Rate processes on fractals: Theory,simulations, and experiments

Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A products we show that the diffusion-limited reaction rate is proportional tot ^– h[A]² or to [A]^x, whereh=1- d _s/2, X=1+2/d _s =(h-2)(h-1), andd _s is the effective spectral dimension. We note that ford = d _s =1, h =1/2 andX = 3, for percolating clustersd _s = 4/3,h = 1/3 andX = 5/2, while for dust ds <1, 1 >h > 1/2 and >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

激光增益系数ζ(ν)和佛克脱函数的近似积分计算—兼论δ函数在近似计算中的应用

本文分析了激光增益系数ζ(υ)和佛克脱积分函数I(υ,υ_0).指出两函数的积分困难均来源于洛伦兹分布函数和多普勒分布函数的褶积.文中进一步分析了洛伦兹函数φ_N和多普勒函数φ_D,并引出函数的峰宽比α,指出当峰宽比α_N>>α_D时,可以把积分号内的φ_N当作δ函数来处理.反之也然.这样就很容易得到ζ(υ)和I(υ,υ_0)的近似积分.     

武定县地域功能区划分方法研究

县级功能区划作为综合区划,既是落实省级主体功能区规划,又是编制县域空间发展规划的基础。首先探讨县级功能区划方法,然后以武定县为例运用主导因素法划分出城镇区、资源开发区、开发预留区、农业区、生态区等功能区。研究发现：(1)县级功能区划既要考虑县域资源环境本底与发展愿景,又要兼顾省级主体功能区对本县定位;(2)区划评价单元须考虑基础数据可获得性及各单项指标评价单元的统一;(3)指标体系选取以省级主体功能区划指标体系为参照,具有可行性;(4)单一区划方法无法合理区划县级各功能区单元,需多种方法相结合。     

DNA纤维的X射线衍射分析与双螺旋结构的发现

概述了DNA化学结构式确立的过程,介绍了x射线衍射分析的概念、原理和方法,阐述了物理学家威尔金斯和物理化学家富兰克林在用实验事实证明DNA双螺旋结构方面所作出的巨大贡献。     

量子数字签名研究进展

量子数字签名是量子理论与经典数字签名的结合,其目的是利用量子效应达到无条件安全的信息交互。介绍了目前提出的几种量子数字签名协议,详细分析了这几种协议的优缺点和效率,提出了量子数字签名协议设计的具体要求,并展望了此领域今后的发展方向。     

The real solution to scalar field equation in 5D black string space

After the nontrivial quantum parameters Ω _n and quantum potentials V _n obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik and Simonsen (Gen. Rel. Grav. 33:1839, 2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon r _e and the outer horizon r _c . Unlike the usual wave function Ψ_ωl in 4D, quantum number n introduces a new functions Ψ_{ωl n} , whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schrödinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function Ψ_{ωl n} may say something to it.     

Rapidly convergent series for high-accuracy calculation of the Voigt function

A rapidly convergent series, based on Fourier expansion of the exponential multiplier, is presented for highly accurate approximation of the Voigt function (VF). The corresponding algorithm enables the rapid calculation, required for its implementation as a subprogram in an interpolation approach. The numerical analysis of this VF approximation suggests that it may be more accurate than 10⁻⁹ in the Humlí?ek regions 3 and 4.     

基于RBF神经网络的较低浓度下同步荧光光谱的溢油鉴别

针对海面溢油样品的含量难以确定,同时考虑到海水掺杂及风化等问题的影响,提出了在较低非线性浓度范围内采集溢油嫌疑样品的同步荧光光谱,获取其训练样本集,利用主成分分析法(Principal com-ponent analysis,PCA)提取其特征光谱,结合径向基函数(Radial basis function,RBF)神经网络对肇事样本和嫌疑样本进行模式识别的方法。通过对相近油源原油样品分类识别研究表明:该方法仅需单次对肇事样本同步光谱测量,再借助数据分析,就可以很好区分相近油源溢油样品,外扰对识别率影响也不大。RBF神经网络算法识别率在92%左右。该结论对海洋环境中溢油的实时检测及油指纹数据信息库的建立有重要意义。     

980 nm脉冲激发下Er3+掺杂材料中4Ⅰ13/2→4Ⅰ15/2跃迁的瞬态行为

在过去的几十年人们对Er3+掺杂的玻璃材料进行了广泛的研究,因为Er3+的4Ⅰ13/2→4Ⅰ15/2跃迁能够给出适合红外光通讯窗口的1.5 μm的发射.据我们所知,目前关于脉冲激光激发下Er3+掺杂材料1.5 μm发射的动力学行为研究报道仍很少.我们引入了转移函数理论,研究了980nm脉冲激发下Er3+的4Ⅰ13/2能级荧光的动力学行为.发现在980nm脉冲激发后,其荧光衰减遵循双指数规律,4Ⅰ13/2能级布居分为指数上升和指数下降两个过程.