. A.; Porcelli, F.; Poedts, S.; Goedbloed, J. P.; Betti, R.
1994-01-01
The interaction of alpha-particles in JET tritium discharges with global Alfven waves via inverse Landau damping is analysed. It is found that alpha-particle driven eigenmodes were stable in the PTE1 and should also be stable in a future 50:50 deuterium-tritium mix discharge aiming at Q(DT) = 1,
International Nuclear Information System (INIS)
Prokopov, P A; Zakharov, Yu P; Tishchenko, V N; Shaikhislamov, I F; Boyarintsev, E L; Melekhov, A V; Ponomarenko, A G; Posukh, V G; Terekhin, V A
2016-01-01
Generation of Alfven waves propagating along external magnetic field B 0 and Collisionless Shock Waves propagating across B 0 are studied in experiments with laser- produced plasma and magnetized background plasma. The collisionless interaction of interpenetrating plasma flows takes place through a so-called Magnetic Laminar Mechanism (MLM) or Larmor Coupling. At the edge of diamagnetic cavity LP-ions produce induction electric field E φ which accelerates BP-ions while LP-ions rotate in opposite direction. The ions movement generates sheared azimuthal magnetic field B φ which could launches torsional Alfven wave. In previous experiments at KI-1 large scale facility a generation of strong perturbations propagating across B 0 with magnetosonic speed has been studied at a moderate value of interaction parameter δ∼0.3. In the present work we report on experiments at conditions of 5∼R2 and large Alfven-Mach number M A ∼10 in which strong transverse perturbations traveling at a scale of ∼1 m in background plasma at a density of ∼3*10 13 cm -3 is observed. At the same conditions but smaller M A ∼ 2 a generation, the structure and dynamic of Alfven wave with wavelength ∼0.5 m propagating along fields B 0 ∼100÷500 G for a distance of ∼2.5 m is studied. (paper)
A 'rational' explanation of resonant surfaces in toroidal plasmas
International Nuclear Information System (INIS)
Cross, R.C.
1983-05-01
Resonant surfaces are of fundamental importance in toroidal plasmas, particularly in relation to stability theory. A simple explanation as to why these surfaces are 'resonant' is given in terms of the propagation of localized torsional Alfven and ion acoustic wave packets. These packets are guided along helical field lines in toroidal plasmas, leading to the formation of unstable standing waves on those field lines which close on themselves after one or more toroidal revolutions
Tsuboi, Kazuma; Seki, Kazuhiko; Ouchi, Yukio; Fujita, Katsuhiko; Kajikawa, Kotaro
2003-02-01
Nonlinear optical responses of a self-assembled monolayer (SAM) containing merocyanine chromophore, 1-alkyl-4-(4-hydroxystyryl) pyridinium bromide (HSP), on gold in water and in ethanol were studied by second-harmonic generation (SHG). The pH dependence of the SHG response clearly showed a solvatochromic characteristic of the merocyanine from a protonated form to a zwitterionic form. A large second-order susceptibility χzzz=5.0× 10-7 esu (2.1× 102 pm/V) was found in a basic solution of ethanol where the merocyanine is in the zwitterionic form. Combination of the SHG and surface plasmon resonance (SPR) spectroscopy measurements also provides us with details of the formation process of the merocyanine SAMs in the ethanol solution of the HSP-terminated-alkyldisulfide, ω,ω\\prime-dithiodi[1-undecyl-4-(4-hydroxystyryl)pyridinium bromide](HSPC11SS). A considerable difference was found in the kinetics between SPR and SHG, because SHG probes the molecules in a noncentrosymmetric fashion on the gold surface while SPR probes the optical thickness of the film. The difference enabled us to separate the chemisorption from the physisorption in the adsorption process. Interestingly, both probes showed slower kinetics in the solution of higher concentration, suggesting association of the disulfide molecules in the solution of high concentration.
Liu, Yang; Hsu, Yung; Chow, Chi-Wai; Yang, Ling-Gang; Yeh, Chien-Hung; Lai, Yin-Chieh; Tsang, Hon-Ki
2016-03-01
We propose and experimentally demonstrate a new 110 GHz high-repetition-rate hybrid mode-locked fiber laser using a silicon-on-insulator microring-resonator (SOI MRR) acting as the optical nonlinear element and optical comb filter simultaneously. By incorporating a phase modulator (PM) that is electrically driven at a fraction of the harmonic frequency, an enhanced extinction ratio (ER) of the optical pulses can be produced. The ER of the optical pulse train increases from 3 dB to 10 dB. As the PM is only electrically driven by the signal at a fraction of the harmonic frequency, in this case 22 GHz (110 GHz/5 GHz), a low bandwidth PM and driving circuit can be used. The mode-locked pulse width and the 3 dB spectral bandwidth of the proposed mode-locked fiber laser are measured, showing that the optical pulses are nearly transform limited. Moreover, stability evaluation for an hour is performed, showing that the proposed laser can achieve stable mode-locking without the need for optical feedback or any other stabilization mechanism.
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2014-01-01
The authors perform an original research on the fundamentals of winning virtuous strategies creation toward the leveraged buyout transactions implementation during the private equity investment in the conditions of the resonant absorption of discrete information in the diffusion - type financial system with the induced nonlinearities at the influences by the Schumpeterian creative disruption processes in the free market economy. We propose that the money is a financial computing process, whic...
Kinetic Alfven Waves at the Magnetopause-Mode Conversion, Transport and Formation of LLBL; TOPICAL
International Nuclear Information System (INIS)
Jay R. Johnson; C.Z. Cheng
2002-01-01
At the magnetopause, large amplitude, low-frequency (ULF), transverse MHD waves are nearly always observed. These waves likely result from mode conversion of compressional MHD waves observed in the magnetosheath to kinetic Alfven waves at the magnetopause where there is a steep gradient in the Alfven velocity[Johnson and Cheng, Geophys. Res. Lett. 24 (1997) 1423]. The mode-conversion process can explain the following wave observations typically found during satellite crossings of the magnetopause: (1) a dramatic change in wave polarization from compressional in the magnetosheath to transverse at the magnetopause, (2) an amplification of wave amplitude at the magnetopause, (3) a change in Poynting flux from cross-field in the magnetosheath to field-aligned at the magnetopause, and (4) a steepening in the wave power spectrum at the magnetopause. We examine magnetic field data from a set of ISEE1, ISEE2, and WIND magnetopause crossings and compare with the predictions of theoretical wave solutions based on the kinetic-fluid model with particular attention to the role of magnetic field rotation across the magnetopause. The results of the study suggest a good qualitative agreement between the observations and the theory of mode conversion to kinetic Alfven waves. Because mode-converted kinetic Alfven waves readily decouple particles from the magnetic field lines, efficient quasilinear transport (D(approx) 109m2/s) can occur. Moreover, if the wave amplitude is sufficiently large (Bwave/B0 and gt; 0.2) stochastic particle transport also occurs. This wave-induced transport can lead to significant heating and particle entry into the low latitude boundary layer across closed field lines.At the magnetopause, large amplitude, low-frequency (ULF), transverse MHD waves are nearly always observed. These waves likely result from mode conversion of compressional MHD waves observed in the magnetosheath to kinetic Alfven waves at the magnetopause where there is a steep gradient in
Plasma mass density, species mix and fluctuation diagnostics using fast Alfven wave
International Nuclear Information System (INIS)
Ikezi, H.; deGrassie, J.S.; Pinsker, R.I.; Snider, R.T.
1996-06-01
The authors propose to employ a fast Alfven wave interferometer and reflectometer as a tokamak diagnostic to measure the plasma mass density, D-T species mix profile, and density fluctuations. Utilize the property that the phase velocity of the fast wave propagating across the magnetic field is the Alfven speed with thermal correction, this fast wave interferometer on the DIII-D tokamak was successfully used to obtain the line integrated density. Since the position of the ion-ion hybrid cut-off in tokamaks is uniquely determined by the species mix ratio and the wave frequency, the reflectometer arrangement finds the species mix profile. The inversion method of reflectometry is discussed. The multiple chord interferometer also measures the mass density fluctuation profile
The analysis of Alfven wave current drive and plasma heating in TCABR tokamak
International Nuclear Information System (INIS)
Ruchko, L.F.; Lerche, E.A.; Galvao, R.M.O.; Elfimov, A.G.; Nascimento, I.C.; Sa, W.P. de; Sanada, E.; Elizondo, J.I.; Ferreira, A.A.; Saettone, E.A.; Severo, J.H.F.; Bellintani, V.; Usuriaga, O.N.
2002-01-01
The results of experiments on Alfven wave current drive and plasma heating in the TCABR tokamak are analyzed with the help of a numerical code for simulation of the diffusion of the toroidal electric field. It permits to find radial distributions of plasma current density and conductivity, which match the experimentally measured total plasma current and loop voltage changes, and thus to study the performance of the RF system during Alfven wave plasma heating and current drive experiments. Regimes with efficient RF power input in TCABR have been analyzed and revealed the possibility of noninductive current generation with magnitudes up to ∼8 kA. The increase of plasma energy content due to RF power input is consistent with the diamagnetic measurements. (author)
Phenomenology of non-Alfvenic turbulence in a uniformly expanding medium
Matthaeus, W. H.; Zank, G. P.
1995-01-01
Transport and decay of magnetohydrodynamic (MHD) turbulence in a weakly inhomogeneous uniformly expanding medium involves a fairly complex formalism, even for the case where no spectral information is required. Here we argue that the phenomenology for decay simplifies greatly if: (1) the cross helicity (Alfvenicity) is small, (2) the dynamical influence of the large scale magnetic field is negligible either because of spectral anisotropy or because the expansion speed is much greater than the corresponding Alfven speed, and (3) the ratio of kinetic energy to magnetic energy for the fluctuations is either unity or some other constant. These conditions are acceptable as an approximation to solar wind turbulence in the outer heliosphere. In these circumstances a reasonable MHD energy-containing phenomenology is essentially that of locally homogeneous Kolmogoroff turbulence in a uniformly expanding medium. Analytical solutions for this model are presented for both undriven and driven cases.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
The Dynamics of Current Carriers In Standing Alfven Waves
Wright, A. N.; Allan, W.; Ruderman, M. S.; Elphic, R. C.
The acceleration of current carriers in an Alfvén wave current system is considered. The model incorporates a dipole magnetic field geometry, and we present an analyt- ical solution of the two-fluid equations by successive approximations. The leading solution corresponds to the familiar single-fluid toroidal oscillations. The next order describes the nonlinear dynamics of electrons responsible for carrying a few µAm-2 field aligned current into the ionosphere. The solution shows how most of the elec- tron acceleration in the magnetosphere occurs within 1 RE of the ionosphere, and that a parallel electric field of the order of 1 mVm-1 is reponsible for energising the electrons to 1 keV. The limitations of the electron fluid approximation are considered, and a qualitative solution including electron beams and a modified E is developed in accord with observations. We find that the electron acceleration can be nonlinear, (ve )ve > ve , as a result of our nonuniform equilibrium field geometry even when ve is less than the Alfvén speed. Our calculation also elucidates the processes through which E is generated and supported.
Alfvenic drift Kelvin-Helmholtz instability in the presence of an equilibrium electric field
Sharma, Avadhesh C.; Srivastava, Krishna M.
1992-01-01
The Alfvenic drift Kelvin-Helmholtz instability of a high-beta plasma in the presence of equilibrium magnetic and electric fields perpendicular to each other are studied. The plasma components are assumed to have 2D sheared velocity in y and z directions. The dispersion relation is derived, and the instability criterion is determined. It is shown that the equilibrium electric field has either stabilizing or destabilizing effect depending on certain conditions discussed in the paper.
Expansion of parameter space for Toroidal Alfven Eigenmode experiments in TFTR
Energy Technology Data Exchange (ETDEWEB)
Wong, K.L.; Wilson, J.R.; Chang, Z.Y.; Fredrickson, E.; Hammett, G.W.; Bush, C.; Nazikian, R.; Phillips, C.K.; Snipes, J.; Taylor, G.
1993-05-01
Several techniques were used to excite toroidal Alfven Eigenmodes in the Tokamak Fusion Test Reactor (TFTR) at magnetic fields above 10 kG. These involve pellet injection to raise the plasma density, variation of plasma current to change the energetic ion orbit and the q-profile, and ICRF heating to produce energetic hydrogen ions at velocities comparable to 3.5 MeV alpha particles. These experimental results are presented and relevance to fusion reactors are discussed.
High-n ideal and resistive shear Alfven waves in tokamaks
International Nuclear Information System (INIS)
Cheng, C.Z.; Chen, L.; Chance, M.S.
1984-05-01
Ideal and resistive MHD equations for the shear Alfven waves are studied in a low-β toroidal model by employing the high-n ballooning formalism. The ion sound effects are neglected. For an infinite shear slab, the ideal MHD model gives rise to a continuous spectrum of real frequencies and discrete eigenmodes (Alfven-Landau modes) with complex frequencies. With toroidal coupling effects due to nonuniform toroidal magnetic field, the continuum is broken up into small continuum bands and new discrete toroidal eigenmodes can exist inside the continuum gaps. Unstable ballooning eigenmodes are also introduced by the bad curvature when β > β/sub c/. The resistivity (n) can be considered perturbatively for the ideal modes. In addition, four branches of resistive modes are induced by the resistivity: (1) Resistive entropy modes which are stable (Δ' < 0) with frequencies approaching zero as n/sup 3/5/, (3) Resistive periodic shear Alfven waves which approach the finite frequency end points of the continuum bands and n/sup 1/2, and (4) Resistive ballooning modes which are purely growing with growth rate proportional to eta/sup 1/3/β/sup 2/3/ as eta → O and β → O
Alfven Wave Reflection Model of Field-Aligned Currents at Mercury
Lyatsky, Wladislaw; Khazanov, George V.; Slavin, James
2010-01-01
An Alfven Wave Reflection (AWR) model is proposed that provides closure for strong field-aligned currents (FACs) driven by the magnetopause reconnection in the magnetospheres of planets having no significant ionospheric and surface electrical conductance. The model is based on properties of the Alfven waves, generated at high altitudes and reflected from the low-conductivity surface of the planet. When magnetospheric convection is very slow, the incident and reflected Alfven waves propagate along approximately the same path. In this case, the net field-aligned currents will be small. However, as the convection speed increases. the reflected wave is displaced relatively to the incident wave so that the incident and reflected waves no longer compensate each other. In this case, the net field-aligned current may be large despite the lack of significant ionospheric and surface conductivity. Our estimate shows that for typical solar wind conditions at Mercury, the magnitude of Region 1-type FACs in Mercury's magnetosphere may reach hundreds of kilo-Amperes. This AWR model of field-aligned currents may provide a solution to the long-standing problem of the closure of FACs in the Mercury's magnetosphere. c2009 Elsevier Inc. All rights reserved.
Propagation of Alfvenic Waves from corona to chromosphere and consequences for solar flares
Fletcher, L.; Russell, A. J.
2013-12-01
Much of the work on Alfven waves in the solar atmosphere is concerned with the transport of energy from the lower atmosphere into the corona. Here we address Alfvenic energy flow in the opposite direction. We suggest that during a solar flare, energy is radiated from the reconnection region in the corona as Alfvenic perturbations and ducted along the magnetic field to the chromosphere, where it is dissipated in electron Landau damping in the upper chromosphere, and (primarily) ion-neutral friction in the mid- to low- chromosphere. We present results of two-fluid numerical simulations of the transport of wave energy across the corona-chromosphere boundary for a number different chromospheric models (e.g. facula, plage, umbra) and evaluate the transmission, heating and acceleration that results. We conclude that for wave periods of a few seconds, between 10 and 20% of wave energy can be transmitted through the corona-chromosphere boundary, and a large fraction (up to 100%) of this is dissipated by ion-neutral friction around the temperature minimum region, which may lead to a white-light flare.
On a new series of integrable nonlinear evolution equations
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.
1980-10-01
Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
On the definition of the momentum of an Alfven wave packet
International Nuclear Information System (INIS)
Khudik, V.N.
1993-01-01
The different definitions of the momentum of a wave disturbance are considered, corresponding to the invariance of the Lagrangian with respect to different kinds of translation in magnetohydrodynamics. It is shown that the value of the momentum of an Alfven wave packet calculated using the definition accepted in the electrodynamics of continuous media is not the same as the total momentum of the particles in the medium and the electromagnetic field in the region within which the packet is localized. 5 refs., 2 figs
Scrape-off measurements during Alfven wave heating in the TCA tokamak
International Nuclear Information System (INIS)
Hofmann, F.; Hollenstein, C.; Joye, B.; Lietti, A.; Lister, J.B.; Pochelon, A.; Gimzewski, J.K.; Veprek, S.
1984-01-01
Plasma parameters and impurity fluxes in the scrape-off layer of the TCA tokamak have been measured during Alfven wave heating. Langmuir probes are used to measure electron density, electron temperature and plasma potential. Collection probes, in conjunction with XPS surface analysis, are used to determine impurity fluxes and ion impact energies. During RF heating, the electron edge temperature rises, the plasma potential drops and impurity fluxes are enhanced. Probe erosion due to impurity sputtering is clearly observed. The measurements are correlated with other diagnostics on TCA. (orig.)
Comment on Propagation and Dissipation of Alfven Waves in Coronal Holes
Chandra, Suresh
2009-03-01
Dwivedi and Srivastava [1] (DS) investigated the propagation and dissipation of Alfven waves in coronal holes after accounting for the viscosity and magnetic diffusivity. After solving a set of equations with the help of computer results are reported by them. We find that the same set of equations can be solved even analytically. Since DS have not reported any values of physical parameters used by them except their expressions, we could not trace out the source of error. One reason for the difference in our results and those of DS can be assigned to some mistakes in their computer program or to the values of parameters used.
Prokopov, Pavel; Zaharov, Yuriy; Tishchenko, Vladimir; Boyarintsev, Eduard; Melehov, Aleksandr; Ponomarenko, Arnold; Posuh, Vitaliy; Shayhislamov, Ildar
2016-03-01
The paper deals with generation of Alfven plasma disturbances in magnetic flux tubes through exploding laser plasma in magnetized background plasma. Processes with similar effect of excitation of torsion-type waves seem to provide energy transfer from the solar photosphere to corona. The studies were carried out at experimental stand KI-1 represented a high-vacuum chamber of 1.2 m diameter, 5 m long, external magnetic field up to 500 Gs along the chamber axis, and up to 2×10^-6 Torr pressure in operating mode. Laser plasma was produced when focusing the CO2 laser pulse on a flat polyethylene target, and then the laser plasma propagated in θ-pinch background hydrogen (or helium) plasma. As a result, the magnetic flux tube of 15-20 cm radius was experimentally simulated along the chamber axis and the external magnetic field direction. Also, the plasma density distribution in the tube was measured. Alfven wave propagation along the magnetic field was registered from disturbance of the magnetic field transverse component B_ψ and field-aligned current J_z. The disturbances propagate at near-Alfven velocity of 70-90 km/s and they are of left-hand circular polarization of the transverse component of magnetic field. Presumably, Alfven wave is generated by the magnetic laminar mechanism of collisionless interaction between laser plasma cloud and background. The right-hand polarized high-frequency whistler predictor was registered which have been propagating before Alfven wave at 300 km/s velocity. The polarization direction changed with Alfven wave coming. Features of a slow magnetosonic wave as a sudden change in background plasma concentration along with simultaneous displacement of the external magnetic field were found. The disturbance propagates at ~20-30 km/s velocity, which is close to that of ion sound at low plasma beta value. From preliminary estimates, the disturbance transfers about 10 % of the original energy of laser plasma.
Design of the RF system for Alfven wave heating and current drive in a TCA/BR tokamak
International Nuclear Information System (INIS)
Ruchko, L.; Andrade, M.L.; Ozono, E.; Galvao, R.M.O.; Degaspari, F.T.; Nascimento, I.C.
1995-01-01
The advanced RF system for Alfven wave plasma heating and current drive in TCA/BR tokamak is presented. The antenna system is capable of exciting the standing and travelling wave M = -1,N = 1,N =-4,-6 with single helicity and thus provides the possibility to improve Alfven wave plasma heating efficiency in TCA/BR tokamak and to increase input power level up to P ≅ 1 MW, without the uncontrolled density rise which was encountered in previous TCA (Switzerland) experiments. (author). 4 refs., 3 figs
Alfvenic Turbulence from the Sun to 65 Solar Radii: Numerical predictions.
Perez, J. C.; Chandran, B. D. G.
2015-12-01
The upcoming NASA Solar Probe Plus (SPP) mission will fly to within 9 solar radii from the solar surface, about 7 times closer to the Sun than any previous spacecraft has ever reached. This historic mission will gather unprecedented remote-sensing data and the first in-situ measurements of the plasma in the solar atmosphere, which will revolutionize our knowledge and understanding of turbulence and other processes that heat the solar corona and accelerate the solar wind. This close to the Sun the background solar-wind properties are highly inhomogeneous. As a result, outward-propagating Alfven waves (AWs) arising from the random motions of the photospheric magnetic-field footpoints undergo strong non-WKB reflections and trigger a vigorous turbulent cascade. In this talk I will discuss recent progress in the understanding of reflection-driven Alfven turbulence in this scenario by means of high-resolution numerical simulations, with the goal of predicting the detailed nature of the velocity and magnetic field fluctuations that the SPP mission will measure. In particular, I will place special emphasis on relating the simulations to relevant physical mechanisms that might govern the radial evolution of the turbulence spectra of outward/inward-propagating fluctuations and discuss the conditions that lead to universal power-laws.
Ion beam generation at the plasma sheet boundary layer by kinetic Alfven waves
International Nuclear Information System (INIS)
Moghaddam-Taaheri, E.; Goertz, C.K.; Smith, R.A.
1989-01-01
The kinetic Alfven wave, an Alfven wave with a perpendicular wavelength comparable to the ion gyroradius, can diffuse ions both in velocity and coordinate spaces with comparable transport rates. This may lead to the generation of ion beams in the plasma sheet boundary layer (PSBL). To investigate the ion beam generation process numerically, a two-dimensional quasi-linear code was constructed. Assuming that the plasma β (the ratio of plasma pressure to the magnetic pressure) varies from β = 1 to β << 1 across the magnetic field, the dynamics of the ion beam generation in the PSBL was studied. It was found that if your start with an ion distribution function which monotonically decreases with velocity along the magnetic field and a density gradient across the magnetic field, ions diffuse in velocity-coordinate space until nearly a plateau is established along the diffusion path. Depending on the topology of the magnetic field at the lobe side of the simulation system, i.e., open or closed field lines, the ion distribution function may or may not reach a steady state. If the field lines are open there, i.e., if the diffusion extends into the lobe, the double diffusion process may provide a mechanism for continuously transferring the ions from the central plasma sheet to the lobe. The authors comment on the effect of the particle loss on the establishment of the pressure balance in the plasma sheet
Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V.
1991-01-01
The present method of addressing the resonance problems that emerge in such MHD phenomena as the resonant absorption of waves at the Alfven resonance point avoids solving the fourth-order differential equation of dissipative MHD by recourse to connection formulae across the dissipation layer. In the second part of this investigation, the absorption of solar 5-min oscillations by sunspots is interpreted as the resonant absorption of sounds by a magnetic cylinder. The absorption coefficient is interpreted (1) analytically, under certain simplifying assumptions, and numerically, under more general conditions. The observed absorption coefficient magnitude is explained over suitable parameter ranges.
Averaging of nonlinearity-managed pulses
International Nuclear Information System (INIS)
Zharnitsky, Vadim; Pelinovsky, Dmitry
2005-01-01
We consider the nonlinear Schroedinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...
International Nuclear Information System (INIS)
Descamps, P.; Wassenhove, G. van; Koch, R.; Messiaen, A.M.; Vandenplas, P.E.; Lister, J.B.; Marmillod, P.
1990-01-01
The use of the discrete Alfven wave spectrum to determine the current density profile and the effective mass density of the plasma in the TEXTOR tokamak is studied; the measurement, the validity of which is discussed, confirms independently the central q(r=0)<1 already obtained by polarimetry. (orig.)
International Nuclear Information System (INIS)
Descamps, P.; Wasserhove, G. van; Koch, R.; Messiaen, A.M.; Vandenplas, P.E.
1989-12-01
The use of the Discrete Alfven Wave spectrum to determine the current density profile and the effective mass density of the plasma in the TEXTOR tokamak is studied; the measurement, the validity of which is discussed, confirms independently the central q(r=0)<1 already obtained by polarimetry. (author) 5 figs., 1 tab., 10 refs
Study of Thermonuclear Alfven Instabilities in Next Step Burning Plasma Experiments
Energy Technology Data Exchange (ETDEWEB)
N.N. Gorelenkov; H.L. Berk; R. Budny; C.Z. Cheng; G.-Y. Fu; W.W. Heidbrink; G. Kramer; D. Meade; and R. Nazikian
2002-07-02
A study is presented for the stability of alpha-particle driven shear Alfven Eigenmodes (AE) for the normal parameters of the three major burning plasma proposals, ITER (International Thermonuclear Experimental Reactor), FIRE (Fusion Ignition Research Experiment), and IGNITOR (Ignited Torus). A study of the JET (Joint European Torus) plasma, where fusion alphas were generated in tritium experiments, is also included to attempt experimental validation of the numerical predictions. An analytic assessment of Toroidal AE (TAE) stability is first presented, where the alpha particle beta due to the fusion reaction rate and electron drag is simply and accurately estimated in 7-20 keV plasma temperature regime. In this assessment the hot particle drive is balanced against ion-Landau damping of the background deuterons and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one the High-n stability code HINST is used . This code is capable of predicting instabilities of low and moderately high frequency Alfven modes. HINST computes the non-perturbative solution of the Alfven eigenmodes including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these tokamaks the spectrum of the least stable AE modes are TAE that appear at medium-/high-n numbers. In HINST TAEs are locally unstable due to the alphas pressure gradient in all the devices under the consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability in all configurations considered here. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three proposals are stable to AEs. In addition NBI ions produce a strong
Nonlinear waves in solar plasmas - a review
International Nuclear Information System (INIS)
Ballai, I
2006-01-01
Nonlinearity is a direct consequence of large scale dynamics in the solar plasmas. When nonlinear steepening of waves is balanced by dispersion, solitary waves are generated. In the vicinity of resonances, waves can steepen into nonlinear waves influencing the efficiency of energy deposition. Here we review recent theoretical breakthroughs that have lead to a greater understanding of many aspects of nonlinear waves arising in homogeneous and inhomogeneous solar plasmas
Zonal Flows Driven by Small-Scale Drift-Alfven Modes
International Nuclear Information System (INIS)
Li Dehui; Zhou Deng
2011-01-01
Generation of zonal flows by small-scale drift-Alfven modes is investigated by adopting the approach of parametric instability with the electron polarization drift included. The zonal mode can be excited by primary modes propagating at both electron and ion diamagnetic drift directions in contrast to the assertion in previous studies that only primary modes propagating in the ion diamagnetic drift directions can drive zonal instabilities. Generally, the growth rate of the driven zonal mode is in the same order as that in previous study. However, different from the previous work, the growth rate is no longer proportional to the difference between the diamagnetic drift frequencies of electrons and ions. (magnetically confined plasma)
Theory of high-n toroidicity-induced shear Alfven eigenmode in tokamaks
International Nuclear Information System (INIS)
Fu, G.Y.; Cheng, C.Z.; Princeton Univ., NJ
1989-07-01
High-n WKB-ballooning mode equation is employed to study toroidicity-induced shear Alfven eigenmodes (TAE) in the δ - α space, where δ = (r/q)(dq/dr) is the magnetic shear, and α = -(2Rq 2 /B 2 )(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for α less than some critical value α c . We also find that these TAE modes reappear in the ballooning mode second stability region for bands of α values. The global envelope structures of these TAE modes are studied by WKB method and are found to be bounded radially if the local mode frequency has a maximum in radius. 15 refs., 14 figs
Experimental study of toroidicity-induced Alfven eigenmode (TAE) stability at high q(0)
Energy Technology Data Exchange (ETDEWEB)
Batha, S.H.; Levinton, F.M. [Fusion Physics and Technology, Torrance, CA (United States); Spong, D.A. [Oak Ridge National Lab., TN (United States)] [and others
1995-07-01
Experiments to destabilize the Toroidicity-induced Alfven Eigenmode (TAE) by energetic alpha particles were performed on the Tokamak Fusion Test Reactor using deuterium and tritium fuel. To decrease the alpha particle pressure instability threshold, discharges with an elevated value of q(0) > 1.5 were used. By raising q(0), the radial location of the low toroidal-mode-number TAE gaps moves toward the magnetic axis and into alignment with the region of maximum alpha pressure gradient, thereby (in theory) lowering the value of {beta}{sub {alpha}}(0) required for instability. No TAE activity was observed when the central alpha particle {beta}{sub {alpha}} reached 0.08% in a discharge with fusion power of 2.4 MW. Calculations show that the fusion power is within a factor of 1.5 to 3 of the instability threshold.
New Digital Control System for the JET Alfv'en Eigenmode Active Spectroscopy Diagnostic
Woskov, P. P.; Stillerman, J.; Porkolab, M.; Fasoli, A.; Testa, D.; Galvao, R.; Pires Dos Resis, A.; Pires de Sa, W.; Ruchko, L.; Blanchard, P.; Figueiredo, J.; Dorling, S.; Farthing, J.; Graham, M.; Dowson, S.; Yu, L.; Concezzi, S.
2012-10-01
The state-of-the-art JET Alfv'en active spectroscopy diagnostic with eight internal inductive antennas is being upgraded from a single 5 kW tube amplifier to eight parallel, 10 -- 1000 kHz, 4 kW solid state class D power switching amplifiers. A new digital control system has been designed with arbitrary constant phase controlled frequency sweeps for traveling mode studies, amplifier gain control through a feedback loop referenced to programmed antenna current profiles, and integration with CODAS for synchronization, triggering, gating, and fault tripping. A combination of National Instruments Real Time LabView software and FPGA circuits is used to achieve the multiple control requirements with better than 1 ms response. System specifications and digital-analog design trade offs for sweep rates, response times, frequency resolution, and voltage levels will be presented.
Modeling nonlinearities in MEMS oscillators.
Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A
2013-08-01
We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.
Nonlinear evolution of drift instabilities
International Nuclear Information System (INIS)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation
Kraft, R. E.
1999-01-01
Single-degree-of-freedom resonators consisting of honeycomb cells covered by perforated facesheets are widely used as acoustic noise suppression liners in aircraft engine ducts. The acoustic resistance and mass reactance of such liners are known to vary with the intensity of the sound incident upon the panel. Since the pressure drop across a perforated liner facesheet increases quadratically with the flow velocity through the facesheet, this is known as the nonlinear resistance effect. In the past, two different empirical frequency domain models have been used to predict the Sound Pressure Level effect of the incident wave on the perforated liner impedance, one that uses the incident particle velocity in isolated narrowbands, and one that models the particle velocity as the overall velocity. In the absence of grazing flow, neither frequency domain model is entirely accurate in predicting the nonlinear effect that is measured for typical perforated sheets. The time domain model is developed in an attempt to understand and improve the model for the effect of spectral shape and amplitude of multi-frequency incident sound pressure on the liner impedance. A computer code for the time-domain finite difference model is developed and predictions using the models are compared to current frequency-domain models.
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
Probing hysteretic elasticity in weakly nonlinear materials
Energy Technology Data Exchange (ETDEWEB)
Johnson, Paul A [Los Alamos National Laboratory; Haupert, Sylvain [UPMC UNIV PARIS; Renaud, Guillaume [UPMC UNIV PARIS; Riviere, Jacques [UPMC UNIV PARIS; Talmant, Maryline [UPMC UNIV PARIS; Laugier, Pascal [UPMC UNIV PARIS
2010-12-07
Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.
Energy Technology Data Exchange (ETDEWEB)
Evans, R. M. [NASA Goddard Space Flight Center, Space Weather Lab, Greenbelt, MD 20771 (United States); Opher, M. [Astronomy Department, Boston University, 675 Commonwealth Avenue, Boston, MA 02215 (United States); Oran, R.; Van der Holst, B.; Sokolov, I. V.; Frazin, R.; Gombosi, T. I. [Center for Space Environment Modeling, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 (United States); Vasquez, A., E-mail: Rebekah.e.frolov@nasa.gov [Instituto de Astronomia y Fisica del Espacio (CONICET-UBA) and FCEN (UBA), CC 67, Suc 28, Ciudad de Buenos Aires (Argentina)
2012-09-10
The heating and acceleration of the solar wind is an active area of research. Alfven waves, because of their ability to accelerate and heat the plasma, are a likely candidate in both processes. Many models have explored wave dissipation mechanisms which act either in closed or open magnetic field regions. In this work, we emphasize the boundary between these regions, drawing on observations which indicate unique heating is present there. We utilize a new solar corona component of the Space Weather Modeling Framework, in which Alfven wave energy transport is self-consistently coupled to the magnetohydrodynamic equations. In this solar wind model, the wave pressure gradient accelerates and wave dissipation heats the plasma. Kolmogorov-like wave dissipation as expressed by Hollweg along open magnetic field lines was presented in van der Holst et al. Here, we introduce an additional dissipation mechanism: surface Alfven wave (SAW) damping, which occurs in regions with transverse (with respect to the magnetic field) gradients in the local Alfven speed. For solar minimum conditions, we find that SAW dissipation is weak in the polar regions (where Hollweg dissipation is strong), and strong in subpolar latitudes and the boundaries of open and closed magnetic fields (where Hollweg dissipation is weak). We show that SAW damping reproduces regions of enhanced temperature at the boundaries of open and closed magnetic fields seen in tomographic reconstructions in the low corona. Also, we argue that Ulysses data in the heliosphere show enhanced temperatures at the boundaries of fast and slow solar wind, which is reproduced by SAW dissipation. Therefore, the model's temperature distribution shows best agreement with these observations when both dissipation mechanisms are considered. Lastly, we use observational constraints of shock formation in the low corona to assess the Alfven speed profile in the model. We find that, compared to a polytropic solar wind model, the wave
Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates
International Nuclear Information System (INIS)
Brizard, A.
1988-09-01
A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs
International Nuclear Information System (INIS)
Ichimura, Makoto; Tanaka, Satoru; Nakamura, Motoyuki
2000-01-01
With a strong ion cyclotron range of frequency (ICRF) heating in the GAMMA 10 tandem mirror, an ion temperature of 10 keV has been attained and a temperature anisotropy has been observed to become greater than 10. Unstable Alfven ion cyclotron (AIC) modes are driven with such a strong temperature anisotropy. High energy ions with energies of more than 50 keV are detected both parallel and perpendicular to the magnetic field lines. With the AIC modes, increase of the high energy ions at the end of the device and decrease of the high energy ions with a pitch angle of nearly 90 degrees are observed. The pitch angle scattering of high energy ions due to the spontaneously excited Alfven modes in the plasma is suggested. (author)
Controlling Parametric Resonance
DEFF Research Database (Denmark)
Galeazzi, Roberto; Pettersen, Kristin Ytterstad
2012-01-01
if the system undergoing it could transform the large amplitude motion into, for example, energy. Therefore the development of control strategies to induce parametric resonance into a system can be as valuable as those which aim at stabilizing the resonant oscillations. By means of a mechanical equivalent......Parametric resonance is a resonant phenomenon which takes place in systems characterized by periodic variations of some parameters. While seen as a threatening condition, whose onset can drive a system into instability, this chapter advocates that parametric resonance may become an advantage...... the authors review the conditions for the onset of parametric resonance, and propose a nonlinear control strategy in order to both induce the resonant oscillations and to stabilize the unstable motion. Lagrange’s theory is used to derive the dynamics of the system and input–output feedback linearization...
International Nuclear Information System (INIS)
Guo, Zhifang; Hong, Minghua; Du, Aimin; Lin, Yu; Wang, Xueyi; Wu, Mingyu; Lu, Quanming
2015-01-01
In this paper, effects of a fast flow in the tail plasma sheet on the generation of kinetic Alfven waves (KAWs) in the high-latitude of the near-Earth magnetotail are investigated by performing a two-dimensional (2-D) global-scale hybrid simulation, where the plasma flow is initialized by the E×B drift near the equatorial plane due to the existence of the dawn-dusk convection electric field. It is found that firstly, the plasma sheet becomes thinned and the dipolarization of magnetic field appears around (x,z)=(−10.5R E ,0.3R E ), where R E is the radius of the Earth. Then, shear Alfven waves are excited in the plasma sheet, and the strong earthward flow is braked by the dipole-like magnetic field. These waves propagate along the magnetic field lines toward the polar regions later. Subsequently, KAWs with k ⊥ ≫k ∥ are generated in the high-latitude magnetotail due to the existence of the non-uniformity of the magnetic field and density in the polar regions. The ratio of the electric field to the magnetic field in these waves is found to obey the relation (δE z )/(δB y )∼ω/k ∥ of KAWs. Our simulation provides a mechanism for the generation of the observed low-frequency shear Alfven waves in the plasma sheet and kinetic Alfven waves in the high-latitude near-Earth magnetotail, whose source is suggested to be the flow braking in the low-latitude plasma sheet
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
Resonance phenomenon in classical cepheids
International Nuclear Information System (INIS)
Takeuti, Mine; Aikawa, Toshiki
1981-01-01
To investigate resonance phenomenon in classical cepheids, the non-linear radial oscillation of stars is studied based on the assumption that the non-adiabatic perturbation is expressed in terms of van der Pol's type damping. Two- and three-wave resonance in this system is applied to classical cepheids to describe their bump and double-mode behavior. The phase of bump and the depression of amplitude are explained for bump cepheids. The double-periodicity is shown by the enhancement of the third overtone in three-wave resonance. Non-linear effect on resonant period is also discussed briefly. (author)
National Research Council Canada - National Science Library
Rassias, Themistocles M
1987-01-01
... known that nonlinear partial differential equations can not be treated in the same systematic way as linear ones and this volume provides, among other things, proofs of existence and uniqueness theorems for nonlinear differential equations of a global nature. However, the basic techniques which have proven to be efficient in dealing with li...
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Influence of gyroradius and dissipation on the Alfven-wave continuum
International Nuclear Information System (INIS)
Connor, J.W.; Tang, W.M.; Taylor, J.B.
1982-01-01
It is well known that in ideal magnetohydrodynamics there is a continuous spectrum of real frequencies associated with a singularity of the shear Alfven waves on the surface k/sub parallel to/v/sub A/ = omega. It is also known that the introduction of first-order gyroradius effects eliminates the continuum. In the present work we examine the influence of the full gyroradius response and of dissipation on the continuum. In the absence of dissipation we first confirm that if only first-order gyroradius effects are incorporated, the continuum disappears. However, when the full gyroradius response is included, this discrete spectrum vanishes, and a new continuum (associated with singularities at k/sub parallel to/v/sub A/ = 0) appears. The introduction of collisional dissipation removes the original MHD continuum leaving discrete modes whose frequency tends to zero with the collision rate as ν/sup 1/3/. collisions also remove the new continuum of the full gyroradius model leaving discrete modes whose frequency tends to zero as (log ν) -1 . Collisionless Landau damping has a similar effect
Hybrid Model of Inhomogeneous Solar Wind Plasma Heating by Alfven Wave Spectrum: Parametric Studies
Ofman, L.
2010-01-01
Observations of the solar wind plasma at 0.3 AU and beyond show that a turbulent spectrum of magnetic fluctuations is present. Remote sensing observations of the corona indicate that heavy ions are hotter than protons and their temperature is anisotropic (T(sub perpindicular / T(sub parallel) >> 1). We study the heating and the acceleration of multi-ion plasma in the solar wind by a turbulent spectrum of Alfvenic fluctuations using a 2-D hybrid numerical model. In the hybrid model the protons and heavy ions are treated kinetically as particles, while the electrons are included as neutralizing background fluid. This is the first two-dimensional hybrid parametric study of the solar wind plasma that includes an input turbulent wave spectrum guided by observation with inhomogeneous background density. We also investigate the effects of He++ ion beams in the inhomogeneous background plasma density on the heating of the solar wind plasma. The 2-D hybrid model treats parallel and oblique waves, together with cross-field inhomogeneity, self-consistently. We investigate the parametric dependence of the perpendicular heating, and the temperature anisotropy in the H+-He++ solar wind plasma. It was found that the scaling of the magnetic fluctuations power spectrum steepens in the higher-density regions, and the heating is channeled to these regions from the surrounding lower-density plasma due to wave refraction. The model parameters are applicable to the expected solar wind conditions at about 10 solar radii.
Geometrical and profile effects on toroidicity and ellipticity induced Alfven eigenmodes
International Nuclear Information System (INIS)
Villard, L.; Fu, G.Y.
1992-04-01
The wave structures, eigenfrequencies and damping rates of toroidicity and ellipticity induced Alfven eigenmodes (TAE, EAE) of low toroidal mode numbers (n) are calculated in various axisymmetric ideal MHD equilibria with the global wave finite element code LION. The importance of safety factor (q) and density (ρ) profiles on continuum damping rates is analysed. For realistic profiles several continuum gaps exist in the plasma discharge. Frequency misalignment of these gaps yields continuum damping rates γ/ω of the order of a few percent. Finite β pol lowers the TAE eigenfrequency. For β values below the Troyon limit the TAE enters the continuum and can thus be stabilized. Finite elongation allows the EAE to exist but triangularity can have a stabilizing effect through coupling to the continuum. The localization of TAE and EAE eigenfunctions is found to increase with the shear and with n. Therefore large shear, through enhanced Landau and collisional damping, is a stabilizing factor for TAE and EAE modes. (author) 16 figs., 28 refs
On the stochastic interaction of monochromatic Alfven waves with toroidally trapped particles
International Nuclear Information System (INIS)
Krlin, L.; Pavlo, P.; Tluchor, Z.; Gasek, Z.
1987-07-01
Monochromatic Alfven wave interaction with toroidaly trapped particles in the intrinsic stochasticity regime is discussed. Both the diffusion in velocities and in the radial position of bananas is studied. Using a suitable Hamiltonian formalism, the effect of wave parallel components E-tilde paral and B-tilde paral is investigated. The stochasticity threshold is estimated for plasma electrons and for thermonuclear alpha-particles (neglecting the effect of B-tilde paral ) by means of direct numerical integration of the corresponding canonical equations. Stochasticity causes transfer between trapped and untrapped regimes and the induced radial diffusion of bananas. The latter effect can considerably exceed neoclassical diffusion. The effect of B-tilde paral was only estimated analytically. It consisted in frequency modulation of the banana periodic motion coupled with a possible Mathieu instability. Nevertheless, for B-tilde paral corresponding to E-tilde paral , the effect seems to be weaker than the effect of E-tilde paral when the thermonuclear regime is considered. (author). 14 figs., 36 refs
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
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
Fast nonlinear susceptibility inversion with variational regularization.
Milovic, Carlos; Bilgic, Berkin; Zhao, Bo; Acosta-Cabronero, Julio; Tejos, Cristian
2018-01-10
Quantitative susceptibility mapping can be performed through the minimization of a function consisting of data fidelity and regularization terms. For data consistency, a Gaussian-phase noise distribution is often assumed, which breaks down when the signal-to-noise ratio is low. A previously proposed alternative is to use a nonlinear data fidelity term, which reduces streaking artifacts, mitigates noise amplification, and results in more accurate susceptibility estimates. We hereby present a novel algorithm that solves the nonlinear functional while achieving computation speeds comparable to those for a linear formulation. We developed a nonlinear quantitative susceptibility mapping algorithm (fast nonlinear susceptibility inversion) based on the variable splitting and alternating direction method of multipliers, in which the problem is split into simpler subproblems with closed-form solutions and a decoupled nonlinear inversion hereby solved with a Newton-Raphson iterative procedure. Fast nonlinear susceptibility inversion performance was assessed using numerical phantom and in vivo experiments, and was compared against the nonlinear morphology-enabled dipole inversion method. Fast nonlinear susceptibility inversion achieves similar accuracy to nonlinear morphology-enabled dipole inversion but with significantly improved computational efficiency. The proposed method enables accurate reconstructions in a fraction of the time required by state-of-the-art quantitative susceptibility mapping methods. Magn Reson Med, 2018. © 2018 International Society for Magnetic Resonance in Medicine. © 2018 International Society for Magnetic Resonance in Medicine.
Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2017-12-01
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (rδrδL>0.5 for k ≲1 h /Mpc ) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21 cm intensity mapping initiatives.
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
4th International Conference on Structural Nonlinear Dynamics and Diagnosis
2018-01-01
This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...
2016-07-01
architectures , practical nonlinearities, nonlinear dynamics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 8. NUMBER OF PAGES...performers from Mesodynamic Architectures (MESO) and uPNT all to include devices in these runs. This cost-sharing was planned, and is necessary for...contributions to the performance of MEMS gyroscopes. In particular, we have demonstrated for the first time that Parametric Amplification can improve the
Nonlinear dynamic characterization of two-dimensional materials
Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.
2017-01-01
Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's
Structural optimization for nonlinear dynamic response
DEFF Research Database (Denmark)
Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.
2015-01-01
resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...
Structured Slow Solar Wind Variability: Streamer Blob Flux Ropes and Torsional Alfven Waves
Lynch, B. J.; Higginson, A. K.
2017-12-01
The slow solar wind exhibits strong variability on timescales from minutes to days, in addition to changing with the heliosphere on longer timescales from months to years. While the large-scale changes are likely due to the emerging or restructuring of coronal flux, the variability in magnetic field and plasma properties on the smaller timescales is likely related to magnetic reconnection processes in the extended solar corona. Higginson et al. (2017, ApJ 840, L10) presented a numerical magnetohydrodynamic simulation which showed that interchange magnetic reconnection is likely responsible for the release of much of the slow solar wind, including along topological features known as the Separatrix-web (S-web). Here, we continue our analysis of the Higginson et al. simulation, focusing now on two specific aspects of structured slow solar wind variability. First, we examine the formation and evolution of three-dimensional magnetic flux ropes that form at the top of the helmet streamer belt by reconnection in the heliospheric current sheet (HCS). Second, we examine the simulated remote and in situ signatures of the large-scale torsional Alfven wave (TAW) which propagates along an S-web arc to high latitudes. We describe the similarities and differences between the reconnection-generated flux ropes in the HCS, which resemble the well-known "streamer blob" observations, and the similarly structured TAW. We discuss the implications of our results for the complexity of the HCS and surrounding plasma sheet, and the potential for particle acceleration, as well as the interchange reconnection scenarios which may generate TAWs in the solar corona. We consider our simulation results within the context of the future Parker Solar Probe and Solar Orbiter observations, and make predictions for the dynamic slow solar wind in the extended corona and inner heliosphere.
Device Applications of Nonlinear Dynamics
Baglio, Salvatore
2006-01-01
This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
This method is termed as Feshbach resonance management or nonlinearity management. The other method is called dispersion management as it involves periodic modulation of the dispersion term of the nonlinear evolution equa- tion which can stabilize soliton solutions. An experimental investigation of nonlinearity.
Spectra of resonance surface photoionization
Energy Technology Data Exchange (ETDEWEB)
Antsiferov, V.V.; Smirnov, G.I.; Telegin, G.G. [Budker Nuclear Physics Institute, Novosibirsk (Russian Federation)
1995-09-01
The theory of nonactivated electron transfer between atoms interacting reasonantly with coherent radiation and a metal surface is developed. The spectral resonances in photoabsorption and surface photoionization are found to be related to nonlinear interference effects in the interaction between discrete atomic levels and the continuum formed by the quasi-continuous electron spectrum of a normal metal. The asymmetry in the resonance surface photoionization spectrum is shown to have a shape typical of the Fano autoionization resonances. 18 refs.
Nonlinear frequency conversion in coupled ring cavities
DEFF Research Database (Denmark)
Buchhave, Preben; Abitan, Haim; Tidemand-Lichtenberg, Peter
2001-01-01
The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power and the op......The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power...... and the optical elements is solved by a numerical root find function of a commercial mathematics software. The method allows computation of the output of sequential nonlinear processes such as laser gain, second harmonic generation and optical parametric amplification as a function of the input diode pump power...
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...
Theoretical Studies of Alfven Waves and Energetic Particle Physics in Fusion Plasmas
Energy Technology Data Exchange (ETDEWEB)
Chen, Liu [Univ. of California, Irvine, CA (United States)
2017-12-20
This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novel findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-08
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
Nonlinear electromagnetic gyrokinetic particle simulations with the electron hybrid model
Nishimura, Y.; Lin, Z.; Chen, L.; Hahm, T.; Wang, W.; Lee, W.
2006-10-01
The electromagnetic model with fluid electrons is successfully implemented into the global gyrokinetic code GTC. In the ideal MHD limit, shear Alfven wave oscillation and continuum damping is demonstrated. Nonlinear electromagnetic simulation is further pursued in the presence of finite ηi. Turbulence transport in the AITG unstable β regime is studied. This work is supported by Department of Energy (DOE) Grant DE-FG02-03ER54724, Cooperative Agreement No. DE-FC02-04ER54796 (UCI), DOE Contract No. DE-AC02-76CH03073 (PPPL), and in part by SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas. Z. Lin, et al., Science 281, 1835 (1998). F. Zonca and L. Chen, Plasma Phys. Controlled Fusion 30, 2240 (1998); G. Zhao and L. Chen, Phys. Plasmas 9, 861 (2002).
Mykhaylenko, Volodymyr S.; Mykhaylenko, Volodymyr V.; Lee, Hae June
2017-10-01
The ion cyclotron instability driven by the strong kinetic Alfven wave is investigated as a possible source of the anisotropic heating of ions in the coronal holes and solar wind. We present a novel model of a plasma with coupled inhomogeneous current and the sheared flow, which follows from the studies of the particles motion in the electric field of the kinetic Alfven wave of the finite wavelength. The investigation is performed employing the non-modal kinetic theory grounded on the shearing modes approach. The solution of the governing linear integral equation for the perturbed potential displays that the flow velocity shear, which for the corona conditions may be above the growth rate of the ion cyclotron instability in plasma with steady current, changes the exponential growth of the ion cyclotron potential on the power function of time, that impedes the growth of the unstable ion cyclotron wave and reduces the turbulent heating rate of ions across the magnetic field. This work was funded by National R&D Program through the National Research Foundation of Korea (NRF) (Grant No. NRF-2015R1D1A1A01061160).
Kinetic Alfven Waves and the Depletion of the Thermal Population in Extragalactic Jets
Jafelice, L. C.; Opher, R.
1990-11-01
problems are intimately related to one another. Jafe- lice and Opher (1987a)(Astrophys. Space Sci. 137, 303)showed that an abundant generation of kinetic Alfven waves (KAw) within EJ and ERS is expected. In the present work we study the chain of processes: a) KAW accelerate thermal electrons along the background magnetic field producing suprathermal runaway electrons; b) which generate Langmuir waves and c) which in turn further accelerate a fraction of the runaway electrons to moderately relativistic energies. We show that assuming that there is no other source of a thermal population but the original one, the above sequence of processes can account for the consumption of thermal electrons in a time scale the source lifetime. Key o : GALAXIES-JETS - HYDROMAGNETICS
Amplitude saturation of MEMS resonators explained by autoparametric resonance
International Nuclear Information System (INIS)
Van der Avoort, C; Bontemps, J J M; Steeneken, P G; Le Phan, K; Van Beek, J T M; Van der Hout, R; Hulshof, J; Fey, R H B
2010-01-01
This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators
Nonlinear acoustic techniques for landmine detection
Korman, Murray S.; Sabatier, James M.
2004-12-01
Measurements of the top surface vibration of a buried (inert) VS 2.2 anti-tank plastic landmine reveal significant resonances in the frequency range between 80 and 650 Hz. Resonances from measurements of the normal component of the acoustically induced soil surface particle velocity (due to sufficient acoustic-to-seismic coupling) have been used in detection schemes. Since the interface between the top plate and the soil responds nonlinearly to pressure fluctuations, characteristics of landmines, the soil, and the interface are rich in nonlinear physics and allow for a method of buried landmine detection not previously exploited. Tuning curve experiments (revealing ``softening'' and a back-bone curve linear in particle velocity amplitude versus frequency) help characterize the nonlinear resonant behavior of the soil-landmine oscillator. The results appear to exhibit the characteristics of nonlinear mesoscopic elastic behavior, which is explored. When two primary waves f1 and f2 drive the soil over the mine near resonance, a rich spectrum of nonlinearly generated tones is measured with a geophone on the surface over the buried landmine in agreement with Donskoy [SPIE Proc. 3392, 221-217 (1998); 3710, 239-246 (1999)]. In profiling, particular nonlinear tonals can improve the contrast ratio compared to using either primary tone in the spectrum. .
Picosecond Nonlinear Resonant Interactions in Semiconductors.
1986-03-01
1985). 3. "Electron-Hole Recombination Spectra and Kinetics in PbTc/PbEuTcSc Multiple Quamtum Wells", W. Goltsos, J. Nakahara, A. V. Nurmikko, and D...Partin, Proc. Int. Conf. Modulated Semiconductor Structures, Kyoto, Surface Science (in press). 4. "Optical Bandgap and Magneto-Optical Effects in (Pb,Eu
International Nuclear Information System (INIS)
Edlund, E.M.; Porkolab, M.; Kramer, G.J.; Lin, L.; Lin, Y.; Tsuji, N.; Wukitch, S.J.
2010-01-01
Experiments conducted in the Alcator C-Mod tokamak at MIT have explored the physics of reversed shear Alfven eigenmodes (RSAEs) during the current ramp. The frequency evolution of the RSAEs throughout the current ramp provides a constraint on the evolution of q min , a result which is important in transport modeling and for comparison with other diagnostics which directly measure the magnetic field line structure. Additionally, a scaling of the RSAE minimum frequency with the sound speed is used to derive a measure of the adiabatic index, a measure of the plasma compressibility. This scaling bounds the adiabatic index at 1.40 ± 0.15 used in MHD models and supports the kinetic calculation of separate electron and ion compressibilities with an ion adiabatic index close to 7/4.
Energy Technology Data Exchange (ETDEWEB)
Podesta, M; Fredrickson, E D; Gorelenkov, N N; LeBlanc, B P; Heidbrink, W W; Crocker, N A; Kubota, S
2010-08-19
The effects of a sheared toroidal rotation on the dynamics of bursting Toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40 557 (2000)]. The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of increased damping is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes.
International Nuclear Information System (INIS)
Podesta, M.; Bell, R.E.; Fredrickson, E.D.; Gorelenkov, N.N.; LeBlanc, B.P.; Heidbrink, W.W.; Crocker, N.A.; Kubota, S.; Yuh, H.
2010-01-01
The effects of a sheared toroidal rotation on the dynamics of bursting Toroidicity-induced Alfven eigenmodes are investigated in neutral beam heated plasmas on the National Spherical Torus Experiment (NSTX) (M. Ono et al., Nucl. Fusion 40 557 (2000)). The modes have a global character, extending over most of the minor radius. A toroidal rotation shear layer is measured at the location of maximum drive for the modes. Contrary to results from other devices, no clear evidence of increased damping is found. Instead, experiments with simultaneous neutral beam and radio-frequency auxiliary heating show a strong correlation between the dynamics of the modes and the instability drive. It is argued that kinetic effects involving changes in the mode drive and damping mechanisms other than rotation shear, such as continuum damping, are mostly responsible for the bursting dynamics of the modes.
International Nuclear Information System (INIS)
Fonseca, A.M.M.; Tsypin, V.S.; Galvao, R.M.O.; Kuznetsov, Y.K.; Nascimento, I.C.; Silva, R.P. da; Saettone, E.A.; Vannucci, A.
2005-01-01
Recent results obtained in TCABR (Tokamak Chauffage Alfven Bresilien) [J. H. F. Severo, I. C. Nascimento, V. S. Tsypin, and R. M. O. Galvao, Nucl. Fusion 43, 1047 (2003)] show a nonmonotonic variation of the poloidal rotation velocity at the position of major magnetic islands. In this paper, the associated effect of the magnetic islands on the radial profile of the electron temperature is discussed. Analytical temperature profiles are used to analyze the experimental data obtained with electron cyclotron emission radiometry. It is shown that the competition between strong anomalous perpendicular diffusive transport and parallel heat convection is the dominant mechanism for the oscillations observed in the radial profile of the electron temperature in TCABR
Applications of the electromagnetic Helmholtz resonator*
Stoneback, Russell Alan
An electromagnetic Helmholtz resonator comprised of a capacitor with an aperture is investigated theoretically and experimentally. It is proposed that this resonance may be described using effective impedances describing the capacitor and aperture, similar to lumped element descriptions of the acoustic Helmholtz resonator. The dipole impedance of an electromagnetic aperture is derived and verified using the finite element method. Incorporating standard network relations, the aperture impedance can be used to calculate radiated power. Measurements of a capacitor demonstrates that the transmitted voltage through the capacitor is modified by induced charges. An induced voltage is introduced, and predictions agree with observations. Measurements of a capacitor with an aperture in the grounded plate indicate that induced currents cancel the imaginary impedance of the aperture, and double the real impedance. The observed impedance is close to predictions using the derived aperture impedance, confirming the utility of the aperture impedance in describing the system. The numerically obtained aperture electromagnetic fields are similar to the Birkeland current distribution and the cross polar cap potential in the Earth's polar ionosphere, motivating a model where the polar ionosphere is treated as an effective aperture. It is proposed that this effective aperture interacts with the capacitor formed between the Earth and ionosphere, creating an electromagnetic Helmholtz resonator. Predictions made with this model agree with measurements of transmitted power and phase velocity by FAST during a geomagnetic substorm, measurements of the Ionospheric Alfven Resonator, and oscillations recorded by ground based magnetometers. The same effective aperture behavior is expected in sunspots and polar coronal holes. A peak is predicted in Alfven wave power across the transition region for waves with a 5 min. period that delivers an average power over 100 W/m2 to the corona, sufficient to
Tischenko, V. N.; Zakharov, Yu. P.; Posukh, V. G.; Berezutsky, A. G.; Boyarintsev, E. L.; Melekhov, A. V.; Miroshnichenko, I. B.; Shaikhislamov, I. F.
2017-10-01
Experimentally, conditions under which a train of periodic laser plasma bunches creates a train of Alfven and a single slow magnetosonic waves which propagate in a tube of the geomagnetic field in the ionosphere were determined.
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Enhanced Nonlinear Effects in Metamaterials and Plasmonics
Directory of Open Access Journals (Sweden)
C. Argyropoulos
2012-07-01
Full Text Available In this paper we provide an overview of the anomalous and enhanced nonlinear effects available when optical nonlinear materials are combined inside plasmonic waveguide structures. Broad, bistable and all-optical switching responses are exhibited at the cut-off frequency of these waveguides, characterized by reduced Q-factor resonances. These phenomena are due to the large field enhancement obtained inside specific plasmonic gratings, which ensures a significant boosting of the nonlinear operation. Several exciting applications are proposed, which may potentially lead to new optical components and add to the optical nanocircuit paradigm.
International Nuclear Information System (INIS)
Monk, P.
1993-01-01
The use of acoustic waves as probes to determine otherwise inaccessible properties of a medium is extremely widespread. Applications include sonar, medical imaging and non-destructive testing. Despite the importance of the applications, there is as yet no acceptable method for solving the full non-linear problem at resonance frequencies (frequencies at which the size of the features under investigations are approximately the wavelength of the incident acoustic field). The medical imaging problem, which consists in trying to determine the sound speed, density and absorption properties of a bounded inhomogeneous medium from scattered acoustic waves is the motivaiton for the investigation described in this paper. We shall present a solution technique for a standard model inverse acoustic scattering problem which consists of reconstructing the refractive index of an inhomogeneity from given far field data (far field data is essentially the measured scattered field at considerable distance from the inhomogeneity). This model inverse problem simplifies the inhomogeneity by neglecting density and absorption but includes two important features of the real problem: nonlinearity and illposedness. Furthermore the method we present can easily by extended to more general problems
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
Overview of magnetic nonlinear beam dynamics in the RHIC
International Nuclear Information System (INIS)
Luo, Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, F.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, G.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.
2009-01-01
In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed
Overview of magnetic nonlinear beam dynamics in the RHIC
Energy Technology Data Exchange (ETDEWEB)
Luo,Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, f.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, g.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.
2009-05-04
In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed.
Nonlinear interaction of waves in an inhomogeneous plasma
International Nuclear Information System (INIS)
Istomin, Ya.N.
1988-01-01
Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered
Scheuer, Jacob; Sun, Xiankai
Circular resonators are promising candidates for a wide range of applications, ranging from optical communication systems through basic research involving highly confined fields and strong photon-atom interactions to biochemical and rotation sensing. The main characteristics of circular resonators are the Q factor, the free spectral range (FSR), and the modal volume, where the last two are primarily determined by the resonator radius. The total internal reflection (TIR) mechanism used for guidance in "conventional" resonators couples these attributes and limits the ability to realize compact devices exhibiting large FSR, small modal volume, and high Q. Recently, a new class of annular resonator, based on a single defect surrounded by radial Bragg reflectors, has been proposed and analyzed. The radial Bragg confinement decouples the modal volume from the Q and paves the way for the realization of compact, low-loss resonators. These properties as well as the unique mode profile of these circular Bragg nanoresonators (CBNRs) and nanolasers (CBNLs) make the devices within this class an excellent tool to realize nanometer scale semiconductor lasers and ultrasensitive detectors, as well as to study nonlinear optics.
Resonant behaviour of MHD waves on magnetic flux tubes. III - Effect of equilibrium flow
Goossens, Marcel; Hollweg, Joseph V.; Sakurai, Takashi
1992-01-01
The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.
Building better oscillators using nonlinear dynamics and pattern ...
Indian Academy of Sciences (India)
work aimed to mitigate the bad effects of resonator nonlinearity on oscillator performance and to exploit the nonlinearity in novel ways to improve the performance. Our focus is on oscillators built from nanomechanical devices, but the ideas apply generally. This paper is a summary of work published in a number of papers ...
Padowitz, David; Matsiev, L; Kolosov, Oleg
2004-01-01
A sensor and methods for making and using the same in which a mechanical resonator is employed, comprising a resonator portion for resonating in a fluid without the substantial generation of acoustic waves; and an electrical connection between the resonator portion for oscillating and a source of an input signal; wherein the portion for resonating, the electrical connection or both includes a base material and a performance-tuning material that is different from the base material.
[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
Multiwave nonlinear couplings in elastic structures
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.
Nonlinear dynamics of the bimodal optical computer
Caulfield, H. John
1999-03-01
In the bimodal optical computer, linear and nonlinear acts occur in rapid succession generating solutions to Ax equals b. Both chaos and stochastic resonance can appear in some cases. This is the first observation of such complexity effects in optical processors.
Nonlinear Faraday rotation in samarium vapor
International Nuclear Information System (INIS)
Barkov, L.M.; Melik-Pashaev, D.A.; Zolotorev, M.S.
1988-01-01
Experiments on nonlinear magnetic optical (Faraday) rotation on resonance transitions of atomic samarium are described. Measurements were carried out on transitions with different angular momenta of upper and lower states: 1→0, 0→1 and 1→1. Qualitative explanations of observed phenomena are given
International Nuclear Information System (INIS)
Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas
2004-01-01
We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise
Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas
2004-01-01
We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems—an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise.
Tsiklauri, David
2015-04-01
Previous studies (e.g., Malara et al., Astrophys. J. 533, 523 (2000)) considered small-amplitude Alfven wave (AW) packets in Arnold-Beltrami-Childress (ABC) magnetic field using WKB approximation. They draw a distinction between 2D AW dissipation via phase mixing and 3D AW dissipation via exponentially divergent magnetic field lines. In the former case, AW dissipation time scales as S 1/3 and in the latter as log(S) , where S is the Lundquist number. In this work [1], linearly polarised Alfven wave dynamics in ABC magnetic field via direct 3D magnetohydrodynamic (MHD) numerical simulation is studied for the first time. A Gaussian AW pulse with length-scale much shorter than ABC domain length and a harmonic AW with wavelength equal to ABC domain length are studied for four different resistivities. While it is found that AWs dissipate quickly in the ABC field, contrary to an expectation, it is found the AW perturbation energy increases in time. In the case of the harmonic AW, the perturbation energy growth is transient in time, attaining peaks in both velocity and magnetic perturbation energies within timescales much smaller than the resistive time. In the case of the Gaussian AW pulse, the velocity perturbation energy growth is still transient in time, attaining a peak within few resistive times, while magnetic perturbation energy continues to grow. It is also shown that the total magnetic energy decreases in time and this is governed by the resistive evolution of the background ABC magnetic field rather than AW damping. On contrary, when the background magnetic field is uniform, the total magnetic energy decrease is prescribed by AW damping, because there is no resistive evolution of the background. By considering runs with different amplitudes and by analysing the perturbation spectra, possible dynamo action by AW perturbation-induced peristaltic flow and inverse cascade of magnetic energy have been excluded. Therefore, the perturbation energy growth is attributed
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Nonlinear waves and pattern dynamics
Pelinovsky, Efim; Mutabazi, Innocent
2018-01-01
This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...
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
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...
Nonlinear optical studies in semiconductor-doped glasses under ...
Indian Academy of Sciences (India)
Abstract. Nonlinear optical studies in semiconductor-doped glasses (SDGs) are per- formed under femtosecond laser pulse excitation. Z-scan experiments with 800 nm wave- length pulses are used to excite SDG samples in the resonance and non-resonance regimes. Schott colour glass filter OG 515 shows stronger ...
International Nuclear Information System (INIS)
Shukla, Nidhi; Mishra, Ruchi; Varma, P; Tiwari, M S
2008-01-01
This work studies the effect of ion and electron beam on kinetic Alfven wave (KAW) with general loss-cone distribution function. The kinetic theory has been adopted to evaluate the dispersion relation and damping rate of the wave in the presence of loss-cone distribution indices J. The variations in wave frequency ω and damping rate with perpendicular wave number k perpendicular ρ i (k perpendicular is perpendicular wave number and ρ i is ion gyroradius) and parallel wave number k parallel are studied. It is found that the distribution index J and ion beam velocity enhance the wave frequency at lower k perpendicular ρ i , whereas the electron beam velocity enhances the wave frequency at higher k perpendicular ρ i . The calculated values of frequency correspond to the observed values in the range 0.1-4 Hz. Increase in damping rate due to higher distribution indices J and ion beam velocity is observed. The effect of electron beam is to reduce the damping rate at higher k perpendicular ρ i . The plasma parameters appropriate to plasma sheet boundary layer are used. The results may explain the transfer of Poynting flux from the magnetosphere to the ionosphere. It is also found that in the presence of the loss-cone distribution function the ion beam becomes a sensitive parameter to reduce the Poynting flux of KAW propagating towards the ionosphere
Modelling nonlinearity in piezoceramic transducers: From equations to nonlinear equivalent circuits.
Parenthoine, D; Tran-Huu-Hue, L-P; Haumesser, L; Vander Meulen, F; Lematre, M; Lethiecq, M
2011-02-01
Quadratic nonlinear equations of a piezoelectric element under the assumptions of 1D vibration and weak nonlinearity are derived by the perturbation theory. It is shown that the nonlinear response can be represented by controlled sources that are added to the classical hexapole used to model piezoelectric ultrasonic transducers. As a consequence, equivalent electrical circuits can be used to predict the nonlinear response of a transducer taking into account the acoustic loads on the rear and front faces. A generalisation of nonlinear equivalent electrical circuits to cases including passive layers and propagation media is then proposed. Experimental results, in terms of second harmonic generation, on a coupled resonator are compared to theoretical calculations from the proposed model. Copyright © 2010 Elsevier B.V. All rights reserved.
Electrothermally Tunable Arch Resonator
Hajjaj, Amal Z.
2017-03-18
This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated microelectromechanical arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. An electrothermal voltage is applied between the anchors of the beam generating a current that controls the axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to an increase in its curvature, thereby increasing its resonance frequencies. We show here that the first resonance frequency can increase monotonically up to twice its initial value. We show also that after some electrothermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators. Analytical results based on the nonlinear Euler Bernoulli beam theory are generated and compared with the experimental data and the results of a multi-physics finite-element model. A good agreement is found among all the results. [2016-0291
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent
2018-03-01
The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.
Electrifying photonic metamaterials for tunable nonlinear optics.
Kang, Lei; Cui, Yonghao; Lan, Shoufeng; Rodrigues, Sean P; Brongersma, Mark L; Cai, Wenshan
2014-08-11
Metamaterials have not only enabled unprecedented flexibility in producing unconventional optical properties that are not found in nature, they have also provided exciting potential to create customized nonlinear media with high-order properties correlated to linear behaviour. Two particularly compelling directions are active metamaterials, whose optical properties can be purposely tailored by external stimuli in a reversible manner, and nonlinear metamaterials, which enable intensity-dependent frequency conversion of light waves. Here, by exploring the interaction of these two directions, we leverage the electrical and optical functions simultaneously supported in nanostructured metals and demonstrate electrically controlled nonlinear optical processes from a metamaterial. Both second harmonic generation and optical rectification, enhanced by the resonance behaviour in the metamaterial absorber, are modulated externally with applied voltage signals. Our results reveal an opportunity to exploit optical metamaterials as self-contained, dynamic electro-optic systems with intrinsically embedded electrical functions and optical nonlinearities.
International Nuclear Information System (INIS)
Tepikian, S.
1989-01-01
Siberian Snakes provide a practical means of obtaining polarized proton beams in large accelerators. The effect of snakes can be understood by studying the dynamics of spin precession in an accelerator with snakes and a single spin resonance. This leads to a new class of energy independent spin depolarizing resonances, called snake resonances. In designing a large accelerator with snakes to preserve the spin polarization, there is an added constraint on the choice of the vertical betatron tune due to the snake resonances
International Nuclear Information System (INIS)
Shore, B.W.
1977-01-01
The long-time average of level populations in a coherently-excited anharmonic sequence of energy levels (e.g., an anharmonic oscillator) exhibits sharp resonances as a function of laser frequency. For simple linearly-increasing anharmonicity, each resonance is a superposition of various multiphoton resonances (e.g., a superposition of 3, 5, 7, . . . photon resonances), each having its own characteristic width predictable from perturbation theory
NONLINEAR TIDES IN CLOSE BINARY SYSTEMS
International Nuclear Information System (INIS)
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-01-01
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing
Quenched noise and nonlinear oscillations in bistable multiscale systems
Kuehn, C.
2017-10-01
Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic setting. Yet, there is no theory regarding the quenched noise scenario of random parameters sampled on fixed time intervals, although this situation is often a lot more natural. Here we study a paradigmatic nonlinear oscillator of van-der-Pol/FitzHugh-Nagumo type under quenched noise as a piecewise-deterministic Markov process. There are several interesting effects such as period shifts and new different trapped types of small-amplitude oscillations, which can be captured analytically. Furthermore, we numerically discover quenched resonance and show that it differs significantly from previous finite-noise optimality resonance effects. This demonstrates that quenched oscillators can be viewed as a new building block of nonlinear dynamics.
849 RESONANCE | September 2013
Indian Academy of Sciences (India)
IAS Admin
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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.
Dispersion characteristics of a nonlinear elastic metamaterial
Directory of Open Access Journals (Sweden)
R. Khajehtourian
2014-12-01
Full Text Available We study wave dispersion in a one-dimensional nonlinear elastic metamaterial consisting of a thin rod with periodically attached local resonators. Our model is based on an exact finite-strain dispersion relation for a homogeneous solid, utilized in conjunction with the standard transfer matrix method for a periodic medium. The nonlinearity considered stems from large elastic deformation in the thin rod, whereas the metamaterial behavior is associated with the dynamics of the local resonators. We derive an approximate dispersion relation for this system and provide an analytical prediction of band-gap characteristics. The results demonstrate the effect of the nonlinearity on the characteristics of the band structure, including the size, location, and character of the band gaps. For example, large deformation alone may cause a pair of isolated Bragg-scattering and local-resonance band gaps to coalesce. We show that for a wave amplitude on the order of one-eighth of the unit cell size, the effect of the nonlinearity in the structure considered is no longer negligible when the unit-cell size is one-fourteenth of the wavelength or larger.
Parametric resonance in concrete beam-columns
Directory of Open Access Journals (Sweden)
Mamta R. Sharma
Full Text Available A dynamic instability, called parametric resonance, is exhibited by undampedelastic beam-columns when under the action of pulsating axial force. The scope of the existing theory of parametric resonance is restricted to physically linear beam-columns undergoing finite lateral displacements. In this Paper, the dynamic behaviour of physically nonlinear elastic cracked concrete beam-columns under pulsating axial force and constant lateral force is investigated. The constitutive equations derived earlier by Authors in the form of force-displacement relations are employed here to formulate equations of motion of the SDOF cantilever with mass lumped at its free end. The expected phenomenon of parametric resonance is exhibited in the form of regular subharmonic resonance at about the frequency ratio of two. Resonance peaks broaden with increase in pulsating force. Like damping, physical nonlinearity is also predicted to stabilize the dynamic response at resonance frequencies. In some particular statically unstable conditions, the loss of dynamic stability is shown to occur by divergence. Unexpectedly, similar phenomenon of parametric resonance is exhibited by these physically nonlinear beam-columns undergoing even small lateral displacements. The contribution made to the theory of parametric resonance and the potential relevance of the proposed theory to design of concrete beam-columns is discussed.
Finite-Difference Time-Domain Integration of Ultrafast Dynamics in Optical Resonators
National Research Council Canada - National Science Library
Basinger, Scott
1993-01-01
.... The resonator is a Fabry-Perot cavity that has a nonlinear absorbing material in the center. When an optical field of the resonant frequency is incident upon the cavity, the field intensity increases inside the cavity...
Nonlinear elliptic differential equations with multivalued nonlinearities
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Nonlinear elliptic differential equations with multivalued ... has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth .... A is upper semicontinuous (as a set-valued map) from every finite dimensional subspace of X into ...
Sahraoui, Fouad; Goldstein, Melvyn L.
2010-01-01
Over the past few decades, large-scales solar wind (SW) turbulence has been studied extensively, both theoretically and observationally. Observed power spectra of the low frequency turbulence, which can be described in the magnetohydrodynamic (MHD) limit, are shown to obey the Kolmogorov scaling, $k"{ -5/3 }$, down the local proton gyrofrequency ($C{ci} \\sim O.l$-Hz). Turbulence at frequencies above $C{ci}$ has not been thoroughly investigated and remains far less well understood. Above $C{ ci}$ the spectrum steepens to $\\sim f"{ -2.5}$ and a debate exists as to whether the turbulence has become dominated by dispersive kinetic Alfven waves (KA W) or by whistler waves, before it is dissipated at small scales, In a case study Sahraoui et al., PRL (2009) have reported the first direct determination of the dissipation range of solar wind turbulence near the electron gyroscale using the high resolution Cluster magnetic and electric field data (up to $10"2$-Hz in the spacecraft reference frame). Above the Doppler-shifted proton scale $C{\\rho i}$ a new inertial range with a scaling $\\sim f"{ -2.3}$ has been evidenced and shown to remarkably agree with theoretical predictions of a quasi-two-dimensional cascade into KA W turbulence. Here, we use a wider sample of data sets of small scale SW turbulence under different plasma conditions, and investigate under which physical criteria the KA W (or the whistler) turbulence may be observed to carry out the cascade at small scales, These new observations/criteria are compared to the predictions on the cascade and the (kinetic) dissipation from the Vlasov theory. Implications of the results on the heating problem of the solar wind will be discussed.
Farrugia, C. J.; Lugaz, N.; Alm, L.; Vasquez, B. J.; Argall, M. R.; Kucharek, H.; Matsui, H.; Torbert, R. B.; Lavraud, B.; Le Contel, O.; Shuster, J. R.; Burch, J. L.; Khotyaintsev, Y. V.; Giles, B. L.; Fuselier, S. A.; Gershman, D. J.; Ergun, R.; Eastwood, J. P.; Cohen, I. J.; Dorelli, J.; Lindqvist, P. A.; Strangeway, R. J.; Russell, C. T.; Marklund, G. T.; Paulson, K.; Petrinec, S.; Phan, T.; Pollock, C.
2017-12-01
We present MMS) observations during two dayside magnetopause crossingsunder hitherto unexamined conditions: (i) when the bow shock is weakening and the solar wind transitioning to sub-Alfvenic flow, and (ii) when it is reforming. Interplanetary conditions consist of a magnetic cloud with (i) a strong B ( 20 nT) pointing south, and (ii) a density profile with episodic decreases to values of 0.3 /cc followed by moderate recovery. During the crossings he magnetosheath magnetic field is stronger than the magnetosphere field by a factor of 2.2. As a result, during the outbound crossing through the ion diffusion region, MMS observed an inversion of relative positions of the X and stagnation (S) lines from that typically the case: the S line was closer to the magnetosheath side. The S-line appears in the form of a slow expansion fan near which most of the energy dissipation is taking place. While in the magnetosphere between the crossings, MMS observed strong field and flow perturbations, which we argue to be due kinetic Alfvén waves.During the reconnection interval, whistler mode waves generated by an electron temperature anisotropy (Tperp>Tpar) were observed. Another aim of the paper isto distinguish bow shock-induced field and flow perturbations from reconnection-related signatures.The high resolution MMS data together with 2D hybrid simulations of bow shock dynamics helped us to distinguish between the two sources. We show examples of bow shock-related effects (such as heating) and reconnection effects such as accelerated flows satisfying the Walen relation.
Resonant modes in Josephson structures
International Nuclear Information System (INIS)
Paterno, G.
1985-01-01
It is well-know that a Josephson junction held at finite voltage V generates an alternating current at a frequency *o=(2e/h)V. When the junction is coupled to an external resonator self-induced dc current modes occur in the structure. The nonlinear interaction with the ac Josephson radiation gives rise to current singularities at voltages corresponding to the resonance frequencies of the resonator. These resonances appear in the dc current voltage characteristics as current singularities. They are due to a conversion of dc power to ac power that in turn is internally dissipated. In a tunneling junction the resonator is formed of the two superconducting electrodes separated by the oxide layer. In a two junctions interferometer the resonant structure is formed of the loop inductance and the junction capacitances. A good knowledge of the behaviour of these singularities is very important when switching properties are considered or ac power has to be extracted from the structure. In this paper we review the behaviour of resonant modes in Josephson junctions coupled to a resonant structure. A comparison between experimental data and the theoretical description at present available is reported
A nonlinear analysis of the EHF booster
International Nuclear Information System (INIS)
Colton, E.P.; Shi, D.
1987-01-01
We have analyzed particle motion at 1.2 GeV with assumption of nonlinearities arising from non-linear space charge forces and from the lattice sextupoles which are tuned to cancel the machine chromaticity. In the first case the motion is as expected and there are no problems as long as the x and y betatron tunes are separated by an integer or more. In the second case the motion is stable so long as the betatron amplitudes do not exceed values corresponding to beam normalized emittance of 100 mm-mr; when this occurs the effects of fifth-order betatron resonances are observed. 3 refs
An Ultra-Efficient Nonlinear Platform: AlGaAs-On-Insulator
DEFF Research Database (Denmark)
Pu, Minhao; Ottaviano, Luisa; Semenova, Elizaveta
]. Though tremendous technological work in those platforms have greatly improved device performances, the relatively low intrinsic material nonlinearities of those materials limit device performances concerning efficiency. Therefore, an integrated nonlinear platform that combines a high material...... ) and microring resonators with quality factors on the order of 105 [6]. The large effective nonlinearity of such platform enables efficient nonlinear processes such as high-speed optical signal processing [7], supercontinuum generation, and Kerr frequency comb generation [8]. Moreover, the required operation...
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
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.
Winckler, J. R.; Erickson, K. N.; Abe, Y.; Steffen, J. E.; Malcolm, P. R.
1985-01-01
Orthogonal probes on a free-flying plasma diagnostics payload are used to study ELF electric disturbances in the auroral ionosphere that are due to the injection of powerful electron beams. Frequency spectrograms are presented for various pitch angles, pulsing characteristics, and other properties of the injected beams; the large scale DC ionospheric convection electric field is measured, together with auroral particle precipitation, visual auroral forms, and ionospheric parameters. In view of the experimental results obtained, it is postulated that the observed ELF waves are in the Alfven and drift modes, and are generated by the positive vehicle potential during beam injection.
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz nonlinear...
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.
On-line control of the nonlinear dynamics for synchrotrons
Bengtsson, J.; Martin, I. P. S.; Rowland, J. H.; Bartolini, R.
2015-07-01
We propose a simple approach to the on-line control of the nonlinear dynamics in storage rings, based on compensation of the nonlinear resonance driving terms using beam losses as the main indicator of the strength of a resonance. The correction scheme is built on the analysis of the resonance driving terms in first perturbative order and on the possibility of using independent power supplies in the sextupole magnets, which is nowadays present in many synchrotron light sources. Such freedom allows the definition of "smart sextupole knobs" attacking each resonance separately. The compensation scheme has been tested at the Diamond light source and proved to be effective in opening up the betatron tune space, resonance free, available to the electron beam and to improve the beam lifetime.
On-line control of the nonlinear dynamics for synchrotrons
Directory of Open Access Journals (Sweden)
J. Bengtsson
2015-07-01
Full Text Available We propose a simple approach to the on-line control of the nonlinear dynamics in storage rings, based on compensation of the nonlinear resonance driving terms using beam losses as the main indicator of the strength of a resonance. The correction scheme is built on the analysis of the resonance driving terms in first perturbative order and on the possibility of using independent power supplies in the sextupole magnets, which is nowadays present in many synchrotron light sources. Such freedom allows the definition of “smart sextupole knobs” attacking each resonance separately. The compensation scheme has been tested at the Diamond light source and proved to be effective in opening up the betatron tune space, resonance free, available to the electron beam and to improve the beam lifetime.
International Nuclear Information System (INIS)
1977-03-01
At the 1975 Particle Accelerator Conference it was reported that a class of resonances were observed in SPEAR II that had not appeared before in SPEAR I. While the existence of sideband resonances of the main betatron oscillation frequencies has been previously observed and analyzed, the resonances observed in SPEAR do not appear to be of the same variety. Experiments were performed at SPEAR to identify the mechanism believed to be the most likely explanation. Some of the current experimental knowledge and theoretical views on the source of these resonances are presented
International Nuclear Information System (INIS)
Tepikian, S.
1988-01-01
Siberian Snakes provide a practical means of obtaining polarized proton beams in large accelerators. The effect of snakes can be understood by studying the dynamics of spin precession in an accelerator with snakes and a single spin resonance. This leads to a new class of energy independent spin depolarizing resonances, called snake resonances. In designing a large accelerator with snakes to preserve the spin polarization, there is an added constraint on the choice of the vertical betatron tune due to the snake resonances. 11 refs., 4 figs
Modelling of a bridge-shaped nonlinear piezoelectric energy harvester
International Nuclear Information System (INIS)
Gafforelli, G; Corigliano, A; Xu, R; Kim, S G
2013-01-01
Piezoelectric MicroElectroMechanical Systems (MEMS) energy harvesting is an attractive technology for harvesting small magnitudes of energy from ambient vibrations. Increasing the operating frequency bandwidth of such devices is one of the major issues for real world applications. A MEMS-scale doubly clamped nonlinear beam resonator is designed and developed to demonstrate very wide bandwidth and high power density. In this paper a first complete theoretical discussion of nonlinear resonating piezoelectric energy harvesting is provided. The sectional behaviour of the beam is studied through the Classical Lamination Theory (CLT) specifically modified to introduce the piezoelectric coupling and nonlinear Green-Lagrange strain tensor. A lumped parameter model is built through Rayleigh-Ritz Method and the resulting nonlinear coupled equations are solved in the frequency domain through the Harmonic Balance Method (HBM). Finally, the influence of external load resistance on the dynamic behaviour is studied. The theoretical model shows that nonlinear resonant harvesters have much wider power bandwidth than that of linear resonators but their maximum power is still bounded by the mechanical damping as is the case for linear resonating harvesters
Nonlinear FMR spectra in yttrium iron garnet
Directory of Open Access Journals (Sweden)
Yu.M. Bunkov, P.M. Vetoshko, I.G. Motygullin, T.R. Safin, M.S. Tagirov, N.A. Tukmakova
2015-12-01
Full Text Available Results of demagnetizing effect studies in yttrium iron garnet Y3Fe5O12 thin films are reported. Experiments were performed on X-Band of electron paramagnetic resonance spectrometer at room temperature. The ferromagnetic resonance (FMR spectra were obtained for one-layer single crystal YIG films for different values of the applied microwave power. Nonlinear FMR spectra transformation by the microwave power increasing in various directions of magnetic field sweep was observed. It is explained by the influence of the demagnetization action of nonequilibrium magnons.
Design and development of a parametrically excited nonlinear energy harvester
International Nuclear Information System (INIS)
Yildirim, Tanju; Ghayesh, Mergen H.; Li, Weihua; Alici, Gursel
2016-01-01
Highlights: • A parametrically broadband energy harvester was fabricated. • Strong softening-type nonlinear behaviour was observed. • Experiments were conducted showing the large bandwidth of the device. - Abstract: An energy harvester has been designed, fabricated and tested based on the nonlinear dynamical response of a parametrically excited clamped-clamped beam with a central point-mass; magnets have been used as the central point-mass which pass through a coil when parametrically excited. Experiments have been conducted for the energy harvester when the system is excited (i) harmonically near the primary resonance; (ii) harmonically near the principal parametric resonance; (iii) by means of a non-smooth periodic excitation. An electrodynamic shaker was used to parametrically excite the system and the corresponding displacement of the magnet and output voltages of the coil were measured. It has been shown that the system displays linear behaviour at the primary resonance; however, at the principal parametric resonance, the motion characteristic of the magnet substantially changed displaying a strong softening-type nonlinearity. Theoretical simulations have also been conducted in order to verify the experimental results; the comparison between theory and experiment were within very good agreement of each other. The energy harvester developed in this paper is capable of harvesting energy close to the primary resonance as well as the principal parametric resonance; the frequency-band has been broadened significantly mainly due to the nonlinear effects as well as the parametric excitation.
Mass, momentum, and energy flux conservation between linear and nonlinear steady-state wave groups
Liu, Zeng; Xu, Dali; Liao, Shijun
2017-12-01
This paper provides a mass, momentum, and energy flux conservation analysis between the linear and nonlinear steady-state wave groups. Convergent high-order solutions for nonlinear wave groups with multiple steady-state near resonances in deep water have been obtained by means of the homotopy analysis method. The small divisors associated with nearly resonant components are transformed to singularities that are originally caused by exact resonances by a piecewise auxiliary linear operator. Both two primary components and other nearly resonant ones are considered in the initial guess to search for finite amplitude wave groups. It is found that as nonlinearity of wave groups increases, more wave components appear in the spectrum due to the nearly resonant interactions. The nonlinear wave fields change from the initial bi-chromatic waves that contain only two nontrivial primary components into the steady-state resonant waves that contain both two primary components and other nearly resonant ones. The conservation of mean rates of mass, momentum, and energy fluxes is established between the nonlinear wave groups and linear waves that are combined by two primary components with the same frequencies as in nonlinear wave groups. Comparison of the linear and nonlinear wave fields shows that the nearly resonant components influence the wave field distribution significantly: the nonlinear free surfaces have more peaked crests, steeper troughs, and more flatten wave nodes, and the related velocities at the crests and troughs increase more rapidly with the nonlinearity. All of these findings are helpful to enrich and deepen our understanding about nonlinear wave groups.
DEFF Research Database (Denmark)
2014-01-01
The present invention relates to a method for detecting photo-thermal absorbance of a material utilising a mechanically temperature sensitive resonator (20) and a sample being arrange in thermal communication with the temperature sensitive resonator. The present invention further relates...
Review on resonance cone fields
International Nuclear Information System (INIS)
Ohnuma, Toshiro.
1980-02-01
Resonance cone fields and lower hybrid heating are reviewed in this report. The resonance cone fields were reported by Fisher and Gould, and they proposed the use of the measurement of resonance cones and structure as a diagnostic tool to determine the plasma density and electron temperature in magnetoplasma. After the resonance cone, a wave-like disturbance persists. Ohnuma et al. have measured bending, reflection and ducting of resonance cones in detail. The thermal modes in inhomogeneous magnetoplasma were seen. The reflection of thermal mode near an electron plasma frequency layer and an insulating plate has been observed. The non-linear effects of resonance cones is reported. Monochromatic electron beam produces the noise of broad band whistler mode. Lower hybrid waves have been the subject of propagation from the edge of plasma to the lower hybrid layer. Linear lower hybrid waves were studied. The lower hybrid and ion acoustic waves radiated from a point source were observed. The parametric decay of finite-extent, cold electron plasma waves was studied. The lower hybrid cone radiated from a point source going along magnetic field lines was observed. Several experimental data on the lower hybrid heating in tokamak devices have been reported. The theories on resonance cones and lower hybrid waves are introduced in this report. (Kato, T.)
Response of MDOF strongly nonlinear systems to fractional Gaussian noises
Energy Technology Data Exchange (ETDEWEB)
Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)
2016-08-15
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
Second harmonic generation in resonant optical structures
Energy Technology Data Exchange (ETDEWEB)
Eichenfield, Matt; Moore, Jeremy; Friedmann, Thomas A.; Olsson, Roy H.; Wiwi, Michael; Padilla, Camille; Douglas, James Kenneth; Hattar, Khalid Mikhiel
2018-01-09
An optical second-harmonic generator (or spontaneous parametric down-converter) includes a microresonator formed of a nonlinear optical medium. The microresonator supports at least two modes that can be phase matched at different frequencies so that light can be converted between them: A first resonant mode having substantially radial polarization and a second resonant mode having substantially vertical polarization. The first and second modes have the same radial order. The thickness of the nonlinear medium is less than one-half the pump wavelength within the medium.
Optical resonance and two-level atoms
Allen, L
1987-01-01
""Coherent and lucid…a valuable summary of a subject to which [the authors] have made significant contributions by their own research."" - Contemporary PhysicsOffering an admirably clear account of the basic principles behind all quantum optical resonance phenomena, and hailed as a valuable contribution to the literature of nonlinear optics, this distinguished work provides graduate students and research physicists probing fields such as laser physics, quantum optics, nonlinear optics, quantum electronics, and resonance optics an ideal introduction to the study of the interaction of electroma
Metamaterial-Enhanced Nonlinear Terahertz Spectroscopy
Directory of Open Access Journals (Sweden)
Zhang X.
2013-03-01
Full Text Available We demonstrate large nonlinear terahertz responses in the gaps of metamaterial split ring resonators in several materials and use nonlinear THz transmission and THz-pump/THz-probe spectroscopy to study the nonlinear responses and dynamics. We use the field enhancement in the SRR gaps to initiate high-field phenomena at lower incident fields. In vanadium dioxide, we drive the insulator-to-metal phase transition with high-field THz radiation. The film conductivity increases by over two orders of magnitude and the phase transition occurs on a several picosecond timescale. In gallium arsenide, we observe high-field transport phenomena, including mobility saturation and impact ionization. The carrier density increases by up to ten orders of magnitude at high fields. At the highest fields, we demonstrate THz-induced damage in both vanadium dioxide and gallium arsenide.
Quantum Nonlinear Optics in Optomechanical Nanoscale Waveguides.
Zoubi, Hashem; Hammerer, Klemens
2017-09-22
We show that strong nonlinearities at the few photon level can be achieved in optomechanical nanoscale waveguides. We consider the propagation of photons in cm-scale one-dimensional nanophotonic structures where stimulated Brillouin scattering (SBS) is strongly enhanced by radiation pressure coupling. We introduce a configuration that allows slowing down photons by several orders of magnitude via SBS from sound waves using two pump fields. Slowly propagating photons can then experience strong nonlinear interactions through virtual off-resonant exchange of dispersionless phonons. As a benchmark we identify requirements for achieving a large cross-phase modulation among two counterpropagating photons applicable for photonic quantum gates. Our results indicate that strongly nonlinear quantum optics is possible in continuum optomechanical systems realized in nanophotonic structures.
Nonlinear Dynamics of Electrostatically Actuated MEMS Arches
Al Hennawi, Qais M.
2015-05-01
In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using a multi- mode Galarkin Reduced Order Model (ROM). We investigate the static response of the arch experimentally where we show several jumps due to the snap-through instability. Experimentally, a case study of in-plane silicon micromachined arch is studied and its mechanical behavior is measured using optical techniques. We develop an algorithm to extract various parameters that are needed to model the arch, such as the induced axial force, the modulus of elasticity, and the initially induced initial rise. After that, we excite the arch by a DC electrostatic force superimposed to an AC harmonic load. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. Also, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Then, we excite the arch by an electric load of two AC frequency components, where we report a combination resonance of the summed type. Agreement is reported among the theoretical and experimental work.
Nonlinear acoustics of micro-inhomogeneous media
Nazarov, Veniamin E.; Ostrovsky, Lev A.; Soustova, Irina A.; Sutin, Aleksandr M.
1988-01-01
Acoustic waves can interact in micro-inhomogeneous media much more intensively than in homogeneous media. This has been repeatedly observed in experiments with ground species, marine sediments, porous materials and metals. This paper considers two models of such media which seem to be applicable to the description of these results. One of them is based on the consideration of nonlinear sound scattering by separate spherical cavities in liquids and solids. The second model is based on the phenomenological stress-deformation relation in solids with microplasticity which often has hysteresis (heritage) properties associated with the micro-inhomogeneities. In metals, for example, it is caused by the movement of dislocations. Different nonlinear effects in such media (harmonic and combination frequency generation, nonlinear, variations of resonance frequency amplitude-dependent losses) are considered. Some results of experiments with metallic resonators supporting the theory developed here are also presented. These mechanisms may determine the nonlinear properties of real soils and rocks summarized in a table given in the paper.
Signatures of Nonlinear Cavity Optomechanics in the Weak Coupling Regime
Børkje, K.; Nunnenkamp, A.; Teufel, J. D.; Girvin, S. M.
2013-08-01
We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong laser drive is detuned by half the mechanical frequency, optomechanically induced transparency also occurs due to resonant two-photon processes. The cavity response to a second probe drive is in this case nonlinear in the probe power. These effects should be observable with optomechanical coupling strengths that have already been realized in experiments.
Single-photon all-optical switching using coupled microring resonators
Indian Academy of Sciences (India)
Abstract. We study the nonlinear phase response of a microring resonator coupled to a bus waveguide and the use of this nonlinear phase shift to store information in the microring resonator and enhance the switching characteristics of a Mach–Zehnder interferometer (MZI). By introducing coupling between adjacent ...
Resonance controlled transport in phase space
Leoncini, Xavier; Vasiliev, Alexei; Artemyev, Anton
2018-02-01
We consider the mechanism of controlling particle transport in phase space by means of resonances in an adiabatic setting. Using a model problem describing nonlinear wave-particle interaction, we show that captures into resonances can be used to control transport in momentum space as well as in physical space. We design the model system to provide creation of a narrow peak in the distribution function, thus producing effective cooling of a sub-ensemble of the particles.
Nonlinear saturation of the trapped-ion mode
International Nuclear Information System (INIS)
LaQuey, R.E.; Mahajan, S.M.; Rutherford, P.H.; Tang, W.M.
1974-11-01
A nonlinear model of the collisional trapped-ion mode in tokamak geometry is presented, in which the energy in long wavelength instabilities is transferred to short wavelength modes which are then damped by ion bounce resonances. Near marginal stability, the saturation of a single unstable Fourier mode is computed. Far from marginal stability, steady state nonlinear solitary waves containing many Fourier modes are found. Particle transport is computed in both cases. (auth)
Nonlinear mechanism of tsunami wave generation by atmospheric disturbances
Pelinovsky, E.; Talipova, T.; Kurkin, A.; Kharif, C.
2001-01-01
The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation ...
Fano resonances from gradient-index metamaterials.
Xu, Yadong; Li, Sucheng; Hou, Bo; Chen, Huanyang
2016-01-27
Fano resonances - resonant scattering features with a characteristic asymmetric profile - have generated much interest, due to their extensive and valuable applications in chemical or biological sensors, new types of optical switches, lasers and nonlinear optics. They have been observed in a wide variety of resonant optical systems, including photonic crystals, metamaterials, metallic gratings and nanostructures. In this work, a waveguide structure is designed by employing gradient-index metamaterials, supporting strong Fano resonances with extremely sharp spectra. As the changes in the transmission spectrum originate from the interaction of guided modes from different channels, instead of resonance structures or metamolecules, the Fano resonances can be observed for both transverse electric and transverse magnetic polarizations. These findings are verified by fine agreement with analytical calculations and experimental results at microwave, as well as simulated results at near infrared frequencies.
Ooi, Kelvin J. A.; Tan, Dawn T. H.
2017-10-01
The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Yokozawa, Hiroki; Twiefel, Jens; Weinstein, Michael; Morita, Takeshi
2017-07-01
Controlling the resonant frequency of ultrasonic transducers is important to achieve the excellent performance of ultrasonic devices. The resonant frequency can be shifted by a nonlinear effect or by increasing the temperature under high-power operation. We propose a resonant frequency control method during the transducer’s operation that enables the dynamic compensation of resonant frequency shifts. To realize this, a transducer with passive piezoelectric parts was fabricated. By controlling the electric boundary condition of the passive piezoelectric parts between short and open by utilizing a metal-oxide-semiconductor field-effect transistor (MOSFET), the stiffness was changed, thus modifying the resonant frequency. In both simulation and experiment, the resonant frequency was modified successfully by controlling the switching duty ratio of the MOSFET. Additionally, a system for exciting a transducer at a resonant state with a wide frequency band was demonstrated.
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.
Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate
Hao, Y. X.; Chen, L. H.; Zhang, W.; Lei, J. G.
2008-05-01
An analysis on the nonlinear dynamics of a simply supported functionally graded materials (FGMs) rectangular plate subjected to the transversal and in-plane excitations is presented in a thermal environment for the first time. Material properties are assumed to be temperature dependent. Based on Reddy's third-order plate theory, the nonlinear governing equations of motion for the FGM plates are derived using Hamilton's principle. Galerkin's method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined parametric and external excitations. The resonant case considered here is 1:1 internal resonance and principal parametric resonance. The asymptotic perturbation method is utilized to obtain four-dimensional nonlinear averaged equation. The numerical method is used to find the nonlinear dynamic responses of the FGM rectangular plate. It was found that periodic, quasi-periodic solutions and chaotic motions exist for the FGM rectangular plates under certain conditions. It is believed that the forcing excitations f1 and f2 can change the form of motions for the FGM rectangular plate.
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
Advances in chemical physics modern nonlinear optics, pt.1
Rice, Stuart A
2009-01-01
Partial table of contents: Hyper-Rayleigh and Hyper-Raman Rotational and Vibrational Spectroscopy (T. Bancewicz & Z. Ożgo). Polarization Properties of Hyper-Rayleigh and Hyper-Raman Scatterings (M. Kozierowski). Fast Molecular Reorientation in Liquid Crystals Probed by Nonlinear Optics (J. Lalanne, et al.). Nonlinear Propagation of Laser Light of Different Polarizations (G. Rivoire). Nonlinear Magneto-Optics of Magnetically Ordered Crystals (R. Zawodny). Dynamical Questions in Quantum Optics (A. Shumovsky). Quantum Resonance Fluorescence from Mutually Correlated Atoms (Z. Fi
Visualization of nonlinear kernel models in neuroimaging by sensitivity maps
DEFF Research Database (Denmark)
Rasmussen, P.M.; Madsen, Kristoffer H; Lund, T.E.
on visualization of such nonlinear kernel models. Specifically, we investigate the sensitivity map as a technique for generation of global summary maps of kernel classification methods. We illustrate the performance of the sensitivity map on functional magnetic resonance (fMRI) data based on visual stimuli. We...... show that the performance of linear models is reduced for certain scan labelings/categorizations in this data set, while the nonlinear models provide more flexibility. We show that the sensitivity map can be used to visualize nonlinear versions of kernel logistic regression, the kernel Fisher...
Nonlinearities in Josephson-photonics
Energy Technology Data Exchange (ETDEWEB)
Kubala, Bjoern; Ankerhold, Joachim [Institute for Complex Quantum Systems and IQST, Ulm University, Ulm (Germany)
2016-07-01
Embedding a voltage-biased Josephson junction within a high-Q superconducting microwave cavity provides a new way to explore the interplay of the tunneling transfer of charges and the emission and absorption of light. While for weak driving the system can be reduced to simple cases, such as a (damped) harmonic or parametric oscillator, the inherent nonlinearity of the Josephson junction allows to access regimes of strongly non-linear quantum dynamics. Classically, dynamical phenomena such as thresholds for higher-order resonances, other bifurcations, and up- and down-conversion have been found. Here, we will investigate how and to which extent these features appear in the deep quantum regime, where charge quantization effects are crucial. Theory allows to employ phase-space quantities, such as the Wigner-density of the cavity mode(s), but also observables amenable to more immediate experimental access, such as correlations in light emission and charge transport, to probe these novel non-equilibrium transitions.
Gradient-based optimization in nonlinear structural dynamics
DEFF Research Database (Denmark)
Dou, Suguang
, 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......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...... coefficients are calculated directly from a nonlinear finite element model. Based on the analysis and the characterization, a new class of optimization problems is studied. In the optimization, design sensitivity analysis is performed by using the adjoint method which is suitable for large-scale structural...
Nonlinear Cyclotron absorption of a hole doppleron in cadmium
Energy Technology Data Exchange (ETDEWEB)
Voloshin, I.F.; Bugal' ter, G.A.; Demikhovskii, V.Y.; Fisher, L.M.; Yudin, V.A.
1977-10-01
We investigated experimentally the nonlinear behavior of the impedance of a cadmium plate in the region of existence of the hole doppleron. It is shown theoretically that this phenomenon can be attributed to nonlinear cyclotron absorption of the wave in the metal. A theory of nonlinear cyclotron absorption of a hole doppleron in cadmium is constructed. The nonlinearity is due to the influence of the wave magnetic field H that alters the trajectories of the resonant electrons responsible for the cyclotron asorption. The Lorentz force connected with the field H modulates the particle velocity along the magnetic field at a characteristic frequency ..omega../sub 0/ proportional to the square root of the wave amplitude. The modulation of the longitudinal particle velocity leads to violation of the condition of their resonant interaction with the wave, as a result of which the absorption coefficient decreases. The nonlinearity is significant when the frequency ..omega../sub 0/ is large compared with the electron-collision frequency. A decrease of the cyclotron absorption changes radically the picture of the surface-impedance oscillations of the plate in the magnetic field. We studied in the experiment the influence of the temperature, of the angle of inclination of the magnetic field, and of the frequency on the nonlinear-effect threshold field that separates the regions of linear and nonlinear behavior of the sample impedance. The measurement results are in qualitative agreement with the conclusions of the theory.
Linear and nonlinear optical properties of azobenzene derivatives.
Krawczyk, P; Kaczmarek, A; Zaleśny, R; Matczyszyn, K; Bartkowiak, W; Ziółkowski, M; Cysewski, P
2009-06-01
The results of computations of spectroscopic parameters of lowest-lying electronic excited states of azobenezene derivatives are presented. The analysis of experimentally recorded spectra was supported by quantum chemical calculations using density functional theory. The theoretically determined resonant (two-photon absorption probabilities) and non-resonant (first-order hyperpolarisability) nonlinear optical properties are also discussed, with an eye towards the performance of recently proposed long-range corrected (LRC) schemes (LC-BLYP and CAM-B3LYP functionals).
Modelling a singly resonant, intracavity ring optical parametric oscillator
DEFF Research Database (Denmark)
Buchhave, Preben; Tidemand-Lichtenberg, Peter; Wei, Hou
2003-01-01
We study theoretically and experimentally the dynamics of a single-frequency, unidirectional ring laser with an intracavity nonlinear singly resonant OPO-crystal in a coupled resonator. We find for a range of operating conditions good agreement between model results and measurements of the laser...
Improved switching using Fano resonances in photonic crystal structures
DEFF Research Database (Denmark)
Heuck, Mikkel; Kristensen, Philip Trøst; Elesin, Yuriy
2013-01-01
difference time domain simulations taking into account the signal bandwidth. The results suggest a significant energy reduction by employing Fano resonances compared to more well established Lorentzian resonance structures. A specific example of a Kerr nonlinearity shows an order of magnitude energy...
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Nonlinear Optics and Applications
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
International Nuclear Information System (INIS)
Panis, T.
2010-12-01
Direct damping rate measurements of Alfven eigenmodes (AE) are obtained using the active MHD spectroscopy system installed on the JET tokamak. The system was recently equipped with new antennas, designed to study especially the modes of intermediate toroidal mode number n, ¦n¦ = 3 -- 15, as the AEs of this range are most prone to destabilization by the fast particles in JET and in future burning plasma experiments such as ITER. The broad n-spectrum that is driven by the new antennas and the more localized structure of intermediate-n AEs has important implications for the ability to measure damping rates of intermediate n. To obtain an extended database of high accuracy individual-n measurements, experimental work on technical and engineering aspects was indispensable both on the excitation side and on the detection side. On the excitation side, the electrical model of the AE exciter has been constructed during this thesis. The model is used to determine the operational capabilities of the exciter with the new antennas, to optimize the antenna currents and to design the relevant impedance matching circuits. On the detection side, the excitation of multiple-n, degenerate AEs at close frequencies prompted for a sophisticated method to correctly estimate the n-spectrum of the plasma response. To this end, a sparse spectrum representation method was adapted to deal with the complex and real-time data produced by the active MHD spectroscopy system. The n-decomposition of the plasma response requires an accurate relative calibration of the magnetic pick-up coils. An in situ method was developed and applied for the calibration of the coils using the direct coupling to the new AE antennas. A large collection of damping rate measurements of, mainly, toroidal AEs (TAEs) was obtained during the 2008/2009 JET experimental campaigns following the technical optimization of the antenna system. Selected measurements of ¦n¦ = 3, 4 and ¦n¦ = 7 TAEs are compared to the plasma
Asteroid proper elements and secular resonances
Knezevic, Zoran; Milani, Andrea
1992-01-01
In a series of papers (e.g., Knezevic, 1991; Milani and Knezevic, 1990; 1991) we reported on the progress we were making in computing asteroid proper elements, both as regards their accuracy and long-term stability. Additionally, we reported on the efficiency and 'intelligence' of our software. At the same time, we studied the associated problems of resonance effects, and we introduced the new class of 'nonlinear' secular resonances; we determined the locations of these secular resonances in proper-element phase space and analyzed their impact on the asteroid family classification. Here we would like to summarize the current status of our work and possible further developments.
Soliton resonance in bose-einstein condensate
Zak, Michail; Kulikov, I.
2002-01-01
A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Esposito, A.; Polosa, A.D.
2016-01-01
Multiquark resonances are undoubtedly experimentally observed. The number of states and the amount of details on their properties has been growing over the years. It is very recent the discovery of two pentaquarks and the confirmation of four tetraquarks, two of which had not been observed before. We mainly review the theoretical understanding of this sector of particle physics phenomenology and present some considerations attempting a coherent description of the so called X and Z resonances. The prominent problems plaguing theoretical models, like the absence of selection rules limiting the number of states predicted, motivate new directions in model building. Data are reviewed going through all of the observed resonances with particular attention to their common features and the purpose of providing a starting point to further research.
Nonlinear Optical Magnetism Revealed by Second-Harmonic Generation in Nanoantennas.
Kruk, Sergey S; Camacho-Morales, Rocio; Xu, Lei; Rahmani, Mohsen; Smirnova, Daria A; Wang, Lei; Tan, Hark Hoe; Jagadish, Chennupati; Neshev, Dragomir N; Kivshar, Yuri S
2017-06-14
Nonlinear effects at the nanoscale are usually associated with the enhancement of electric fields in plasmonic structures. Recently emerged new platform for nanophotonics based on high-index dielectric nanoparticles utilizes optically induced magnetic response via multipolar Mie resonances and provides novel opportunities for nanoscale nonlinear optics. Here, we observe strong second-harmonic generation from AlGaAs nanoantennas driven by both electric and magnetic resonances. We distinguish experimentally the contribution of electric and magnetic nonlinear response by analyzing the structure of polarization states of vector beams in the second-harmonic radiation. We control continuously the transition between electric and magnetic nonlinearities by tuning polarization of the optical pump. Our results provide a direct observation of nonlinear optical magnetism through selective excitation of multipolar nonlinear modes in nanoantennas.
DEFF Research Database (Denmark)
Brooks, Anthony Lewis
2013-01-01
tailored channeling of sensory stimulus aligned as ‘art-making’ and ‘game playing’ core experiences. Thus, affecting brain plasticity and human motoric-performance via the adaptability (plasticity) of digital medias result in closure of the human afferent-efferent neural feedback loop closure through...... the unencumbered motion-to-computer-generated activities - ‘Music Making’, ‘Painting’, ‘Robotic’ and ‘Video Game’ control. A focus of this position paper is to highlight how Aesthetic Resonance, in this context, relates to the growing body of research on Neuroaesthetics to evolve Neuroaesthetic Resonance....
A Broadband Ultrathin Nonlinear Switching Metamaterial
Directory of Open Access Journals (Sweden)
E. Zarnousheh Farahani
2017-05-01
Full Text Available In this paper, an ultrathin planar nonlinear metamaterial slab is designed and simulated. Nonlinearity is provided through placing diodes in each metamaterial unit cell. The diodes are auto-biased and activated by an incident wave. The proposed structure represents a broadband switching property between two transmission and reflection states depending on the intensity of the incident wave. High permittivity values are presented creating a near zero effective impedance at low power states, around the second resonant mode of the structure unit cell; as the result, the incident wave is reflected. Increasing the incident power to the level which can activate the loaded diodes in the structure results in elimination of the resonance and consequently a drop in the permittivity values near the permeability one as well as a switch to the transmission state. A full wave as well as a nonlinear simulations are performed. An optimization method based on weed colonization is applied to the unit cell of the metamaterial slab to achieve the maximum switching bandwidth. The structure represents a 24% switching bandwidth of a 10 dB reduction in the reflection coefficient.
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
Indian Academy of Sciences (India)
IAS Admin
817. RESONANCE ⎜ September 2013. Page 2. 818. RESONANCE ⎜ September 2013. Page 3. 819. RESONANCE ⎜ September 2013. Page 4. 820. RESONANCE ⎜ September 2013. Page 5. 821. RESONANCE ⎜ September 2013. Page 6. 822. RESONANCE ⎜ September 2013. Page 7. 823. RESONANCE ⎜ September ...
Indian Academy of Sciences (India)
IAS Admin
996. RESONANCE. November 2013. Page 2. 997. RESONANCE. November 2013. Page 3. 998. RESONANCE. November 2013. Page 4. 999. RESONANCE. November 2013. Page 5. 1000. RESONANCE. November 2013. Page 6. 1001. RESONANCE. November 2013. Page 7. 1002. RESONANCE. November 2013 ...
Indian Academy of Sciences (India)
IAS Admin
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A Sound Processor for Cochlear Implant Using a Simple Dual Path Nonlinear Model of Basilar Membrane
Kim, Kyung Hwan; Choi, Sung Jin; Kim, Jin Ho
2013-01-01
We propose a new active nonlinear model of the frequency response of the basilar membrane in biological cochlea called the simple dual path nonlinear (SDPN) model and a novel sound processing strategy for cochlear implants (CIs) based upon this model. The SDPN model was developed to utilize the advantages of the level-dependent frequency response characteristics of the basilar membrane for robust formant representation under noisy conditions. In comparison to the dual resonance nonlinear mode...
DEFF Research Database (Denmark)
Hjelholt, Morten; Jensen, Tina Blegind
2015-01-01
IT projects are often complex arrangements of technological components, social actions, and organizational transformation that are difficult to manage in practice. This paper takes an analytical discourse perspective to explore the process of legitimizing IT projects. We introduce the concept of ...... as part of a feedback loop to re-attach the localized IT project to the broader national discourse. The paper concludes with reflections on how to actively build on resonating statements as a strategic resource for legitimizing IT projects...... of resonating statements to highlight how central actors navigate in various discourses over time. Particularly, the statements and actions of an IT project manager are portrayed to show how individuals can legitimize actions by connecting statements to historically produced discourses. The case study...... of an IT project in a Danish local government spans a two-year time period and demonstrates a double-loop legitimization process. First, resonating statements are produced to localize a national IT initiative to support the specificity of a local government discourse. Second, the resonating statements are used...
Leavey, Sean; Rae, Katherine; Murray, Adam; Courtial, Johannes
2012-09-01
Autostereograms, or "Magic Eye" pictures, are repeating patterns designed to give the illusion of depth. Here we discuss optical resonators that create light patterns which, when viewed from a suitable position by a monocular observer, are autostereograms of the three-dimensional shape of one of the mirror surfaces.
Hagedorn, Peter
1982-01-01
Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Geometrical nonlinear free vibration of multi-layered graphene sheets
International Nuclear Information System (INIS)
Wang Jinbao; He Xiaoqiao; Kitipornchai, S; Zhang Hongwu
2011-01-01
A nonlinear continuum model is developed for the nonlinear vibration analysis of multi-layered graphene sheets (MLGSs), in which the nonlinear van der Waals (vdW) interaction between any two layers is formulated explicitly. The nonlinear equations of motion are studied by the harmonic-balance methods. Based on the present model, the nonlinear stiffened amplitude-frequency relations of double-layered graphene sheets (DLGSs) are investigated in the spectral neighbourhood of lower frequencies. The influence of the vdW interaction on the vibration properties of DLGSs is well illustrated by plotting the resulting modes' shapes, in which in-phase and anti-phase vibrations of DLGSs are studied. In particular, the large-amplitude vibration which associates with the anti-phase resonant frequencies, separating DLGS into single-layered GSs, is a promising application that needs to be explored further. In contrast, the vibration modes that are associated with the resonant frequencies are nonidentical and give various vibration patterns, which indicates that MLGSs are highly suited to being used as high-frequency resonators.
Highly Tunable Electrostatic Nanomechanical Resonators
Kazmi, Syed Naveed Riaz
2017-11-24
There has been significant interest towards highly tunable resonators for on-demand frequency selection in modern communication systems. Here, we report highly tunable electrostatically actuated silicon-based nanomechanical resonators. In-plane doubly-clamped bridges, slightly curved as shallow arches due to residual stresses, are fabricated using standard electron beam lithography and surface nanomachining. The resonators are designed such that the effect of mid-plane stretching dominates the softening effect of the electrostatic force. This is achieved by controlling the gap-to-thickness ratio and by exploiting the initial curvature of the structure from fabrication. We demonstrate considerable increase in the resonance frequency of nanoresonators with the dc bias voltages up to 108% for 180 nm thick structures with a transduction gap of 1
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter...
Kerr nonlinearity and plasmonic bistability in graphene nanoribbons
DEFF Research Database (Denmark)
Christensen, Thomas; Yan, Wei; Jauho, Antti-Pekka
2015-01-01
due to field enhancement, and the total nonlinearity is significantly affected by the field inhomogeneity of the plasmonic excitation. Finally, we discuss the emergence of a plasmonic bistability which exists for energies red-shifted relative to the linear resonance. Our results offer insights...
Compact titanium dioxide waveguides with high nonlinearity at telecommunication wavelengths
DEFF Research Database (Denmark)
Guan, Xiaowei; Hu, Hao; Oxenløwe, Leif Katsuo
2018-01-01
.43 mu m(2)) and a low loss (5.4 +/- 1 dB/cm) at telecommunication wavelengths around 1550 nm have been fabricated and measured. A microring resonator having a 50 mu m radius has been measured to have a loaded quality factor of 53500. Four-wave mixing experiments reveal a nonlinear parameter...
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Nonlinear optical studies in semiconductor-doped glasses under ...
Indian Academy of Sciences (India)
Eg is the band gap of the semiconductor and hω is the excitation photon energy. Very limited studies were conducted in resonance excitation region in SDGs with high-intensity femtosecond laser pulses. Z-scan is now recognized as a standard technique [7] to study nonlinear optical properties and is widely used because ...
A nonlinear approach to analyse the development of tropical ...
Indian Academy of Sciences (India)
The development of atmospheric disturbances in the tropical region is explained using vibrational resonance, a nonlinear phenomenon. As the Lorenz system is the most plausible model to describe the convective process in a tropical region, the influence of vertical wind shear and tropical waves on the system leading to ...
parametric nonlinear quasivariational inequalities
Directory of Open Access Journals (Sweden)
Zeqing Liu
2005-01-01
uniqueness results and sensitivity analysis of solutions are also established for the system of generalized nonlinear parametric quasivariational inequalities and some convergence results of iterative sequence generated by the algorithm with errors are proved.
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE...... of a proposed NSE system with high dynamic performance. The goal of the work is to achieve a state-of-the art transient time of 10 µs. In order to produce the arbitrary nonlinear curve, the exponential function of a typical diode is used, but the diode can be replaced by other nonlinear curve reference...... simulation of nonlinear source systems with higher output power. In this work, a module will consist of two fundamental units: an isolated power supply and an NSE. The isolated power supply has to possess a very low circuit input-to-output capacitance (very low Cio) in order to reduce the effect...
2013-01-01
filter, Bayesian decision theory, Generalized Likelihood Ratio Test (GLRT), and constant false alarm rate ( CFAR ) processing (31). Once the...Abbreviations, and Acronyms CFAR constant false alarm rate CNR cognitive nonlinear radar EM electromagnetic FCC Federal Communications Comission
Nonlinear Optical Terahertz Technology
National Aeronautics and Space Administration — We develop a new approach to generation of THz radiation. Our method relies on mixing two optical frequency beams in a nonlinear crystalline Whispering Gallery Mode...
Nonlinear differential equations
Struble, Raimond A
2017-01-01
Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.
Nonlinear ambipolar diffusion waves
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T.; Rowlands, G.
1985-07-01
The evolution of a plasma perturbation in a neutral gas is considered using the ambipolar diffusion approximation. A nonlinear diffusion equation is derived and, in the one-dimensional case, exact solutions of shock type are obtained.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...