Stochastic Simulation of Turing Patterns

We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction-diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie＇s algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion pro- cesses are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Sfochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.     

Intrinsic envelope fluctuations and modulation-detection thresholds for narrow-band noise carriers

A model is presented which calculates the intrinsic envelope power of a bandpass noise carrier within the passband of a hypothetical modulation filter tuned to a specific modulation frequency. Model predictions are compared to experimentally obtained amplitude modulation (AM) detection thresholds. In experiment 1, thresholds for modulation rates of 5, 25, and 100 Hz imposed on a bandpass Gaussian noise carrier with a fixed upper cutoff frequency of 6 kHz and a bandwidth in the range from 1 to 6000 Hz were obtained. In experiment 2, three noises with different spectra of the intrinsic fluctuations served as the carrier: Gaussian noise, multiplied noise, and low-noise noise. In each case, the carrier was spectrally centered at 5 kHz and had a bandwidth of 50 Hz. The AM detection thresholds were obtained for modulation frequencies of 10, 20, 30, 50, 70, and 100 Hz. The intrinsic envelope power of the carrier at the output of the modulation filter tuned to the signal modulation frequency appears to provide a good estimate for AM detection threshold. The results are compared with predictions on the basis of the more complex auditory processing model by Dau et al.     

光纤1/f热噪声的实验研究

光纤热噪声是限制光纤传感、测量系统性能的最终因素.但是低频区域呈1/f谱特性的光纤热噪声的形成机制迄今仍然存在争论.实验研究了光纤1/f热噪声水平与光纤内杂质离子浓度和光纤施加张力的关系,验证了这类热噪声来源于光纤内部的机械耗散引起的长度自发抖动,符合热机械噪声的理论假设.     

Effects of strong noise on attractors of dynamical systems

Stationary solutions of the Fokker-Planck equation are found by expansions of the probability distribution with respect to the reciprocal noise strength. It is shown that this expansion is convergent. Explicit representations for the probability distribution are obtained by numerical simulations for the Lorenz model and for a model of generators with inertial nonlinearity (GIN). The obtained distributions show an increasing amount of fine structure with decreasing noise which more and more reflects the fractal attractor structure. Results of measurements of the power spectrum of the GIN and of the distribution in the phase space are presented in dependence on the noise strengths.     

High frequency intensity noise spectra of axial mode groups in the radiation from CW GaAIAs diode lasers

The dependence of the intrinsic random intensity noise spectrum of the radiation from CW DH GaAIAs diode multimode lasers on optical wavelength has been investigated for the first time in a wide frequency range 30 MHz to 3 GHz. It was generally observed, that a lasing mode which is optically isolated from the rest of the radiation, shows much stronger intensity fluctuations as compared to the fluctuations of the total output, particularly in the frequency range below the intrinsic natural resonance frequency of the laser. The magnitude of the fluctuations decreases when the number of modes in the detected radiation increases. Our experimental results are compared to computer solutions which were obtained with a simple, analytical laser noise model. Good qualitative agreement between theory and experiment is demonstrated.     

Stochasticity in the yeast mating pathway

We report stochastic simulations of the yeast mating signal transduction pathway. The effects of intrinsic and external noise, the influence of cell-to-cell difference in the pathway capacity, and noise propagation in the pathway have been examined. The stochastic temporal behaviour of the pathway is found to be robust to the influence of inherent fluctuations, and intrinsic noise propagates in the pathway in a uniform pattern when the yeasts are treated with pheromones of different stimulus strengths and of varied fluctuations. In agreement with recent experimental findings, extrinsic noise is found to play a more prominent role than intrinsic noise in the variability of proteins. The occurrence frequency for the reactions in the pathway are also examined and a more compact network is obtained by dropping most of the reactions of least occurrence.     

Binaural processing of modulated interaural level differences

Two experiments are presented that measure the acuity of binaural processing of modulated interaural level differences (ILDs) using psychoacoustic methods. In both experiments, dynamic ILDs were created by imposing an interaurally antiphasic sinusoidal amplitude modulation (AM) signal on high-frequency carriers, which were presented over headphones. In the first experiment, the sensitivity to dynamic ILDs was measured as a function of the modulation frequency using puretone, and interaurally correlated and uncorrelated narrow-band noise carriers. The intrinsic interaural level fluctuations of the uncorrelated noise carriers raised the ILD modulation detection thresholds with respect to the pure-tone carriers. The diotic fluctuations of the correlated noise carriers also caused a small increase in the thresholds over the pure-tone carriers, particularly with low ILD modulation frequencies. The second experiment investigated the modulation frequency selectivity in dynamic ILD processing by imposing an interaurally uncorrelated bandpass noise AM masker in series with the interaurally antiphasic AM signal on a pure-tone carrier. By varying the masker center frequencies relative to the signal modulation frequency, broadly tuned, bandpass-shaped patterns were obtained. Simulations with an existing binaural model show that a low-pass filter to limit the binaural temporal resolution is not sufficient to predict the results of the experiments.     

Mean values and fluctuations in the fragmentation of mesoscopic systems using an exactly solvable model with strict particle conservation and quantum symmetry

A detailed discussion of self-similarities in fragment-size distributions and fluctuations is presented using an exactly solvable model of fragmentation (the “chain model”). The effects of particle-number conservation and quantum symmetry can rigorously be considered in systems ranging from microscopic to macroscopic. Due to the analyticity of the model the various scalings can be studied free of any statistical noise. Using a tuning parameter we can generate self-similar distributions with realistic power-laws and/or fluctuations which show intermittency. Finite-size effects neither destroy nor cause intermittency. The relation of self-similarity in both the averages and the fluctuations can be studied analytically. It is found that they are unlinked - there are cases where the size-distribution is a power-law with realistic exponents τ between ?2 and ?3 but no intermittency. Two cases will even be shown which have indistinguishable fragment distributions but very different factorial moments. We also discuss the interpretation of both the size and slope of the factorial moments in terms of multiplicity and bin mixing. We show that while either is sufficient to produce large moments, one must have bin mixing to produce large slopes. The two types of mixing are necessarily linked in constrained systems such as described by our model.     

Noisy saltatory spike propagation: The breakdown of signal transmission due to channel noise

Noisy saltatory spike propagation along myelinated axons is studied within a stochastic Hodgkin-Huxley model. The intrinsic noise (whose strength is inversely proportional to the nodal membrane size) arising from fluctuations of the number of open ion channels influences the dynamics of the membrane potential in a node of Ranvier where the sodium ion channels are predominantly localized. The nodes of Ranvier are linearly coupled. As a measure for the signal propagation reliability, we focus on the ratio between the number of initiated spikes and the transmitted spikes. This work supplements our earlier study [A. Ochab-Marcinek, G. Schmid, I. Goychuk and P. Hänggi, Phys. Rev E 79, 011904 (2009)] towards stronger channel noise intensity and supra-threshold coupling. For strong supra-threshold coupling the transmission reliability decreases with increasing channel noise level until the causal relationship is completely lost and a breakdown of the spike propagation due to the intrinsic noise is observed.     

Noise suppression in femtosecond mid-infrared light sources

An experimental and theoretical study of intrinsic correlations and noise-suppression mechanisms in two-stage femtosecond mid-IR light sources is presented. The setup, based on parametric amplification in BBO and subsequent difference-frequency mixing in AgGaS(2), delivers approximately 100-fs mid-IR pulses with 1-2-muJ energy. Exceptionally low pulse-energy fluctuations of only 0.2% in the mid-IR (lambda approximately 3-6 mum) are found, which are much smaller than the Ti:sapphire amplifer noise. The noise suppression is analyzed and found to stem from the interplay between dispersion and pump depletion.     

Sources of 1/F noise in gallium arsenide IMPATT diodes

The quasistatic approximation is used to analyze 1/F noise in IMPATT diodes in the static and dynamic (self-oscillating) modes. Sources of 1/F noise are defined in accordance with the fluctuator model: allowance is made for fluctuations of the charge of traps and fluctuations of the electron drift velocity caused by their scattering by traps and metastable neutral centers. It is shown that the fluctuations of the voltage across the diode and the fluctuations of the oscillation frequency are mainly determined by the fluctuations of the trap charge, while the fluctuations of the oscillation amplitude are determined by scattering by neutral centers. A method is developed to determine the intensity of noise sources using the results of measurements of the fluctuations in the static and dynamic modes of IMPATT diodes and a method of checking the model as a whole is checked. Experimental results are presented and these show satisfactory agreement with the calculations. Zh. Tekh. Fiz. 67, 65–70 (August 1997)     

Thermodynamic phase noise in fibre interferometers

Phase noise due to thermodynamic fluctuations in the optical path length is evaluated in this paper for basic fibre interferometers. In Mach-Zehnder and Michelson interferometers, where the temperature phase fluctuation (TPF) is that intrinsic to the fibre, this noise has been reported to be comparable to shot noise and a possible limit to sensor sensitivity in practical cases. We show that in Sagnac interferometers, used in fibre gyro and in Faraday current sensors, the TPF noise is decreased with respect to that intrinsic to the fiber because propagation in the same optical path leads to a correlation of the phase fluctuations. In addition, we show that in Fabry-Perot and ring resonators, as multiple reflections increase the effective path length, TPF noise is enhanced and can be dominant over shot noise even for moderate fibre lengths.     

Anyon Quantum Transport and Noise Away from Equilibrium

The quantum transport of anyons in one space dimension is investigated. After establishing some universal features of non-equilibrium systems in contact with two heat reservoirs in a generalized Gibbs state, the abelian anyon solution of the Tomonaga–Luttinger model possessing axial-vector duality is focused upon. In this context a non-equilibrium representation of the physical observables is constructed, which is the basic tool for a systematic study of the anyon particle and heat transport. The associated Lorenz number is determined and the deviation from the standard Wiedemann–Franz law induced by the interaction and the anyon statistics is explicitly described. The quantum fluctuations generated by the electric and helical currents are investigated and the dependence of the relative noise power on the statistical parameter is established.     

基于噪声辅助非均匀采样复数据经验模态分解的混沌信号降噪

鉴于非均匀采样复数据经验模态分解(NSBEMD)相对传统分解方法的优势和噪声的NSBEMD特性,提出了一种基于噪声辅助NSBEMD的混沌信号自适应降噪方法.该方法首先以含噪混沌信号和高斯白噪声分别为实、虚部来构造复数据并进行NSBEMD,然后根据虚部各IMF的能量来估算实部各IMF中包含的噪声能量,最后根据噪声能量的估计值对实部IMF进行奇异值分解(SVD)降噪.噪声估计实验验证了噪声能量估计方法的可行性,而Lorenz信号和太阳黑子月平均数的降噪实验则表明,相对于现有EMD降噪方法,本文方法能够进一步消除噪声,更清晰地恢复出混沌吸引子的拓扑结构.     

Stochastic simulation of variations in the autoignition delay time of premixed methane and air

A mesoscopic stochastic particle model for homogeneous combustion is introduced. The model can be used to investigate the physical fluctuations in a system of coupled chemical reactions with energy (heat) release/consumption. In the mesoscopic model, the size of the homogeneous gas volume is an additional variable, which is eliminated in macroscopic continuum models by the thermodynamic limit N→∞. Thus, continuous homogeneous models are macroscopic models wherein fluctuations are excluded by definition. Fluctuations are known to be of particular importance for systems close to the autoignition limits. The new model is used to investigate the stochastic properties of the autoignition delay time in a homogeneous system with stoichiometric premixed methane and air. Temperature and species concentrations during autoignition of sub-macroscopic volumes, including physically meaningful fluctuations, are presented. It is found that different realizations mainly differ in the time when ignition occurs; besides this the development is similar. The mesoscopic range and the macroscopic limit are identified. Which range a specific system is assigned to is not only a question of the length scale or particle number, but also depends on the complete thermodynamic state. The stochastic algorithm yields the correct results for the macroscopic limit compared to the continuous balance equations. The sensitivity of the results to two different detailed reaction mechanisms (for the same system) is studied and found to be low. We show that when approaching the autoignition limit by decreasing the temperature, the fluctuations in the autoignition delay time increase and an increasing number of realizations will have exceedingly long ignition delay times, meaning they are in practice not autoignitable. With this result the mesoscopic simulations offer an explanation of the transition between autoignitable and non-autoignitable conditions. The calculated distributions were compared with ten repetitions of the same experiment. A mesoscopic distribution that matches the experimental results was found.     

Influence of multiplicative noise on properties of first order dynamical phase transition

Critical phenomena in distributed dynamical two-dimensional nonlinear system near the point of the Turing instability are discussed. The system is considered in the presence of thermal fluctuations and multiplicative noise (MN) representing fluctuations of the bifurcation parameter. Since such a noise of the control parameter can have macroscopic (not thermal) nature, the intensity is considered as sufficiently large in comparison with the amplitude of thermal fluctuations, and it is shown that in the system the first order phase transition occurs with the characteristics which are independent on the thermal noise. Hence the discontinuous transtion could be observable in experimental situations where this would not be possible in the absence of MN (like the Rayleigh-Benard problem). When the correlation length of MN is small, the transition results in the formation of a complex state possessing only short-range order, and when MN is spatially uniform, a quasi-one-dimensional structure will be formed.     

Role of stochastic fluctuations in the charge on macroscopic particles in dusty plasmas

The currents which charge a macroscopic particle placed in a plasma consist of discrete charges; hence, the charge can undergo random fluctuations about its equilibrium value. These random fluctuations can be described by a simple model which, if the mechanisms for charging of macroscopic particles are known, makes it possible to determine the dependence of the temporal and amplitude characteristics of the fluctuations on the plasma parameters. This model can be used to study the effect of charge fluctuations on the dynamics of the macroscopic particles. The case of so-called plasma-dust crystals (i.e., highly ordered structures which develop because of strong interactions among macroscopic particles) in laboratory gaseous discharge plasmas is considered as an example. The molecular dynamics method shows that, under certain conditions, random fluctuations in the charge can effectively heat a system of macroscopic particles, thereby impeding the ordering process. Zh. éksp. Teor. Fiz. 115, 2067–2079 (June 1999)     

Diffusive Fluctuations for One-Dimensional Totally Asymmetric Interacting Random Dynamics

We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with are the Aldous–Diaconis–Hammersley process and the related stick model. The A-D-H process represents a particle configuration on the line, or a 1-dimensional interface on the plane which moves in one fixed direction through random local jumps. The stick model is the process of local slopes of the A-D-H process, and has a conserved quantity. The results describe the fluctuations of these systems around the deterministic evolution to which the random system converges under hydrodynamic scaling. We look at diffusive fluctuations, by which we mean fluctuations on the scale of the classical central limit theorem. In the scaling limit these fluctuations obey deterministic equations with random initial conditions given by the initial fluctuations. Of particular interest is the effect of macroscopic shocks, which play a dominant role because dynamical noise is suppressed on the scale we are working. Received: 4 October 2001 / Accepted: 12 March 2002