Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system ofmultiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are allrooted andcontractible to a point:adjacent one to another, and, on a torus,homotopic to zero. (2) the loops can encircle one another and, on a torus, canwind around it. Forcase 1, the grand canonical partition function and multiple correlation functions are calculated exactly as those of multiple rooted spanningtrees or of a massive 2Dfree field, critical at zero mass (zero fugacity). The conformally invariant continuum limit on a Manhattantorus is studied in detail. The melt entropy is calculated exactly. We also consider the relevant effect of free boundary conditions. The number of single HAWs on Manhattan lattices with other perimeter shapes (rectangular, Kagomé, triangular, and arbitrary) is studied and related to the spectral theory of the Dirichlet Laplacian. This allows the calculation of exact shape-dependent configuration exponents y. An exact surface critical exponent is obtained. Forcase 2, nested and winding Hamiltonian circuits are allowed. An exact equivalence to thecritical Q-state Potts model exists, whereQ ^1/2 is the walk fugacity. The Hamiltonian system is then always critical (forQ<-4). The exact critical exponents, in infinite numbers, are universal and identical to those of theO(n=Q ^1/2) model in its low-temperature phase, i.e. are those of dense polymers. The exact critical partition functions on the torus are given from conformai invariance theory. These models 1 and 2 yield the two first exactly solved models of polymer melts.     

三维格子Boltzmann方法研究上升双气泡的运动特性

应用格子Boltzmann三维模型，对双气泡在静水中的运动进行数值研究.采用八点差分和十八点差分格式分别求解一阶▽φ和二阶▽²φ可以有效避免气液密度比过大造成的数值不稳定问题.结果表明：当两个相同直径的气泡在上升时，位置靠上的气泡形状变化像单气泡上升一样，而位置靠下的气泡会受到前一个气泡尾迹的影响，并有很明显的形状变化.当两个气泡直径不同时，不管初始位置如何，大气泡总会对小气泡造成强烈的影响.     

电枢超导型高温超导电机原理样机的温度场数值模拟研究

本文对一种电枢绕组部分采用高温超导线圈,转子励磁部分采用永磁体的新型高温超导原理样机进行了整体温度场的数值模拟计算,主要包括稳态冷却过程、瞬态冷却过程及零件配合面径向变形量计算三个方面的内容.通过对边界条件及传热条件的简化,建立了电机的近似平面轴对称传热模型,得出了高温超导线圈处冷却至工作温度(77K左右)所需的时间.另外还计算出零件配合面上的径向变形量,可据此制订低温尺寸公差,为零件的机械加工提供了指导.     

第七讲微电子技术发展与物理学

微电子学的基础是近代固体物理．微电子技术的快速发展又推动了物理学许多分支的进展．今天，当微电子的基本器件MOSFET缩小接近其终极时，作为下一代的基础，一批基于新的物理效应的纳电子器件又被提了出来．为了突破传统的二值开关系统的共同极限，新的信息处理系统，如量子信息处理，正在大力研究之中．不久的将来，可望出现一次新的信息电子革命．这次革命又将建立在现代物理学及现代生物学的基础之上．     

Fast Encoding Method for Image Vector Quantization Based on Multiple Appropriate Features to Estimate Euclidean Distance

The encoding process of finding the best-matched codeword (winner) for a certain input vector in image vector quantization (VQ) is computationally very expensive due to a lot of k-dimensional Euclidean distance computations. In order to speed up the VQ encoding process, it is beneficial to firstly estimate how large the Euclidean distance is between the input vector and a candidate codeword by using appropriate low dimensional features of a vector instead of an immediate Euclidean distance computation. If the estimated Euclidean distance is large enough, it implies that the current candidate codeword could not be a winner so that it can be rejected safely and thus avoid actual Euclidean distance computation. Sum (1-D), L₂ norm (1-D) and partial sums (2-D) of a vector are used together as the appropriate features in this paper because they are the first three simplest features. Then, four estimations of Euclidean distance between the input vector and a codeword are connected to each other by the Cauchy–Schwarz inequality to realize codeword rejection. For typical standard images with very different details (Lena, F-16, Pepper and Baboon), the final remaining must-do actual Euclidean distance computations can be eliminated obviously and the total computational cost including all overhead can also be reduced obviously compared to the state-of-the-art EEENNS method meanwhile keeping a full search (FS) equivalent PSNR.     

用e+e－→h′s反应中类双喷注事例研究部分子末态的色联接

借助JETSET事例产生器对e⁺e^－→h′s反应中的类双喷注事例进行研究.研究发现,在QCD微扰与非微扰的界面上,部分子系统的色中性流和色分离单态两种不同色联接方式导致了强子末态某些可观测量的显著差别.因此,它们可以用于判别部分子的色联接方式.     

槽中双孤子互作用的微扰求解

孤子运动的Miles方程是一个具特征的非线性Schrdinger型方程.借求孤子解的微扰法,导出所遵循的矩阵方程,和孤子解的修正量δu(x,λ).并据双孤子解,计算了它的周期互作用状态 关键词： Miles方程 微扰双孤子解     

第Ⅰ种非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文利用多模压缩态理论,研究了第Ⅰ种非对称两态叠加多模叠加态光场|Ψ_Ⅰ^(ab)Ⅰ>_q的偶数阶等阶N次方Y压缩特性.结果发现:在压缩阶数N取偶数情况下,只要构成态|Ψ_Ⅰ^(ab)Ⅰ>_q的两个量子光场态的强度(即平均光子数)不相等,则当各模的初始相位φ_j^(a)、φ_j^(b)(j＝1,2,3,…,q)、态间的初始相位差(θ_pq^(bI)-θ_nq^(aR))以及与上述的两个量子光场态相对应的各单模相干态光场的光子干涉项之和 ＝[R_j^(a)R_j^(b)cos(φ_j^(a)-φ_j^(b))]等满足一定条件时,态|Ψ_Ⅰ^(ab)Ⅰ>_q可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.这一结果与现有文献报道的结果截然不同.     

二个强飞秒延时激光脉冲的相对相位对Na2+光解离的影响

报道了Na₂⁺离子的三个低激发态1Σu、2Σg、2Σu在二个光脉冲作用下的解离动量谱,激光波长为680nm,各脉冲功率为1×10¹²W/cm²,脉宽50fs,从研究结果可见,其单光子、双光子、三光子激发的对应的解离峰及峰值随相对相位而变,并且这种影响随延时增大而减小.     

2(1/2)维等离子体粒子模拟分布式并行程序设计

设计了两种粒子模拟的并行算法,并对其进行了比较,基于消息传递环境开发2(1/2)维粒子模拟并行程序,测试并分析了并行性能.粒子模拟算法中,给出了一个初始化粒子三维Maxwell速度分布的算法,并对常用的电磁场的Lindman吸收边界作了推广.最后对激光钻孔问题作了粒子模拟计算,验证了该并行程序.