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1.
A thin plate, excited by a harmonic external forcing of increasing amplitude, shows transitions from a periodic response to a chaotic state of wave turbulence. By analogy with the transition to turbulence observed in fluid mechanics as the Reynolds number is increased, a generic transition scenario for thin vibrating plates, first experimentally observed, is here numerically studied. The von Kármán equations for thin plates, which include geometric non-linear effects, are used to model large amplitude vibrations, and an energy-conserving finite difference scheme is employed for discretisation. The transition scenario involves two bifurcations separating three distinct regimes. The first regime is the periodic, weakly non-linear response. The second is a quasiperiodic state where energy is exchanged between internally resonant modes. It is observed only when specific internal resonance relationships are fulfilled between the eigenfrequencies of the structure and the forcing frequency; otherwise a direct transition to the last turbulent state is observed. This third, or turbulent, regime is characterized by a broadband Fourier spectrum and a cascade of energy from large to small wavelengths. For perfect plates including cubic non-linearity, only third-order internal resonances are likely to exist. For imperfect plates displaying quadratic nonlinearity, the energy exchanges and the quasiperiodic states are favored and thus are more easily obtained. Finally, the turbulent regime is characterized in the light of available theoretical results from wave turbulence theory. 相似文献
2.
Lee J 《Chaos (Woodbury, N.Y.)》1992,2(4):537-563
In spectral form the 2D incompressible Navier-Stokes equations in a square periodic region will be represented by 430 complex Fourier amplitudes which correspond to isotropic truncation of the upper wave number 16. For small viscosity, we have found five equilibrium states I-V in the entire range of forcing; I-fixed point, II-circle, III-closed orbit, IV-torus, and V-chaos. The fixed-point equilibrium state is the laminar flow. As the forcing passes through a critical value, the fixed point evolves directly to equilibrium state III under a typical multimode forcing. The chaotic transition takes place on a 2-torus-like manifold (equilibrium state IV) which is the product space of a circle and the closed orbit of equilibrium state III, similar to the quasiperiodic 2-torus of Ruelle and Takens. For sufficiently large forcing, the evolution of equilibrium state V is nothing but a simulation of quasistationary 2D turbulence. From the Lyapunov exponents of turbulent flows, we have evaluated the constants in the theoretical results of Foias and his colleagues, which relate the determining mode and fractal dimension with the enstrophy dissipation wave number of 2D turbulence. 相似文献
3.
O. Cadot A. Boudaoud C. Touzé 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(3):399-407
A vibrating plate is set into a chaotic state of wave turbulence by either a periodic or a random local forcing. Correlations
between the forcing and the local velocity response of the plate at the forcing point are studied. Statistical models with
fairly good agreement with the experiments are proposed for each forcing. Both distributions of injected power have a logarithmic
cusp for zero power, while the tails are Gaussian for the periodic driving and exponential for the random one. The distributions
of injected work over long time intervals are investigated in the framework of the fluctuation theorem, also known as the
Gallavotti-Cohen theorem. It appears that the conclusions of the theorem are verified only for the periodic, deterministic
forcing. Using independent estimates of the phase space contraction, this result is discussed in the light of available theoretical
framework. 相似文献
4.
Thermal measurements on a converting dilute3He-superfluid4He solution in the quasiperiodic regime show a transition from a mode-locked periodic state to chaotic time dependence via intermittency. The type of intermittency is discussed in the context of standard models of the phenomenon. In a region just below the onset of intermittency, injection of external multiplicative noise with noise amplitude above a certain threshold level induces the chaotic state. This noise-induced transition can be understood to be due to perturbations of a system with a barely stable attractor; the noise causes the system to escape the weakly attracting periodic points. We present a numerical simulation of a 1D map with external noise which explains some aspects of the noise-induced behavior, and a 2D map which has certain features of the intermittency. 相似文献
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7.
We show that it is possible to organize regular filamentation patterns in air by imposing either strong field gradients or phase distortions in the input-beam profile of an intense femtosecond laser pulse. A comparison between experiments and 3+1 dimensional numerical simulations confirms this concept and shows for the first time that a control of the transport of high intensities over long distances may be achieved by forcing this well ordered propagation regime. In this case, deterministic effects prevail in multiple femtosecond filamentation, and no transition to the optical turbulence regime is obtained [Phys. Rev. Lett. 83, 2938 (1999)]]. 相似文献
8.
Feedback and external forcing are applied to an array of chaotic electrochemical oscillators through variations in the applied potential. We see transitions from intermittent clusters to stable chaotic clusters to stable periodic clusters to synchronized states as the feedback gain and forcing amplitude, respectively, are varied. With forcing up to four clusters are observed in stable states. The transition to synchronization with feedback occurs by the increase in the size of one cluster at the expense of the others. 相似文献
9.
The paper considers an excitable Hodgkin-Huxley system subjected to a strong
periodic forcing in the presence of random noise. The influence of the forcing
frequency on the response of the system is examined in the realm of suprathreshold
amplitudes. Our results confirm that the presence of noise has a detrimental effect on
the neuronal response. Fluctuations can induce significant delays in the detection of
an external signal. We demonstrate, however, that this negative influence may be
minimized by a resonant activation effect: Both the mean escape time and its standard
deviation exhibit a minimum as functions of the forcing frequency. The
destructive influence of noise on the interspike interval can also be reduced. With
driving signals in a certain frequency range, the system can show stable periodic
spiking even for relatively large noise intensities. Outside this frequency range,
noise of similar intensity destroys the regularity of the spike trains by suppressing
the generation of some of the spikes. 相似文献
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11.
One-dimensional maps have proved to be useful models for understanding the transition to turbulence. We investigate a smooth perturbation of the well-known logistic system in order to examine numerically the change in the bifurcation behavior which is observed, when the Schwarzian derivative is allowed to become positive. We find coexistence of a fixed point attractor and a periodic or chaotic two-band-attractor. The chaotic two-band attractor can disappear by yielding a preturbulent state which will asymptotically settle down to a fixed-point. The chaotic behavior of some systems can be destroyed by arbitrarily small amounts of external noise. The concept of (ε, δ)-diffusions is used to describe the sensitivity of attractors against external noise. We also observe a direct transition from a fixed-point to a chaotic one-band attractor. This can be interpreted as type-III-intermittency of Pomeau and Manneville but with an almost linear scaling behavior of the Lyapunov exponent. 相似文献
12.
Robert J. Deissler 《Journal of statistical physics》1985,40(3-4):371-395
The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested. 相似文献
13.
Boundary-layer transition has been expected to be an important contributor to sensor flow-induced self-noise. The pressure fluctuations caused by this spatially bounded, and intermittent, phenomenon encompass a very wide range of wavenumbers and temporal frequencies. Here, we analyze the wavevector–frequency spectrum of the wall pressure fluctuations due to subsonic boundary-layer transition as it occurs on a flat plate under zero-pressure gradient conditions. Based on previous measurements of the statistics of the boundary-layer intermittency, it is found that transition induces higher low-streamwise wavenumber wall pressure levels than does a fully developed turbulent boundary layer that might superficially exist at the same location and at the same Reynolds number. The transition zone spanwise wavenumber pressure components are virtually unchanged from the fully developed turbulent boundary-layer case. The results suggest that transition may be more effective than the fully developed turbulent boundary layer in forcing structural excitation at low Mach numbers, and it may have a more intense radiated noise contribution. This may help explain increases in measured sensor self-noise when the sensors are placed near the transition zone. We believe, based on the presented analytical calculation and numerical simulation, that the rapid growth and subsequent decay of turbulent spots in the intermittent transition zone causes the higher low-(streamwise) wavenumber spectra. 相似文献
14.
B. Gütlich H. Zimmermann C. Denz R. Neubecker M. Kreuzer T. Tschudi 《Applied physics. B, Lasers and optics》2005,81(7):927-936
Under feedback extended nonlinear optical systems spontaneously show a variety of periodic patterns and structures. Control
gives new insight into these phenomena and it can open the way for potential application of nonlinear optical structures.
We briefly review methods to control localized states in single feedback experiments. Application of a Fourier control method
allows to modify interaction behavior of the localized states. As a further approach we study a forcing method, using externally
created light fields as additional input to the system. Recent experiments show that the forcing method enables to favor addressing
positions for localized structures. We demonstrate static addressing and favoring of addressing positions. We extend the forcing
method to a dynamic forcing scheme, which allows to move and reposition localized states. Additionally forcing is used to
balance experimental imperfections.
PACS 05.45.Gg; 42.60.Jf; 42.65.Tg 相似文献
15.
We construct a typical model for the Poincaré map of doubly periodic flows, which presents numerically a transition to chaotic behavior. After the frequency locking phenomenon, we observe two types of transitions to turbulence. The first one involves successive subharmonic instabilities of a periodic solution. The second one occurs after the disappearance of a periodic solution and can be either intermittent or discontinuous with hysteresis. 相似文献
16.
ZHAO Ying-Kui CHEN Shi-Gang WANG Guang-Rui 《理论物理通讯》2008,49(2):521-524
There is a phase transition between quasi-periodic state and intermittent chaos in GOY model with a critical value δ0. When we add a modulated periodic externa/force to the system, the phase transition can also be found with a critical value δe. Due to coupling between the force and the intrinsic fluctuation of the velocity on shells in GOY model, the stability of the system has been changed, which results in the variation of the critical value. For proper intensity and period of the force, δe is unequal to δ0. The critical value is a nonlinear function of amplitude of the force, and the fluctuation of the velocity can resonate with the external force for certain period Te. 相似文献
17.
Y.-C. Lai K. Park L. Rajagopalan 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,69(1):65-70
We investigate a class of nonlinear wave equations subject to
periodic forcing and noise, and address the issue of energy optimization.
Numerically, we use a pseudo-spectral method to solve the nonlinear stochastic
partial differential equation and compute the energy of the system as a
function of the driving amplitude in the presence of noise.
In the fairly general setting where the system possesses two coexisting
states, one with low and another with high energy, noise can induce
intermittent switchings between the two states. A striking finding is that,
for fixed noise, the system energy can be optimized by the driving in a
form of resonance. The phenomenon can be explained by the Langevin dynamics
of particle motion in a double-well potential system with symmetry breaking.
The finding can have applications to small-size devices such as
microelectromechanical resonators and to waves in fluid and plasma. 相似文献
18.
Jun Ma Chun-Ni Wang Jun Tang Ya-Feng Xia 《International Journal of Theoretical Physics》2009,48(1):150-157
Periodical forcing is used to control the spiral wave and turbulence in the modified Fithzhugh-Nagumo equation (MFHNe) when
excitability is changed. The decisive parameter ε of (MFHNe), which describes the ratio of time scales of the fast activator u and the slow inhibitor variable v, is supposed to increase linearly to simulate the excitability modulation in the media. In the numerical simulation, a local
periodical stimulus is imposed on the left border of the media and the periods of external forcing are adjusted according
to the approximate formula ω
∝1/ε
1/3 so that using the most appropriate frequency for the external forcing can approach a shorter transient period. It is found
that the spiral wave and turbulence can be removed successfully by using an appropriate periodical forcing on the left border
of the media. The mean activator and distribution of frequency of all the sites are also used to analyze the transition of
spiral wave. 相似文献
19.
Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force
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Jinlian Jiang 《中国物理 B》2022,31(6):60203-060203
The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored. Unlike the existing work in detecting early warning signals, this paper presents the most probable transition paths to characterize the regime shifts. The most probable transition paths are obtained by minimizing the Freidlin-Wentzell (FW) action functional and Onsager-Machlup (OM) action functional, respectively. The most probable path shows the movement trend of the lake eutrophication system under noise excitation, and describes the global transition behavior of the system. Under the excitation of Gaussian noise, the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths. Under the excitation of Gaussian white noise and periodic force, we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution. 相似文献
20.
We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect. 相似文献