Fluctuation dynamics and 1/f spectra characterizing the acoustic cavitation of liquids

The dynamics of acoustic cavitation in water and glycerin is studied experimentally. The power spectra and distribution functions of fluctuations are determined. In transient regimes, bubble structures in the form of fractal clusters are formed near the ultrasonic radiator. The power spectra have the form 1/f, and the distribution functions of local fluctuations differ from the Gaussian ones and exhibit the scale invariance property.     

Noise induced oscillations in time delayed semiconductor laser system

The paper reports a detailed analysis of the chaotic dynamics of a theoretical model of a time delayed semi conductor laser. The periodic, quasi-periodic and chaotic nature is investigated with phase-plots, bifurcation analysis and lyapunov exponents. The effect of the system when induced by colored and bounded sine-Wiener noise has been examined extensively. The nature of the noise-induced propagating waves is investigated with the help of wavelet power spectra. It has been observed that the additive noise can suppress the chaotic dynamics of the system. Also the system is more chaotic in the presence of multiplicative noise. Moreover, the additive and multiplicative noise can modulate the output power upto a certain level, with constant input parameters.     

花簇分形无标度网络中节点影响力的区分度

大量研究表明分形尺度特性广泛存在于真实复杂系统中, 且分形结构显著影响网络上的传播动力学行为. 虽然复杂网络的节点传播影响力吸引了越来越多学者的关注, 但依旧缺乏针对分形网络结构的节点影响力的系统研究. 鉴于此, 本文基于花簇分形网络模型, 研究了分形无标度结构上的节点传播影响力. 首先, 对比了不同分形维数下的节点影响力, 结果表明, 当分形维数很小时, 节点影响力的区分度几乎不随节点度变化, 很难区分不同节点的传播影响力, 而随着分形维数的增大, 从全局和局域角度都能很容易识别网络中的超级传播源. 其次, 通过对原分形网络进行不同程度的随机重连来分析网络噪声对节点影响力区分度的影响, 发现在低维分形网络上, 加入网络噪声之后能够容易区分不同节点的影响力, 而在无穷维超分形网络中, 加入网络噪声之后能够区分中间度节点的影响力, 但从全局和局域角度都很难识别中心节点的影响力. 所得结论进一步补充、深化了基于花簇分形网络的节点影响力研究, 研究结果对实际病毒传播的预警控制提供了一定的理论借鉴.     

Simulation of fractal cluster growth on a substrate under ion bombardment

Ion-stimulated growth of a fractal cluster on the substrate is simulated in regimes that are intermediate between diffusion- and reaction-limited aggregations. It is shown that the fractal dimension of a growing cluster and the type of formed epitaxial structure are due to the sequence of ion-stimulated processes with different fractal dimensions. The algorithm for revealing the ion stimulation mechanism of processes based on fractal laws is proposed.     

Chaotic dynamics of spin-valve oscillators

Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously anticipated. We explicitly show that the transition to chaotic dynamics occurs through a series of period doubling bifurcations. In chaotic regime, two dramatically different power spectra, one with a well-defined peak and the other with a broadly distributed noise, are identified and explained.     

Dephasing of solid-state qubits at optimal points

Motivated by recent experiments with Josephson-junction circuits, we analyze the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We study the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. For 1/f noise strong higher-order effects influence the evolution.     

Dynamics of transition processes and structure formation in critical heat-mass transfer regimes during liquid boiling and cavitation

The results of experimental studies concerning the development of critical phenomena and structure formation in the process of boiling in falling films and during liquid cavitation are given. In conditions of stepwise and periodic pulsed surges of a thermal load, the parameters of formed metastable regular structures and critical parameters of heat-releasing surface drying are shown to be determined by the dynamics of moving wetting boundaries in the process of system self-organization. In the case of high-intensity heat fluxes, decomposition of a falling film is determined by propagation regimes of self-maintaining boiling fronts with a complex shape of intermediate structures. The study of ultrasonic cavitation of water, glycerin, and vacuum oil shows that structures of interacting gas-vapor bubbles (having the form of fractal clusters) are formed near the emitter surface. Spatial structures are characterized by a low-frequency divergence of the power spectra and a scale-invariant function of the fluctuation distributions. The experimental results are in good qualitative agreement with the numerical simulations performed within the theory of 1/f fluctuations in the case of nonequilibrium phase transitions in a spatially distributed system.     

Apparent anomalous behavior of the power spectrum of 1/f noise and its explanation

The explanation is given for the apparent anomalous behavior of the power spectrum of 1/f noise as if it corresponded to the total infinite power of noise sources. Physical mechanisms eliminating the apparent anomalies are described. With these mechanisms, the finite and integrable 1/f-noise power spectra fitting the known physical concepts of noise processes are obtained in the low-and high-frequency limits.     

Chaotic transmission of waves and "cooling" of signals

Ray dynamics in waveguide media exhibits chaotic motion. For a finite length of propagation, the large distance asymptotics is not uniform and represents a complicated combination of bunches of rays with different intermediate asymptotics. The origin of the phenomena that we call "chaotic transmission," lies in the nonuniformity of the phase space with sticky domains near the boundary of islands. We demonstrate different fractal properties of ray propagation using underwater acoustics as an example. The phenomenon of the kind of Levy flights can occur and it can be used as a mechanism of cooling of signals when the width of spatial spectra dispersion is significantly reduced. (c) 1997 American Institute of Physics.     

On the origin of slow processes of charge transport in porous media

Dielectric relaxation spectra in porous media reveal the importance of slow processes of charge transport with polarisation currents down at least to mHz. The spatial scale of the relaxation is frequency-dependent, potentially allowing information about the structure of the medium to be obtained from the AC conductivity. Many mechanisms of relaxation have been proposed, but we review only two in any depth. These two approaches relate long relaxation times on the one hand to diffusion limited relaxation, on the other, to geometrical limitations on conduction pathways. For equidimensional non-fractal particles, the first (second) generates a quadratic (linear) dependence of relaxation time on particle (or pore) size. In each a fractal model of the pore space generates a power-law AC conductivity with the power of the frequency a function of the fractal dimensionality, but the powers have different relationships with system parameters. Comparison with data does not support either interpretation generally, though some data sets agree with each. Since surface conduction yields a quadratic dependence for particles elongated in one dimension, but more complex dependences for fractal interfaces, it seems easier and more productive to start from the perspective that surface conduction processes are the basis for the relaxation.     

Generation of fractal-spectrum signals

Development of communications systems reliably operating in an unfavorable electromagnetic environment is today a challenging problem because of a high density of interfering signals generated by numerous radioelectronic systems (especially in cities) and a large amount of electromagnetic noise of different natures. The search for new types of noise-immune signals is a key direction in designing communications system reliably operating in a noisy environment. Using a fractal wavelet signal as an example, we consider the theoretical and experimental data on synthesizing wide-band fractal signals on a 2-GHz sinusoidal carrier and discuss their basic properties. It is shown that such signals have self-similar fractal spectra and a high noise immunity and, therefore, can be applied in noise-immune communications.     

基于分形编码的M型恒星光谱次型自动识别

根据天体光谱自身的局部分形特征,对光谱中400~510,600~700和780~900 nm三个波段的数据分形编码,并以编码中匹配数据块位置与最小匹配误差为特征,将分形方法应用于天体光谱次型识别。实验表明,分形方法不受LAMOST流量定标误差、仪器效率曲线的影响,具有一定的抗噪性,可以有效地自动识别LAMOST与SDSS的M型恒星光谱次型。     

Bispectrum Analysis of One-Dimensional Regular Fractals with Additive Random Noise

The bispectrum of the Cantor set that is a typical regular fractal is calculated and its fractalities are shown. A relation between the bispectrum and the fractal dimension of the object is elucidated. Effects of additive random noise on the scaling property of the bispectrum are compared with those of the corresponding power spectrum.     

An entropy-based stability analysis of extreme fluctuations in a system featuring a 1/<Emphasis Type="Italic">f</Emphasis> spectrum

Extreme fluctuations are modeled by a point system of stochastic equations, in which power spectra inversely proportional to the frequency are produced under the effect of white noise. The distribution of extreme fluctuations corresponds to the maximum of statistical entropy, which points to their stability in nature. By calculating the spectral entropy of random processes, it becomes possible to investigate their stability directly from power spectra without the need to calculate the amplitude distribution functions. The spectral entropy as a function of white noise amplitude has a minimum. The position of the spectral entropy minimum corresponds to the critical state of the system in which the spectra of fluctuating quantities are inversely proportional to the frequency.     

Pulse-Width Jitter Measurement for Laser Diode Pulses

Theoretical analysis and experimental measurement of pulse-width fitter of diode laser pulses are presented. The expression of pulse power spectra with all amplitude jitter, timing jitter and pulse-width jitter is deduced. The power spectra with and without pulse-width fitter are that the pulse-width jitter will contribute considerably numerically simulated. The simulation results indicate noise to the pulse power spectrum while the product of pulse width and angular frequency is larger than 1. The experimental measurement of pulse-width fitter of a gain-switched Fabry-Perot laser diode with 2.4 GHz repetition rate is also reported. In comparison of the noise power spectra of the first, fourth and seventh harmonics of the pulse repetition rate, 2.3ps pulse-width jitter is obtained.     

小通道氮气-水两相流三谱切片波动特性及其流型表征

将三谱切片与波动特性分析方法相结合, 组建了一种新的非线性分析方法, 并讨论了时间序列长度与快速傅里叶变换(FFT)长度对三谱切片的波动特征值的影响, 发现在无噪声干扰情况下, 序列长度与FFT 长度与矢量类间距值成正比, 在有噪声干扰情况下, 近似成反比关系.将该分析方法应用到分形序列(Brown)、混沌序列(Lorenz)和周期序列(正弦), 检验了波动特性方法的抗噪能力和表征复杂度能力. 结果表明: 该波动特性分析方法较其他功率谱分析方法对分形和混沌序列具有较好的抗噪能力, 而对周期序列的抗噪能力相对较弱; 该波动特性方法对序列内在复杂度的表征具有较好的效果.在此基础上, 对水力直径为1.15 mm的矩形小通道(w×h=2 mm×0.81 mm)中的 矩形通道内氮气-水两相流型的差压信号进行了研究. 通过对流型差压信号三谱切片的分析揭示了不同流型的主振荡模式二次耦合现象, 提取不同流型三谱切片的波动特征值, 实现了小通道氮气-水两相流典型流型的准确识别, 同时也为其他不同介质的多相流动特性分析与流型辨识提供了一个新的思路. 关键词： 三谱切片 波动特性 流型识别 流型动力学     

Non-Markovian stochastic resonance

The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e., the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian-SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR-theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.     

基于分形编码的天体光谱降噪方法

为了降低噪声影响,恢复光谱的连续谱和谱线等主要特征,以便准确测量谱线的等值宽度,文章根据天体光谱自身具有局部自相似性,而随机白噪声不具有自相似性,首次将分形方法应用于天体光谱降噪.实验表明,分形降噪方法对于准确测量谱线的等值宽度、星系红移等参数是有效的,此外,还可以实现数据压缩.分形方法适用于海量光谱的降噪和数据存储.     

Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator driven by weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.