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1.
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. 相似文献
2.
B. L. Hu Albert Roura Enric Verdaguer 《International Journal of Theoretical Physics》2004,43(3):749-766
We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized 2-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributions: intrinsic and induced fluctuations. We show that traditional criteria on the stability of semiclassical gravity are incomplete because these criteria based on the linearized semiclassical Einstein equation can only provide information on the expectation value and the intrinsic fluctuations of the metric perturbations. By contrast, the framework of stochastic semiclassical gravity provides a more complete and accurate criterion because it contains information on the induced fluctuations as well. The Einstein–Langevin equation therein contains a stochastic source characterized by the noise kernel (the symmetrized 2-point quantum correlation function of the stress tensor operator) and yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. These points are illustrated with the example of Minkowski space-time as a solution to the semiclassical Einstein equation, which is found to be stable under both intrinsic and induced fluctuations. 相似文献
3.
For just over a decade, stochastic gene expression has been the focus of many experimental and theoretical studies. It is now widely accepted that noise in gene expression can be decomposed into extrinsic and intrinsic components, which have orthogonal contributions to the total noise. Intrinsic noise stems from the random occurrence of biochemical reactions and is inherent to gene expression. Extrinsic noise originates from fluctuations in the concentrations of regulatory components or random transitions in the cell's state and is imposed to the gene of interest by the intra- and extra-cellular environment. The basic assumption has been that extrinsic noise acts as a pure input on the gene of interest, which exerts no feedback on the extrinsic noise source. Thus, multiple copies of a gene would be uniformly influenced by an extrinsic noise source. Here, we report that this assumption falls short when multiple genes share a common pool of a regulatory molecule. Due to the competitive utilization of the molecules existing in this pool, genes are no longer uniformly influenced by the extrinsic noise source. Rather, they exert negative regulation on each other and thus extrinsic noise cannot be determined by the currently established method. 相似文献
4.
A.A. Semenov C.H. Woo E.A. Koptelov 《Applied Physics A: Materials Science & Processing》2001,73(3):335-340
The random nature of diffusing jumps and cascade occurrence produce stochastic fluctuations of the point-defect fluxes. The
effect of such fluctuations on the kinetics of void growth is investigated in the present paper. It is found that the non-linear
coupling between the stochastic fluctuations and the void sizes may lead to the instability of void evolution within the mean-field
theory, when the sizes of voids and their growth rates are both relatively small. The growth rate of voids becomes dominated
by the stochastic component, causing the smaller voids to shrink away. This effect is investigated in terms of a non-equilibrium
phase transition induced by a purely random stochastic noise. The derived conditions for this non-equilibrium transition are
compared favourably with experimental observations.
Received: 5 June 2000 / Accepted: 9 October 2000 / Published online: 21 March 2001 相似文献
5.
In a system of non-linear chemical reactions called the Brusselator, we show that intrinsic noise can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed. 相似文献
6.
The correlation between intrinsic noise and extrinsic noise in a stochastic system is reviewed in this paper. And the contribution of the correlation between intrinsic noise and extrinsic noise to the power spectrum is quantified by simulation through a model in a stochastic system. In addition, the effects of the correlations between intrinsic noise and extrinsic noise to the power spectrum are analyzed clearly. Finally, it is shown that our results can be used to describe the transmission of the noise in modules in more complex stochastic systems. 相似文献
7.
Two distinct mechanisms for filtering noise in an input signal are identified in a class of adaptive sensory networks. We
find that the high-frequency noise is filtered by the output degradation process through time-averaging; while the low-frequency
noise is damped by adaptation through negative feedback. Both filtering processes themselves introduce intrinsic noises, which
are found to be unfiltered and can thus amount to a significant internal noise floor even without signaling. These results
are applied to E. coli chemotaxis. We show unambiguously that the molecular mechanism for the Berg-Purcell time-averaging scheme is the dephosphorylation
of the response regulator CheY-P, not the receptor adaptation process as previously suggested. The high-frequency noise due
to the stochastic ligand binding-unbinding events and the random ligand molecule diffusion is averaged by the CheY-P dephosphorylation
process to a negligible level in E. coli. We identify a previously unstudied noise source caused by the random motion of the cell in a ligand gradient. We show that
this random walk induced signal noise has a divergent low-frequency component, which is only rendered finite by the receptor
adaptation process. For gradients within the E. coli sensing range, this dominant external noise can be comparable to the significant intrinsic noise in the system. The dependence
of the response and its fluctuations on the key time scales of the system are studied systematically. We show that the chemotaxis
pathway may have evolved to optimize gradient sensing, strong response, and noise control in different time scales. 相似文献
8.
O. V. Muzychuk 《Radiophysics and Quantum Electronics》1998,41(10):874-881
Some probability characteristics of the Brownian motion in a symmetric potential profile with two equilibrium states subjected
to a random force are obtained. Two types of potential fluctuations are considered: the delta-correlated Gaussian noise and
the stochastic telegraph process with Poisson statistics of jumps. The stationary probability distributions of the particle
coordinate are found, and the dependence on the properties of parametric and additive noise is studied. It is shown that nonzero
equilibrium states approach each other and vanish as a result of strong potential fluctuations. Relaxation of intensity and
variance of coordinate fluctuations are studied numerically for the case of delta-correlated random forces. The influence
of the value of parametric and additive noise, system nonlinearity, and initial conditions on the relaxation process is determined.
Architectural and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii,
Radiofizika, Vol. 41, No. 10, pp. 1290–1300, October 1998. 相似文献
9.
通过将广义Langevin方程中的系统内噪声建模为分数阶高斯噪声,推导出分数阶Langevin方程, 其分数阶导数项阶数由系统内噪声的Hurst指数所确定.讨论了处于强噪声环境下的线性过阻尼分数阶 Langevin方程在周期信号激励下的共振行为,利用Shapiro-Loginov公式和Laplace变换, 推导了系统响应的一、二阶稳态矩和稳态响应振幅、方差的解析表达式.分析表明,适当参数下, 系统稳态响应振幅和方差随噪声的某些特征参数、周期激励信号的频率及系统部分参数的变化出现了 广义的随机共振现象. 相似文献
10.
We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films. Starting from the incompressible
Navier-Stokes equations with thermal noise, we derive a fourth-order degenerate parabolic stochastic partial differential
equation which includes a conservative, multiplicative noise term—the stochastic thin-film equation. Technically, we rely
on a long-wave-approximation and Fokker–Planck-type arguments. We formulate a discretization method and give first numerical
evidence for our conjecture that thermal fluctuations are capable of accelerating film rupture and that discrepancies with
respect to time-scales between physical experiments and deterministic numerical simulations can be resolved by taking noise
effects into account. 相似文献
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13.
Macroscopic systems (e.g., hydrodynamics, chemical reactions, electrical circuits, etc.) manifest intrinsic fluctuations of molecular and thermal origin. When the macroscopic dynamics is deterministically chaotic, the intrinsic fluctuations may become amplified by several orders of magnitude. Numerical studies of this phenomenon are presented in detail for the Lorenz model. Amplification to macroscopic scales is exhibited, and quantitative methods (binning and a difference-norm) are presented for measuring macroscopically subliminal amplification effects. In order to test the quality of the numerical results, noise induced chaos is studied around a deterministically nonchaotic state, where the scaling law relating the Lyapunov exponent to noise strength obtained for maps is confirmed for the Lorenz model, a system of ordinary differential equations. 相似文献
14.
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. 相似文献
15.
Fulinski A 《Chaos (Woodbury, N.Y.)》1998,8(3):549-556
The role of barrier fluctuations in membrane enzymatic processes, in particular in the active transport of ions through cell membranes, is examined. For enzymes embedded in the cell membrane the role of the barrier height (activation energy) is played by the membrane electric potential. This barrier height can be modulated either by internal fluctuations or by external electrical fields, either random or periodic. Existing experimental data on active transport of Na(+) and Rb(+) in human erythrocytes (catalyzed by Na(+)-K(+)-ATPase) can be interpreted as evidence of stochastic resonance between the external ac field and the fluctuations of the membrane potential. The obtained results suggest that the significant part of these fluctuations is supplied by the stimulated action of neighbor voltage-gated ionic channels. This supports the idea that intrinsic noise plays a constructive role in one of most important and most frequent biophysical processs, viz. ion transmission through cell membranes. Means of further experimental verification of this conjecture are proposed. (c) 1998 American Institute of Physics. 相似文献
16.
D. O. Kharchenko I. O. Lysenko S. V. Kokhan 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,76(1):37-48
We have considered phase separation processes in binary stochastic systems with thermal diffusion and ballistic mixing representing
irradiation influence. Introducing fluctuations of thermal flux and an external source of atom relocations due to ballistic
diffusion into dynamics of a globally conserved field, we have shown that there are two competing mechanisms of phase transitions
type of “order-disorder”: thermally assisted diffusion and irradiation induced atomic exchange. We have studied dynamics of
the structure function at early stages of decomposition. In the framework of the mean field theory we have derived the effective
Fokker-Planck equation to describe phase separation processes. It was shown that the ordering processes can be controlled
by both regular and stochastic parts of external source influence. A reentrant behavior of a mean field order parameter versus
the external noise intensity and fluctuations correlation radius is found. 相似文献
17.
讨论了一个双模环型激光增益噪声模型,其中考虑了完全饱和效应且乘法噪声由增益系数涨落引起。在共振及两模具有相同泵参数时,获得了光强联合定态分布的精确解析表达式。通过与现有的双模激光摸型(其中乘法噪声由损失系数涨落引起)的比较,发现乘法噪声系数的非线性效应减弱了乘法噪声给激光光强统计性质带来的反常特性,并且这种减弱随着乘法噪声增强或损失系数减小而愈加明显。 相似文献
18.
Can-Jun Wang Ke-Li Yang 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(8):173
The correlated noise-based switches and stochastic resonance are investigated in a bistable single gene switching system driven by an additive noise (environmental fluctuations), a multiplicative noise (fluctuations of the degradation rate). The correlation between the two noise sources originates from on the lysis-lysogeny pathway system of the λ phage. The steady state probability distribution is obtained by solving the time-independent Fokker-Planck equation, and the effects of noises are analyzed. The effects of noises on the switching time between the two stable states (mean first passage time) is investigated by the numerical simulation. The stochastic resonance phenomenon is analyzed by the power amplification factor. The results show that the multiplicative noise can induce the switching from “on” → “off” of the protein production, while the additive noise and the correlation between the noise sources can induce the inverse switching “off” → “on”. A nonmonotonic behaviour of the average switching time versus the multiplicative noise intensity, for different cross-correlation and additive noise intensities, is observed in the genetic system. There exist optimal values of the additive noise, multiplicative noise and cross-correlation intensities for which the weak signal can be optimal amplified. 相似文献
19.
The influence of spatio-temporal external multiplicative fluctuations on a single kink in a bistable distributed system is studied. For this purpose we derive a stochastic dynamic equation for the position of the shifted kink. An analytical estimate for spatio-temporally uncorrelated fluctuations is represented and discussed. We draw the conclusion that multiplicative noise induces a propagation of the most probable kink into the region of larger noise. This effect is demonstrated in numerical simulations. 相似文献