用一种分数阶算法研究非马尔可夫过程中阻尼与涨落的竞争机制

基于分数阶朗之万方程和随机行走理论, 建立了一种用于研究非马尔可夫系统中随机变量随时间演化的数值模拟算法, 称之为分数阶随机行走模拟法. 进一步运用此算法分别数值研究了无阻尼有涨落、 有阻尼无涨落和阻尼与涨落兼备三种情况下, 受欠扩散分数阶朗之万方程约束的随机变量随时间的演化行为. 结果显示阻尼和涨落存在竞争关系: 高斯型涨落的影响会随着时间的增长被"抹平", 从而凸显阻尼使系统趋于平衡的作用; 而长尾型涨落则由于包含"小概率大贡献"事件, 使得长时间演化之后系统变量仍以一定概率出现突然变化. 关键词： 非马尔可夫 欠扩散 阻尼与涨落 分数阶朗之万方程     

朗之万方程及其在蛋白质折叠动力学中的应用

研究了朗之万方程的动力学性质,并用它模拟了蛋白质分子的折叠过程.首先在相空间中对朗之万方程做连续映射,发现做布朗运动的粒子在位置坐标上存在明显的概率分布,这表明蛋白质折叠过程中分子空间构型是非遍历的.此外,本文还通过数值模拟得到了去折叠态蛋白质的紧密度指标,并验证了它与实验结果以及其他理论方法的一致性.本文还提出了一种利用重整化方法研究熔球体状态蛋白质的理论模型,并提供了考虑疏水基影响的蛋白质折叠过程的模拟思路. 关键词： 朗之万方程 蛋白质折叠非遍历性 紧密度指标 重整化     

基于三磷酸腺苷调节的分子马达单向能量跃迁模型

分子马达的梯跳运动和在过阻尼溶液中动力学原理尚未揭示清楚, 从分子马达输运特点和实验现象出发, 构建满足朗之万方程的单向能量跃迁模型, 并通过Monte Carlo方法分析了分子马达的随机动力学行为. 结果表明, 在合适的跃迁能量作用下, 分子马达可以利用噪声进行稳定的梯跳运动和有效的输运, 但负载力会减弱分子马达系统的输运能力; 轨道周期势虽影响分子马达速度的大小但不会改变其运动方向, 分子马达运动方向由跃迁能量决定; 另外, 虽然在不同的噪声强度时平均速度不为零, 但是分子马达系统的高效输运对噪声有一定选择性. 关键词： 分子马达 能量跃迁 朗之万方程 噪声强度     

一维势阱中被噪声驱动的粒子的逃逸问题

通过计算机数值模拟直接解朗之万方程，得到一维势阱中被高斯白噪声驱动的粒子的逃逸率，并与理论结果进行了对照。     

量子点接触中有关电导0.7结构的研究

研究了由鞍形势描述的量子点接触中的电子输运性质,利用Hartree-Fock近似与低维纳米器件中Thomas-Fermi近似方法处理了电子-电子之间的相互作用,采用格点格林函数方法计算了零温下体系的电导、电子的自旋积累以及散粒噪声,重现了0.7结构这个反常的实验现象.计算结果加深了我们关于半导体纳米器件中的强关联互作用对自旋输运影响的理解.     

非平衡涨落问题的微观唯象分析理论(Ⅰ)——一种新的广义不可逆热力学理论与热涨落中涨落—耗散表示式的非平衡修正

本文给出非平衡涨落问题的微观唯象分析理论——非平衡涨落的统计学描述理论。该理论的基础是广义非平衡熵与描述涨落几率的爱因斯坦表示式的推广。通过计算求得刚体热传导中比能与热通量的非平衡涨落的二阶矩。导出对热涨落的通用涨落-耗散表示式的非平衡修正,同时发现该修正相当于固体电介质中的光子热输运与金属中电子热输运的数值修正。     

InAlN/GaN异质结二维电子气波函数的变分法研究

使用变分法推导了InAlN/GaN异质结二维电子气波函数和基态能级的解析表达式,并讨论了InAlN/GaN异质结结构参数对二维电子气电学特性的影响.在假设二维电子气来源于表面态的前提下,使用了一个包含两个变分参数的尝试波函数推导电子总能量期望值,并通过寻找能量期望极小值确定变分参数.计算结果显示,二维电子气面密度随InAlN厚度的增大而增大,且理论结果与实验结果一致.二维电子气面密度增大抬高了基态能级与费米能级,并保持二者之差增大以容纳更多电子.InAlN/GaN界面处的极化强度失配随着In组分增大而减弱,二维电子气面密度随之减小,并导致基态能级与费米能级减小.所建立的模型能够解释InAlN/GaN异质结二维电子气的部分电学行为,并为电子输运与光学跃迁的研究提供了解析表达式.     

基于冲击力模型的分子马达动力学分析

从分子马达输运特点和实验现象出发,建立满足朗之万方程的冲击力模型,分析分子马达定向输运的动力学行为.研究发现:在合适的冲击力和噪声强度的共同作用下,分子马达可以稳定的梯跳跃迁运动和有效的输运;分子马达在轨运动的方向由冲击力的方向决定;另外,虽然在不同的噪声强度时平均速度都不为零,但是整个分子马达系综的高效输运对噪声强度有一定的选择性;系综的平均速度随着负载力的增大而减小,甚至会产生反方向的运动.     

蛋白质电子晶体学

介绍了蛋白质电子晶体学的基本概念，研究对象以及电子显微学三维重构的原理，概括地描述了蛋白质二维晶体生长技术、电镀样品的制备与观察方法和数据处理流程，通过一些典型事例，说明了蛋白质电子晶体学的发展现状，并展望了该学科的发展前景。     

n型金属氧化物半导体场效应晶体管噪声非高斯性研究

基于n型金属氧化物半导体场效应晶体管（nMOSFET）噪声的数涨落模型,采用高阶统计量双相干系数平方和研究了nMOSFET噪声的非高斯性.通过对nMOSFET实际测试噪声的分析,发现nMOSFET器件噪声存在非高斯性;小尺寸器件噪声的非高斯性强于大尺寸器件;在器件的强反型线性区,其非高斯性随着漏压的增加而增加.文中还通过蒙特卡罗模拟和中心极限定理理论对nMOSFET噪声的非高斯性作了深入的探讨. 关键词： 噪声 非高斯性 n型金属氧化物半导体场效应晶体管 氧化层陷阱     

激光场中两维色噪声的近似计算

从色散型介质中三次激光模型出发，通过泛函导数，应用小于τ近拟计算两维色噪声，得到激光场定态强度分布，研究了定态强度分布的极值点随抽运参量和强度噪声相关时间的变化情况。应用平移1／N展开方法，得到激光场瞬态解，即本征值随抽运参量的变化情况。研究结果表明，抽运参量和噪声相关时间是激光系统出现一级相变类比的关键因素，相位噪声相关时间对强度谱分布中的线宽影响较大。     

Noise at the crossover from Wigner liquid to Wigner glass

Using a simple classical model for interacting electrons in two dimensions with random disorder, we show that a crossover from a Wigner liquid to a Wigner glass occurs as a function of charge density. The noise power increases strongly at the crossover and the characteristics of the 1/f(alpha) noise change. When the temperature is increased, the noise power decreases. We compare these results with recent noise measurements in systems with two-dimensional metal-insulator transitions.     

The stochastic heat equation: Feynman-Kac formula and intermittence

We study, in one space dimension, the heat equation with a random potential that is a white noise in space and time. This equation is a linearized model for the evolution of a scalar field in a space-time-dependent random medium. It has also been related to the distribution of two-dimensional directed polymers in a random environment, to the KPZ model of growing interfaces, and to the Burgers equation with conservative noise. We show how the solution can be expressed via a generalized Feynman-Kac formula. We then investigate the statistical properties: the two-point correlation function is explicitly computed and the intermittence of the solution is proven. This analysis is carried out showing how the statistical moments can be expressed through local times of independent Brownian motions.     

Monte Carlo analysis of polymer translocation with deterministic and noisy electric fields

Polymer translocation through the nanochannel is studied by means of a Monte Carlo approach, in the presence of a static or oscillating external electric voltage. The polymer is described as a chain molecule according to the two-dimensional “bond fluctuation model”. It moves through a piecewise linear channel, which mimics a nanopore in a biological membrane. The monomers of the chain interact with the walls of the channel, modelled as a reflecting barrier. We analyze the polymer dynamics, concentrating on the translocation time through the channel, when an external electric field is applied. By introducing a source of coloured noise, we analyze the effect of correlated random fluctuations on the polymer translocation dynamics.     

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

一种基于非完整二维相空间分量置换的混沌检测方法

由于混沌时间序列和随机过程具有很多类似的性质, 因而在实际中很难将两者区分开来. 混沌信号检测与识别是混沌时间序列分析中一个重要的课题. 混沌信号是由确定性的混沌映射或混沌系统产生的, 相比于高斯白噪声序列, 其在非完整的二维相空间中表现出更加丰富的结构特性. 本文通过研究混沌时间序列和高斯白噪声序列在非完整二维相空间中的分布特性, 利用混沌信号的非线性动力学特性, 提出了一种基于非完整二维相空间分量置换的混沌信号检测方法. 该方法首先由接收序列得到非完整的二维相空间, 基于第一维分量大小关系实现对第二维分量的置换与分组, 进一步求得F检验统计量. 然后利用混沌系统的局部特性, 获取非完整二维相空间的动力学结构信息, 实现对混沌序列的有效检测. 在高斯白噪声条件下对多种混沌信号进行了信号检测的数值仿真. 仿真结果表明: 相比置换熵检测, 本文所提算法所需数据量小、计算简单以及具有更低的时间复杂度, 同时对噪声具有更好的鲁棒性.     

Exponential decay and scaling laws in noisy chaotic scattering

In this Letter we present a numerical study of the effect of noise on a chaotic scattering problem in open Hamiltonian systems. We use the second order Heun method for stochastic differential equations in order to integrate the equations of motion of a two-dimensional flow with additive white Gaussian noise. We use as a prototype model the paradigmatic Hénon-Heiles Hamiltonian with weak dissipation which is a well-known example of a system with escapes. We study the behavior of the scattering particles in the scattering region, finding an abrupt change of the decay law from algebraic to exponential due to the effects of noise. Moreover, we find a linear scaling law between the coefficient of the exponential law and the intensity of noise. These results are of a general nature in the sense that the same behavior appears when we choose as a model a two-dimensional discrete map with uniform noise (bounded in a particular interval and zero otherwise), showing the validity of the algorithm used. We believe the results of this work be useful for a better understanding of chaotic scattering in more realistic situations, where noise is presented.     

T(1)--T(2) correlation spectra obtained using a fast two-dimensional Laplace inversion

Spin relaxation is a sensitive probe of molecular structure and dynamics. Correlation of relaxation time constants, such as T(1) and T(2), conceptually similar to the conventional multidimensional spectroscopy, have been difficult to determine primarily due to the absense of an efficient multidimensional Laplace inversion program. We demonstrate the use of a novel computer algorithm for fast two-dimensional inverse Laplace transformation to obtain T(1)--T(2) correlation functions. The algorithm efficiently performs a least-squares fit on two-dimensional data with a nonnegativity constraint. We use a regularization method to find a balance between the residual fitting errors and the known noise amplitude, thus producing a result that is found to be stable in the presence of noise. This algorithm can be extended to include functional forms other than exponential kernels. We demonstrate the performance of the algorithm at different signal-to-noise ratios and with different T(1)--T(2) spectral characteristics using several brine-saturated rock samples.     

Colored noise in a two-dimensional nonlinear system

A two-dimensional decoupling theory is developed when colored noise is included in a nonlinear dynamical system. By a functional analysis, the colored noise is transformed to an effective noise that includes the noise correlation time, the mean dynamical variable, and the original noise strength. When the two-dimensional decoupling theory is applied to single-mode and two-mode dye laser systems, the mean, variance, and effective eigenvalue of laser intensity are calculated. Excellent agreement between theoretical analysis, numerical simulations, and experimental measurements are obtained. It is seen that the increase of noise correlation time can reduce the fluctuations in the laser system. It is also shown that there is relatively large fluctuation in the phase when the laser undergoes from thermal light to coherent light when the theory is applied to a single mode dye laser. Received 20 August 2001 and Received in final form 4 December 2001     

批量高速二维码视觉检测识别系统

针对工业实际项目提出一种高效、准确的二维码识别方法,并开发了基于机器视觉的二维码高速、批量识别系统。首先根据被测二维码在目标子空间内的位置,提出利用几何关系定位每个二维码感兴趣区域并批量处理二维码的方法。在此基础上,采用添加高斯噪声的方式模拟生产实际中可能产生的噪声,评估系统抗噪能力。最后分析系统识别率与二维码运动速度的关系并比较实验结果。通过实验验证,在1800张的测试数据集中,二维码移动速度在296.8 mm/s情况下,无噪声图像中每个二维码定位识别平均时间为17.8 ms,有噪声图像为21.3 ms,识别率均为100%,该系统满足实时在线检测需求。