Lattice animals: A fast enumeration algorithm and new perimeter polynomials

A fast computer algorithm for enumerating isolated connected clusters on a regular lattice and its Fortran implementation are presented. New perimeter polynomials are calculated for the square, the triangular, the simple cubic, and the square lattice with next nearest neighbors.     

Counting lattice animals: A parallel attack

A parallel algorithm for the enumeration of isolated connected clusters on a regular lattice is presented. The algorithm has been implemented on 17 RISC-based workstations to calculate the perimeter polynomials for the plane triangular lattice up to clustersizes=21. New data for perimeter polynomials D_s up toD ₂₁, total number of clustersg _s up tog ₂₂, and coefficientsb _r in the low-density series expansion of the mean cluster size up tob ₂₁ are given.     

基于综合特征的光纤周界安防系统高效入侵事件识别

在光纤周界安防系统中,急需对入侵事件实现准确而高效的识别,对事件特征做简练而恰当的描述是其关键所在.本文提出一种基于综合特征的入侵事件识别方法,该方法引入全相位滤波器组将输入信号并行分解为多个频率通道,以提取这些通道的归一化功率值;进而与信号过零率相结合,构成包含时域信息、频域信息的综合特征向量;最后将该特征向量馈入径向基函数神经网络即可准确识别出攀爬、敲击、晃动、剪切四种常见的入侵动作.实验证明,本文方法相比于现有的经验模态分解方法,不仅提高了精度,而且显著加快了识别速度.     

Enumerations of Lattice Animals and Trees

We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, =4.062570(8), for the growth constant of lattice animals, and, ₀=3.795254(8), for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, =0.64115(5), for the size exponent.     

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp [pA−Jb] to a polygon with area A and b bends. For convex and column-convex polygons, we calculate the average area for positive values of the pressure. For large pressures, the area has the asymptotic behaviour , where , and ρ<1. The constant K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for J≠0. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.     

倾斜油水两相流流型混沌吸引子形态周界测度分析

在两维相空间中定义了吸引子形态周界特征量（吸引子面积、长轴、短轴）,考察了吸引子周界特征量随时间延迟的变化规律.发现在吸引子展开过程的第一区域内,其吸引子周界特征量变化率具有不变性.通过对正弦信号、噪声信号和混沌信号进行仿真分析,发现采用吸引子周界特征量可以对这些不同信号进行有效分类.在采集倾斜油水两相流电导波动信号基础上,对水为连续相的倾斜油水两相流流型进行了吸引子形态周界测度分析,发现吸引子面积增长率是描述吸引子形态的不变特征量,该特征量对水为连续相的拟段塞水包油（D O/W PS）和局部逆流水包油（ 关键词： 倾斜油水两相流 流型识别 吸引子形态 周界测度     

Correlations between zeros of a random polynomial

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1, 1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit-translation-invariant correlations. Then we calculate the correlations between the straightened zeros of theO(1) random polynomial.     

Wave propagation in layered piezoelectric rectangular bar: An extended orthogonal polynomial approach

Wave propagation in multilayered piezoelectric structures has received much attention in past forty years. But the research objects of previous research works are only for semi-infinite structures and one-dimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes an extension of the orthogonal polynomial series approach to solve the wave propagation problem in a two-dimensional (2-D) piezoelectric structure, namely, a multilayered piezoelectric bar with a rectangular cross-section. Through numerical comparison with the available reference results for a purely elastic multilayered rectangular bar, the validity of the extended polynomial series approach is illustrated. The dispersion curves and electric potential distributions of various multilayered piezoelectric rectangular bars are calculated to reveal their wave propagation characteristics.     

Eigenvalue spectrum with chebyshev polynomial approximation of the transport equation in slab geometry

Using certain well-known properties of chebyshev polynomials, a simple and highly efficient approach to evaluate eigenvalue in radiation transport is presented. The spectrum of eigenvalues has been studied for slabs with isotropic scattering of different magnitudes of the cross section parameter c (i.e., the mean number of neutrons emitted per collision). It is shown that in the presence of the chebyshev polynomial approximation (T_N) there are both discrete and continuum of eigenvalues. It is found that the T_N method gives very good agreement with conventional spherical harmonics approximation (P_N).     

Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in ${\mathbb{C}}^2$ is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing–van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing–van der Pol system are constructed.     

Application of jacobi polynomial methods to the one-speed transport equation

The transport equations associated with radiation damage studies are often solved using expansions in Legendre polynomials. The radiation damage distribution functions which satisfy these equations may be sharply peaked in the forward direction, while the Legendre polynomials, as a set, are isotropic. This situation requires the use of many terms in the Legendre expansion in order to adequately represent the distribution functions. The Jacobi polynomials, on the other hand, can have strong peaking built into their associated weight function. To test the usefulness of the Jacobi polynomials we use them to solve the simple, one-speed, neutron transport equation. The results are then compared to the exact theory and to the results of applying Legendre methods to the same problem. This sample calculation demonstrates the advantage of the Jacobi polynomials in strongly non-isotropic situations.     

Marriage of exact enumeration and 1/d expansion methods: Lattice model of dilute polymers

We consider the properties of a self-avoiding polymer chain with nearestneighbor contact energy on ad-dimensional hypercubic lattice. General theoretical arguments enable us to prescribe the exact analytic form of then-segment chain partition functionC _n ,and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data ind=2–6. This exact form provides the main ingredient to produce a large-n expansion ind ^–1of the chain free energy through fifth order with the full dependence on the contact energy retained. The -dependent chain connectivity constant and free energy amplitude are evaluated within thed ^–1expansion toO(d ^–5). Our general formulation includes for the first time self-avoiding walks, neighboravoiding walks, theta, and collapsed chains as particular limiting cases.     

A convenient expression of the time-derivative,of arbitrary order k,of the zero zn(t) of a time-dependent polynomial pN(z;t) of arbitrary degree N in z,and solvable dynamical systems

Let p_N (z; t) be a (monic) time-dependent polynomial of arbitrary degree N in z, and let z_n ≡ z_n (t) be its N zeros: . In this paper we report a convenient expression of the k-th time-derivative of the zero z_n (t). This formula plays a key role in the identification of classes of solvable dynamical systems describing the motion of point-particles moving in the complex z-plane while nonlinearly interacting among themselves; one such example, featuring many arbitrary parameters, is reported, including its variation describing the motion of many particles moving in the real Cartesian xy-plane and interacting among themselves via rotation-invariant Newtonian equations of motion (”accelerations equal forces”).     

星间光通信系统中多样化波前畸变的小波重构

用小波变换方法对星间光通信中的多样化波前畸变进行重构,并分析了小波重构方法的两项参考指标：重构精度和重构算法复杂度。基于对这两项指标的综合考虑,提出一种最优小波基函数的选取方法。仿真数据表明,利用最优小波基函数选取方法对波前畸变进行重构,较之传统的Zernike多项式拟合方法,具有重构精度高且计算量小的特点。     

New Operator Ordering Formulas Related to Hermite Polynomials Derived by Virtue of IWOP Technique

By virtue of the technique of integration within an ordered product of operators and the fundamentaloperator identity Hn(X) = 2n : Xn :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,:: is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermite polynomials,but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → :f(X) :is also discussed.     

脊加载椭圆波导的多项式表示分析方法

采用Rayleigh-Ritz方法和多项式表示对脊加载椭圆波导的传输特性进行了分析.数值计算与电磁仿真软件结果能很好地符合.研究了不同尺寸对脊波导带宽的影响，对这类结构的优化具有指导意义.     

New Operator Ordering Formulas Related to Hermite Polynomials Derived by Virtue of IWOP Technique

By virtue of the technique of integration within an ordered product of operators and the fundamental operator identity Hn(X)=2^n : X^n :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,: : is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermitc polynomials, but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → : f(X) :is also discussed.     

Tunka-133: Status 2008 and development of methods for data analysis

The activity on creation of a array with an area of 1 km² for recording extensive air showers using Cherenkov light began in the Tunka valley in 2006. The new array will allow one to study cosmic rays in the energy range 10¹⁵–10¹⁸ eV by the unified method. In the winter of 2007–2008, the array operated with 4 clusters, 7 detectors in each cluster. Experimental data obtained during 270 h of fair weather in moonless nights demonstrated unique capabilities of the new array, related with the possibility of recording the pulse shape with a step of 5 ns from each detector.     

荧光光谱法快速鉴别花生油、芝麻油和调和油

比较分析了不同品种、同品种不同厂家、不同批次的市售花生油、芝麻油、调和油的分子荧光光谱差异特征,结合系统聚类分析法进行品种鉴别。结果表明:3种食用植物油的荧光光谱图具有各自不同特征,同一品种不同厂家的谱图存在一定的差异,同品种同厂家不同批次的也有微小差异。提取荧光谱图特征信息,利用系统聚类和三维聚类识别模式,从宏观上简便、直观、快速地鉴别3种食用植物油的品种。     

Study of Topological Structure of Vacuum by Lattice QCD

Overlap fermions and improved 5Li cooling are compared, which exhibits that these two filter methods can produce similar structures. Then the overlap fermions and improved 5Li cooling are combined to calculate the topological charge and identify the structure of the vacuum. The results are consistent with instanton liquid model .