Interaction of noise with excitable dynamics

In this paper, the interaction of noise with excitable dynamics of a three-electrode electrochemical cell is examined. Different scenarios involving both external and internal noise sources are considered. In the case of external noise, aperiodic stochastic resonance and regulation of the noise-induced spiking behaviour are investigated. In the case of internal noise, the interaction of intrinsic electrochemical noise with autonomous nonlinear dynamics is studied. The amplitude of this internal noise, determined by the concentration of chloride ions, is monotonically increased and the provoked dynamics are analysed. Our results indicate that internal noise, similar to its external counterpart, is able to induce regularity in the system response.     

柴油机间歇性排气噪声自适应有源前馈控制的DSP仿真

分析了柴油机排气噪声的特征，利用自适应有源前馈系统对噪声进行控制；对间歇性噪声的控制进行了建模分析；对柴油机的排气噪声进行了有源消声的初步设计；参考柴油机实际工况，利用高速信号处理芯片TMS320F2812进行了编程及调试；通过实测数据和DSP仿真实验验证了所采用方法的有效性。     

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.     

Patchiness in plankton populations

We consider and contrast two mechanisms for the production of spatial pattern in an excitable medium model for plankton populations. The first is Turing or diffusion-driven instability. We find that, since in a turbulent environment the effective diffusivities of phytoplankton and zooplankton are similar, this mechanism is unlikely to produce observable spatial pattern in the ocean. The second mechanism is spatially varying forcing of the system. In order to display the sensitivity to small spatial variation in forcing, we consider the dynamics of an ordinary differential equation system with spatial perturbations to parameters and initial conditions. In the absence of diffusion the excitable nature of the system means that small perturbations can produce very sharp spatial structures, when diffusion is introduced, we find that this patchiness can persist on realistic scales.     

Theory of the flow and conduction of inhomogeneous media

A basic model of an inhomogeneous medium is outlined and, by a combination of the methods of flow theory and reduction to an elementary cell, an analytic dependence is obtained for the conduction of such a medium.     

Noise-induced coherence in an excitable system with frequency-dependent feedback

The influence of the properties of an excitable system on the characteristics of the coherence resonance effect have been studied by experimental and numerical methods. The transition from monostable to bistable regime is accompanied by the appearance of a false maximum in the regularity parameter of the power spectrum plotted as a function of the noise intensity. An increase in the dimensionality of the system activates a mechanism whereby the noise reveals oscillatory dynamics, also resulting in the appearance of an additional maximum in the regularity parameter.     

Enhancement of coherent laser radar performance by predetection amplification

A long-path carbon dioxide laser amplifier, based on a coaxial radio frequency discharge gain medium combined with a Herriott cell folding system, is investigated as a predetection amplifier in a coherent laser radar system. The amplifier signal gain and noise characteristics are measured, and the signal-to-noise enhancement produced in a Doppler radar system is determined over a range of operating conditions of the amplifier. A maximum enhancement factor of 12.4 dB is measured for a cw gain cell, which is in good agreement with the theoretical prediction.     

The effect of spatiotemporal fluctuations on the pulse propagation

We have studied the influence of uncorrelated Gaussian fluctuations on the propagation of pulses in an excitable medium modeled by the FitzHugh-Nagumo system under an external point action. Depending on the properties of this medium, one of the two possible scenarios is realized in the noise-induced suppression of propagating pulses. The first scenario can be classified as the noise-induced incoherence (breakage of the links) between adjacent elements of the medium. The second scenario is related to a spontaneous generation of pulses in the medium under the action of fluctuations. These models are applied to analysis of some recent biological experiments devoted to the dynamics of calcium waves.     

基于概率简单叠加法则的动力可靠度高效计算方法

基于计算单元失效域的重要抽样法和区域分解法是计算高维输入随机变量条件下小失效概率的高效算法。该文在此基础上,首先利用基于计算单元失效域的重要抽样法的思想,引入构成总失效域的由持时内的时间点划分出的单元失效域,其次利用区域分解法的思想,引入构成总失效域互斥的单元失效域,最后根据两种单元失效域的关系和概率简单叠加法则,即可计算总失效概率。其中关键问题是计算结构反应时单位脉冲响应函数的确定和落入各个互斥单元失效域的样本数的确定。算例部分对受高斯白噪声激励作用的单自由度线性体系和多自由度线性体系,分别应用该文方法、基于计算单元失效域的重要抽样法和区域分解法进行了计算,并用Monte-Carlo法进行了验证,结果表明计算动力可靠度,尤其是小失效概率时,该文方法对比Monte-Carlo法计算效率有明显提高,并同基于计算单元失效域的重要抽样法和区域分解法一样高效。     

Switching process between bistable positions of multiquantum flux tubes in a thin-film type I superconductor

A superconducting memory device based on a bistable vortex position represents an interesting storage medium for future Josephson computers. In order to study the operational mode of such a single-flux quantum memory cell, we use as a model system multiquantum flux tubes in a thin-film type I superconductor (Pb). By employing high-resolution stroboscopic magnetooptical flux detection, we are able to globally visualize both spatial and temporal behavior of rapidly switching individual flux tubes. All experimental results agree reasonably well with theoretical model considerations of the energy balance during the elementary switching process.Supported by a grant from the Deutsche Forschungsgemeinschaft.     

Multiple crack problems of antiplane elasticity in an infinite body

Twe elementary solutions are presented for case of a pair of normal or tangential concentrated unit forces acting at a point of both edges of a single crack in an infinite plane isotropic elastic medium. Using these two elementary solutions and the principle of superposition, we found that the multiple crack problems can be easily converted into a system of Fredholm integral equations. Finally, the system obtained is solved numerically and the values of the stress intensity factors at the crack tips can be easily calculated. Two numerical examples are given in this paper. A system of Fredholm integral equations is complex form is also presented. We found that the system of Fredholm integral equations can be easily reduced from the system of singular integral equations given by Panasyuk[1]     

General case of multiple crack problems in an infinite plate

General case of multiple crack problems in an infinite plate is a case that the tractions applied on two edges of each crack are arbitrary, generally, are not in equilibrium. Two elementary solutions are present to solve the proposed problem. The first (second) elementary solution is defined as a solution that two pairs of normal and tangential concentrated forces are applied at a point of both edges of a single crack in an infinite isotropic elastic medium, with same magnitude and opposite direction (with same magnitude and same direction). Using the two elementary solutions and the principle of superposition, we found the proposed problem can be converted into a system of Fredholm integral equations. Finally, the system is solved numerically and SIF values at the crack tips can be easily calculated. In order to explain our study, one numerical example is given in this paper.     

Nonequilibrium phase transitions induced by external noise in distributed systems

A formalism is proposed to describe nonequilibrium phase transitions induced by external multiplicative noise in distributed systems. This approach can reduce the problem to an investigation of a regular differential equation whose roots correspond to possible phase states in the system. By means of this theory the relative probability of the existence of one state can be compared with another and the number of possible states identified, and the genesis of the system under the action of fluctuations of the external medium can be traced. Pis’ma Zh. Tekh. Fiz. 25, 91–95 (February 26, 1999)     

Multiple crack problems of antiplane elasticity in an infinite body by using fredholm integral equation approach

Two elementary solutions are present to solve the proposed problem. The first (second) elementary solution is defined as a solution that one pair of longitudinal concentrated forces is applied at a prescribed point of both edges of a single crack in infinite isotropic medium, with same magnitude and opposite direction (with same magnitude and same direction). Using the two elementary solutions and the principle of superposition, we found the proposed problem can be easily converted into a system of Fredholm integral equations. The system is solved numerically and SIF values at the crack tips can be easily calculated. Several numerical examples are given.     

Some elementary solutions of the heat equation and related equations

An elementary connection is shown between certain time dependent boundary value problems for the heat equation and problems of steady state heat conduction (or diffusion) in a medium with a radially varying thermal conductivity. Solutions are given for growing ellipsoids, transient heating of wedges and transient bending of wedge shaped plates.     

Low Space-bandwidth Product Signal Extrapolation Using a New Robust Iterative Random Grain Allocation Scheme

Abstract

The extrapolation in the space domain of a partially observed low space-bandwidth product (SBP) sequence or, equivalently, the resolution of the Fourier spectra in the frequency domain, in the presence of appreciable noise, is considered. The unknown sequence estimate is based on a number of acquired samples on a given measurement interval and the prior knowledge of the signal frequency bandlimit. Using an approach similar to a Monte-Carlo method, the extrapolated sequence samples are constructed from variably sized elementary grains. The new iterative algorithm, at each iteration step, based on a random-number generator, decides both the sample position to be considered and the sign of a grain that might be added to the current sample value. A sample update in each iteration step is either accepted or rejected in accordance with an appropriate decision rule. While exploiting the extrapolated sequence frequency bandlimit as a constraint, this decision rule is based on a non-increasing l₁-norm of a cumulative error vector. As the extrapolated sequence approaches its final form, the elementary grain size is decreased to allow for subtle sample updates. A heuristic schedule for gradual change of the elementary grain size, similar to the temperature schedule of the simulated annealing method, is used. A pre-processing, which compensates for the model inconsistency that is due to either the presence of noise and/or the lack of precision of the linear degradation operator, is also introduced. Furthermore, it is shown that an additional constraint, such as a given signal upper bound, greatly improves the quality of reconstruction. Several simulation examples, for the extrapolation of low-SBP sinusoidal and other arbitrary sequences and in the presence of a high level of noise, are presented.     

Excess conduction noise of electrolytic media under electrical equilibrium conditions

The results of an investigation of the noise of an electrolytic cell voltage under electrical equilibrium conditions when the cell is filled with normal solutions of CdCl₂ at concentrations of 0.3 n. and 0.5 n. and a Kratz–Myers medium are presented. The fundamental electrical characteristics of the cell and the noise of the three media, namely, the resistance, the spectral power density of the noise and the exponent γ in the 1/ƒ ^γ relation are determined.     

Relevance of phenotypic noise to adaptation and evolution

Biological processes are inherently noisy, as highlighted in recent measurements of stochasticity in gene expression. Here, the authors show that such phenotypic noise is essential to the adaptation of organisms to a variety of environments and also to the evolution of robustness against mutations. First, the authors show that for any growing cell showing stochastic gene expression, the adaptive cellular state is inevitably selected by noise, without the use of a specific signal transduction network. In general, changes in any protein concentration in a cell are products of its synthesis minus dilution and degradation, both of which are proportional to the rate of cell growth. In an adaptive state, both the synthesis and dilution terms of proteins are large, and so the adaptive state is less affected by stochasticity in gene expression, whereas for a non-adaptive state, both terms are smaller, and so cells are easily knocked out of their original state by noise. This leads to a novel, generic mechanism for the selection of adaptive states. The authors have confirmed this selection by model simulations. Secondly, the authors consider the evolution of gene networks to acquire robustness of the phenotype against noise and mutation. Through simulations using a simple stochastic gene expression network that undergoes mutation and selection, the authors show that a threshold level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during growth and development shapes any network's robustness, not only to noise but also to mutations. The authors also establish a relationship between developmental and mutational robustness.     

Intensity noise reduction of twin beams by a passive semiconductor medium

Abstract

A passive optical system is proposed to explore the intensity quantum correlation of two twin beams to reduce the photon noise of one of them. It consists of using a semiconductor medium inside an optical cavity, which behaves as a nonlinear medium presenting a crossed Kerr effect. The intensity fluctuations of one beam modify the resonance condition of the cavity for the other beam and therefore its intensity. The medium is described microscopically within the two-level atom model. It is shown that, under typical experimental conditions, this system may produce noise reduction.