Intermittency at critical transitions and aging dynamics at the onset of chaos

We recall that at both the intermittency transitions and the Feigenbaum attractor, in unimodal maps of non-linearity of order ζ > 1, the dynamics rigorously obeys the Tsallis statistics. We account for theq-indices and the generalized Lyapunov coefficients λ^q that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the onset of chaos with the appearance of a special value for the entropic indexq. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.     

Intermittency in branching processes

We study the intermittency properties of two branching processes, one with a uniform and another with a singular splitting kernel. The asymptotic intermittency indices, as well as the leading corrections to the asymptotic linear regime are explicitly computed in an analytic framework. Both models are found to possess a monofractal spectrum with ? _q =q ? 1 and inverse logarithmic corrections. Relations with previous results are discussed.     

Saturation of transient resonant nonlinear processes in sodium vapor

We present direct observation of the saturation of resonant optical processes in atomic systems, using a picosecond laser pump. Analysis requires the accounting of some new factors such as self-action and self-induced transparency.     

Distinction of the competing processes in nonlinear resonant frequency mixing in atoms

A coherent transient response technique is applied, for the first time, to distinguish between the influence of competing processes such as saturation of atomic transition and effects due to laser-induced nonlinear polarization on nonlinear resonant mixing. Experimental research is performed for the 3s–5s two-photon transition in sodium vapour. Delaying the probe picosecond pulse after the exciting one, variations of efficiency and phase-matched ratio upon incident intensity and exciting wavelength are investigated.     

Predator-prey cycles from resonant amplification of demographic stochasticity

We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is infinitely large, is the Volterra system (with density-dependent prey reproduction) which is well known to fail to predict cycles. This difference in behavior can be traced to a resonant amplification of demographic fluctuations which disappears only when the number of individuals is strictly infinite. Our results indicate that additional biological mechanisms, such as predator satiation, may not be necessary to explain observed predator-prey cycles in real (finite) populations.     

Renormalization method for the onset of stochasticity in a hamiltonian system

An approximate renormalization procedure is derived for the hamiltonian $\text{H(v, x, t)=}\text{v}{}^2\text{2}\text{? M}\text{cos}\text{x ? P}\text{cos}\text{k(x ? t)}$. It gives an estimate of the threshold of the large-scale stochastic instability which agrees within 5 to 10% with the results given by direct numerical integration of the canonical equations.     

The dissipative effects on stochasticity of the nonlinear oscillator

The effects of dissipation on the stochasticity of a nonlinear oscillator in the presence of a perturbing field are studied analytically. It is shown that the dissipation has two different and opposite effects on the stochasticity depending on the external frequency in the non time asymptotic domain. In the low frequency regime the stochasticity is enhanced while high frequency diminishes the stochasticity. These results may be related to some aspects of recent numerical studies.     

Coherent two phonon/photon processes in resonant photodesorption via laser-molecular vibrational coupling

Photodesorption rates are predicted in a quantum statistical theory based on a master equation in which desorption procedes by an incoherent sequence of phonon- and photon-assisted transitions. Including coherent two-phonon, two-photon, and one-phonon plus one-photon processes, our results are extended to more strongly bound adsorption systems, and predict photodesorption lineshapes that can be asymmetric near saturation.     

Intermittency route to rheochaos in wormlike micelles with flow-concentration coupling

We show experimentally that the route to chaos is via intermittency in a shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate, where the strength of flow-concentration coupling is tuned by the addition of salt sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar lengths between burst events shows that our data is consistent with type-II intermittency. The coupling of flow to concentration fluctuations is evidenced by the "butterfly" intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements. The scattered depolarized intensity in SALS, sensitive to orientational order fluctuations, shows the same time dependence (like intermittency) as that of shear stress.     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

双层粘接板界面的超声非线性谐振特性分析

采用声-力-电类比建立粘接界面非线性力学行为的等效非线性振荡电路,以求解双层粘接板的超声非线性谐振频率。理论上导出非线性谐振频率方程,确定双层粘接板非线性谐振频率与激励幅度、三阶弹性劲度系数的解析关系。双层粘接铝板的超声实验发现:在不良粘接情形下,超声谐振频率发生偏移,其值大于粘接完好区,且激发了较强的三次谐波,但二次谐波幅度变化不大。实验结果表明三次谐波幅度上升,超声谐振频率也显著增大,与理论导出非线性谐振频率变化规律相吻合,且三次谐波与基波、二次谐波的比值反映了非线性谐振频率变化趋势,证实粘接层三阶劲度系数是产生非线性共振频率偏移的主要因素。     

Intermittency in multiparticle production at high energy

We present predictions of random cascading models for multiparticle production at high energy. Standard and correlated factorial moments in rapidity are shown to provide stringent tests of the intermittency patterns characteristic of random cascades. Using the central limit theorem we show how to test directly for the existence of a cascading process. Finally, we discuss how to take into account statistical corrections.     

Estimating the nonlinear resonant frequency of a single pile in nonlinear soil

Analytical expressions are determined for the nonlinear resonant frequency (or natural frequency) of the fundamental lateral mode of a pile. A pile with a floating toe, with and without pile cap is considered in this paper. The influence of a nonlinear soil spring model that varies with depth and a nonlinear damping model that is strain amplitude dependent is considered. A non-dimensional equation of motion for the system dynamics is derived from an energy based formulation. This equation is a Duffing's type nonlinear differential system that has nonlinear damping. Harmonic balance with numerical continuation is employed to determine the nonlinear resonance curves of the system. Comparison with some experimental results is made.     

Optical resonant processes in thin excited films

It is shown that coherent processes of elastic scattering of resonant radiation form a “buffer” electromagnetic field near the boundary of excited media. This part of radiation is not governed by the standard refractive index, but precisely this part of radiation forms the beams reflected and refracted by the excited medium. The presence of the “buffer” field causes the suppression of stimulated emission near the boundary and leads to the appearance of a frequency angular broadening of the beam transmitted through a thin film of excited atoms at an oblique angle.     

Coherent and incoherent processes in resonant photoemission

3 threshold. At threshold, the emission feature changes character and after a rather narrow transition region it appears at constant emission energy instead. Clear signatures of interference between the direct photoemission and autoionization channels are identified. Received: 6 March 1997     

Electron-phonon coupling in transition metals and resonant scattering

An explicit formula is derived for the electron-phonon coupling of transition metals in terms of parameters that are used in first principle transition metal band structure calculations. Its relevance and systematics are discussed.     

Nonlinear mode coupling in doubly resonant frequency doublers

The concept of a doubly resonant frequency doubler can be used for a variety of experiments concerning both classical phenomena like efficient frequency doubling at low power levels and quantum effects like squeezed states of light or Quantum Non Demolition (QND) measurements. In many of these experiments the strength of the nonlinear coupling of fundamental and second-harmonic modes is of crucial importance. First we treat the general theory for the calculation of the coupling parameter, which depends not only on properties of the nonlinear material but also on resonator geometry and some optical phases. On this basis we discuss in detail the situation for two different monolithic resonator geometries, namely a linear (standing-wave) and a ring (travelling-wave) cavity. Finally we compare theoretical predictions for these resonators to the experimentally achieved results.     

Increased nonlinear coupling between turbulence and low-frequency fluctuations at the L-H transition

The nonlinear coupling between small scale high-frequency turbulence and larger scale lower-frequency fluctuations increases transiently in transitions to improved confinement in the DIII-D tokamak. This increase starts before the rapid turbulence suppression and E x B shear-flow development in the region that becomes the H-mode transport barrier/shear flow region. After the transition, the coupling returns to L-mode levels. These results are consistent with expectations for spontaneous transitions to improved confinement triggered by a turbulence-driven sheared flow.