Noise-induced coupling and phase transition in initially homogeneous bistable system

We show that a colored spatial noise induces a heterogeneous behavior and coupling of initially uncoupled single bistable units. A formal approximation reduces a non-Markovian stochastic process described by the initial set of equations into Markovian process in terms of Langevin equation, for which a simple piecewise linear emulation was used to represent the nonlinear deterministic force. It turned out that the coupling leads to a phase transition due to the noise-induced diffusive term. As an example, a typical bistable noisy system with symmetric double-well potential was studied.     

耦合双稳系统的随机共振控制

两个双稳系统经非线性耦合而成为多稳态系统,该耦合系统与单一双稳系统相比具有较高的理论研究和实际应用价值.解析地分析了耦合系统在含噪弱周期信号作用下的响应特性,给出了耦合系数和双稳系统参数对随机共振的影响,表明耦合系统的随机共振是在带状的双势阱作用下产生的,还构建了反馈耦合控制原理框图.这为在双稳类系统中人为地产生随机共振或使共振效应更加强烈即随机共振的控制及其应用提供了可靠的理论依据.数值仿真结果与理论分析完全符合. 关键词： 耦合双稳系统 随机共振 控制     

The effect of dissipation on coherent quantum tunnelling in a double-well system: Two-level model using an adjoint equation approach

We examine the effect of dissipation on coherent quantum tunnelling between the two lowest levels of a double-well system using an adjoint equation approach developed previously in the treatment of quantum-optical problems. Dissipation is modelled by a linear coupling to a bath of harmonic oscillators. The high frequency portion of the bath is adiabatically eliminated using a cumulant expansion technique, which generates frequency renormalisation terms. Making a low temperature assumption, an approximate two-level model is developed in the form of three coupled stochastic differential equations. With a decorrelation approximation, the two-level equations can be solved to yield familiar results. However, the adjoint equation also permits the use of direct stochastic simulation as a means of solution, and simulations are carried out for a range of parameters. A comparison with the decorrelation approximation is made.     

基于Laguerre多项式逼近法的随机双势阱Duffing系统的分岔和混沌研究

应用Laguerre正交多项式逼近法研究了含有随机参数的双势阱Duffing系统的分岔和混沌行为.系统参数为指数分布随机变量的非线性动力系统首先被转化为等价的确定性扩阶系统，然后通过数值方法求得其响应.数值模拟结果的比较表明，含有随机参数的双势阱Duffing系统保持着与确定性系统相类似的倍周期分岔和混沌行为，但是由于随机因素的影响，在局部小区域内随机参数系统的动力学行为会发生突变. 关键词： 双势阱Duffing系统 指数分布概率密度函数 Laguerre多项式逼近 随机分岔     

Statistical techniques analysis of SST and SLP in the Persian Gulf

Thirty-four years of data (1967-2000) are used to investigate the variability pattern relevant to air-sea interaction in the Persian Gulf. The patterns are derived using statistical techniques, such as empirical orthogonal function (EOF) and singular value decomposition (SVD). Statistical analysis methods are applied to determine the coupled modes of variability of monthly sea surface temperature (SST) and sea level pressure (SLP). The significant of the air-sea interaction is found by a strong resemblance between EOF and SVD eigenvectors and expansion coefficients of SST and SLP. We find that the four leading EOF patterns of SST together account for 99.8% of the total monthly SST variance and 94.4% of the SLP variance. The zero contour in the first SST EOF identified the front which separates the Persian Gulf cyclonic gyres.The SVD modes provide more information on the coupling between the fields than the modes obtained by EOF methods. Lagged correlation analysis between SVD1(SLP) and SVD1(SST) indicates that the coupling is strongest when SLP leads SST by −12, −6, 6 and 12 months. Therefore, the first mode of the SVD analysis seems to depict an air-to-sea forcing, in which the sea response to the atmospheric changes appears with an semiannual and interannual time lag.The two leading SVD modes of variability of the coupled SST and SLP fields account for 99.6% of the total variance. The main patterns of both variables of variability of both variables independently provide considerable information on the coupling, but only one of the two variables dominates each of the two first coupled modes.The first coupled mode of variability between the SST and atmospheric pressure can be described as a strengthening and weakening of the cyclonic gyres, which seems to force fluctuations in a north-south dipole structure in the SST by Ekman upwelling which is a wind-related process. The atmospheric forcing of the SST changes is detectable in the sea with a lag of 1 and 6 months.     

Selective effects of noise by stochastic multi-resonance in coupled cells system

By investigating a stochastic model for intracellular calcium oscillations proposed by Höfer, we have analyzed the transmission behavior of calcium signaling in a one-dimensional two-way coupled hepatocytes system. It is shown that when the first cell is subjected to the external noise, the output signal-to-noise ratio (SNR) in the cell exhibits two maxima as a function of external noise intensity, indicating the occurrence of stochastic bi-resonance (SBR). It is more important that when cells are coupled together, the resonant behavior in the 1st cell propagates along the chain with different features through the coupling effect. The cells whose locations are comparatively close to or far from the 1st cell can show SBR, while the cells located in the middle position can display stochastic multi-resonance (SMR). Furthermore, the number of cells that can show SMR increases with coupling strength enhancing. These results indicate that the cells system may make an effective choice in response to external signaling induced by noise, through the mechanism of SMR by adjusting coupling strength.     

Assessment of ForeFire/Meso-NH for wildland fire/atmosphere coupled simulation of the FireFlux experiment

Numerical simulations using a coupled approach between Meso-NH (Non-Hydrostatic) LES (Large Eddy Simulation) mesoscale atmospheric model and ForeFire wildland fire area simulator are compared to experimental data to assess the performance of the proposed coupled approach in predicting fine-scale properties of the dynamics of wildland fires. Meso-NH is a non-hydrostatic, large eddy simulation capable, atmospheric research model. ForeFire insures a front tracking of the fire front by means of Lagrangian markers evolving on the earth’s surface according to a physical rate-of-spread model. The atmospheric model forces the fire behavior through the surface wind field, whereas the fire forces the atmosphere simulation through surface boundary conditions of heat and vapor fluxes. The FireFlux experiment, an experimental 32 Ha burn of tall grass instrumented with wind profilers and thermocouples, was designed specifically to estimate the atmospheric perturbation introduced by wildland fire. Comparisons of the simulations at different resolutions with the large-scale experiment validate the chosen coupling methodology and the choice of a coupled approach with a meso-scale atmospheric model for the prediction of wildland fire propagation. Distinct fire propagation behavior is simulated between coupled and non-coupled simulation. While the simulations did not reproduce high frequency perturbations, it is shown that the atmospheric model captures well atmospheric perturbations induced by combustion at the ground level in terms of behavior and amplitude.     

Feedback control in a coupled Brownian ratchet

On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.     

A quantitative criterion validating coupling power proportionality in statistical energy analysis

The response of two general spring-coupled elements is investigated to develop a unifying approach to the weak coupling criterion in Statistical Energy Analysis (SEA). First, the coupled deterministic equations of motion are expressed in the bases given by the uncoupled elements’ eigenmodes. Then, an iterative solution is expressed as a succession of exchanges between elements, where uncoupled motion provides the start approximation, converging if the ‘coupling eigenvalue’ is less than unity, in which case coupling is said to be weak. This definition is related to whether response is ‘local’ or ‘global’, encompassing a number of previously defined coupling strength definitions, applying for deterministically described structures. A stochastic ensemble is defined by that its members are equal to the investigated structure but the elements have random frequencies. It is required that the coupling eigenvalue be less than unity for all members of the ensemble. This requirement generates the title subject of the article: ‘the modal interaction strength’. It is similar to the previously defined coupling strength criterion characterising the ensemble average energy flow in uni-dimensional waveguides. Finally, SEA models are formulated in terms of the uncoupled elements’ modal data.     

双势阱中冷原子的关联隧穿

研究了在不同的相互作用和隧穿耦合强度比值情况下双势阱中冷原子的隧穿现象.两格点Bose-Hubbard模型不能完全解释实验.为此,对此模型做了高阶修正.取双势阱的基态和第一激发态作基矢,写出哈密顿量的表示,解释了用两格点Bose-Hubbard模型分析实验时参数不能定量符合的原因.另外,通过计算两阱中原子纠缠度的变化,结合三态上原子布居数分布,直观描述了整个隧穿过程.     

双势阱中冷原子的关联隧穿

研究了在不同的相互作用和隧穿耦合强度比值情况下双势阱中冷原子的隧穿现象.两格点Bose-Hubbard模型不能完全解释实验.为此,对此模型做了高阶修正.取双势阱的基态和第一激发态作基矢,写出哈密顿量的表示,解释了用两格点Bose-Hubbard模型分析实验时参数不能定量符合的原因.另外,通过计算两阱中原子纠缠度的变化,结合三态上原子布居数分布,直观描述了整个隧穿过程.     

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.     

Complex behavior of globally coupled Hamiltonian elements

We study the effects of global coupling on a set of elements whose individual dynamics is that of a one-dimensional Hamiltonian system subject to a double-well symmetric potential. Since the coupled set is in turn a Hamiltonian system, complete entrainment or synchronization is not possible due to the conservation of the phase-space volume. Instead, global coupling gives rise to a new kind of collective behavior, where the elements — initially scattered at random in the phase plane — become distributed in a complex, fractal structure. We suggest that this form of spontaneous organization should be generic in the evolution of globally coupled Hamiltonian elements.     

Synchronization in an array of linearly stochastically coupled networks with time delays

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.     

Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling

We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. For a large number of one-dimensional continuous stochastic elements coupled non-homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean-field oscillations on it. Namely, the exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker-Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker-Planck equation into a series of eigenfunctions of the stationary Fokker-Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis in the mean-field behavior are observed in the stochastic network at finite noise intensities. In the limit of small noise intensities the critical coupling strength is shown to remain finite, provided that the delay in the coupling function is not infinitely small. Delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold.     

Synchronization experiments with an atmospheric global circulation model

Synchronization in a chaotic system with many degrees of freedom is investigated by coupling two identical global atmospheric circulation models. Starting from different initial conditions, the two submodels show complete synchronization as well as noncomplete synchronization depending on the coupling strength. The relatively low value of the coupling strength threshold for complete synchronization indicates the potential importance of synchronization mechanisms involved in climate variability. In addition, the results suggest synchronization experiments as a valuable additional method to analyze complex dynamical models, e.g., to estimate the largest Lyapunov exponent. (c) 2001 American Institute of Physics.     

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.     

自催化三分子模型内噪声随机共振

运用化学Langevin方程 ,数值研究了内噪声对单个和单向耦合自催化三分子模型动力学行为的影响 .研究发现 ,对于单个振子体系 ,内噪声可以诱导持续振荡 ,而且随着系统尺度的增大 ,信噪比经过一个极大值 ,从而证明了内噪声随机共振和最佳尺度效应的存在 ;对于单向耦合系统 ,信噪比还随耦合强度的变化而经过极大值 .此外 ,边界条件对耦合体系的内噪声随机共振行为有很大影响 ,非零流条件下 ,耦合可以增强内噪声随机共振 ,而零流条件下 ,耦合会抑制随机共振 ;当耦合强度适宜时 ,每个振子发生随机共振时的尺度几乎相同 ,表明最佳体系尺度和耦合强度有助于体系达到最佳的化学反应状态 .     

Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance

Low-frequency variability (LFV) of the atmosphere refers to its behavior on time scales of 10–100 days, longer than the life cycle of a mid-latitude cyclone but shorter than a season. This behavior is still poorly understood and hard to predict. The present study compares various model reduction strategies that help in deriving simplified models of LFV.Three distinct strategies are applied here to reduce a fairly realistic, high-dimensional, quasi-geostrophic, 3-level (QG3) atmospheric model to lower dimensions: (i) an empirical–dynamical method, which retains only a few components in the projection of the full QG3 model equations onto a specified basis, and finds the linear deterministic and the stochastic corrections empirically as in Selten (1995) [5]; (ii) a purely dynamics-based technique, employing the stochastic mode reduction strategy of Majda et al. (2001) [62]; and (iii) a purely empirical, multi-level regression procedure, which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in Kravtsov et al. (2005) [3]. The empirical–dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi-level regression models; the extended Kalman filter was used for the parameter estimation.Overall, the reduced models perform better when more statistical information is used in the model construction. Thus, the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full QG3 model’s LFV, i.e. its autocorrelations and spectra, as well as the nonlinear properties, i.e. the persistent flow regimes that induce non-Gaussian features in the model’s probability density function. The empirical–dynamical models capture the basic statistical properties of the full model’s LFV, such as the variance and integral correlation time scales of the leading LFV modes, as well as some of the regime behavior features, but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes. Dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical–dynamical models, but do much less well on the full QG3 model’s nonlinear dynamics. These results are discussed in terms of their implications for a better understanding and prediction of LFV.     

Absortive and dispersive optical properties in molecular systems

Solute-solvent collisions for a two-level molecular system interacting with a four-wave mixing signal are analyzed in the present contribution. The system is described using the optical stochastic Bloch equations (OSBE), where Bohr’s frequency is treated a stochastic variable due to the random collisions with the solvent. The resulting equations for the Fourier components associated to the coherence are averaged over all the realizations of the stochastic variable, using an approximant for the Voigt’s function as a probability distribution. In this model we were able to calculate the optical susceptibilities at different frequencies, depicted as numerical surfaces for the behavior of the optical properties.