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.     

Thermodynamic properties of the SU(2)f chiral quark–loop soliton

We consider a chiral one-loop hedgehog soliton of the bosonized SU(2)_f Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent quarks. Energy and radius of the soliton are determined in self-consistent mean-field approximation. Quasi-classical corrections to the soliton energy are derived by means of the pushing and cranking approaches. The corresponding inertial parameters are evaluated. It is shown that the inertial mass is equivalent to the total internal energy of the soliton. Corrected nucleon and δ isobar masses are calculated in dependence on temperature and density of the medium. As a result of the self-consistently determined internal structure of the soliton the scaling between constituent quark mass, soliton mass and radius is noticeably disturbed. Received: 26 September 1997     

多媒体数据库管理系统MBASE－I的结构和语言

介绍多媒体数据库管理系统Ｍｂａｓｅ－Ｉ的系统结构、功能和语言特征，并论述其内核软件的构造特点及主要工作原理。     

On the Diffusion in a Lattice Gas Model: Group-Theoretic Approach

Motivated by some recent results concerning the model of a noninteracting one-dimensional lattice gas with an order preservation of particles where multiple occupancy of the sites is not excluded, we give new symmetries and new reductions of the corresponding continuum nonlinear partial differential equation. Closed-form analytic solutions are found.     

Spline collocation methods for nonlinear Volterra integral equations with unknown delay

In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation.     

Neutral particle modelling assumptions: Theory and experiment

The neutral particle recycling models that have been used to date in numerical plasma confinement simulations are by no means equivalent but may lead, instead, to divergent results. As a consequence of this confinement studies based on individual neutral assumptions must be received with a healthy degree of scepticism. We go on to compare experimental observations of the time development of plasma density, temperature, and neutral pressure made in an electrostatic surface trap with numerical plasma simulations incorporating a number of alternative neutral models.     

盆地数值模拟的研究现状及发展

盆地数值模拟是目前世界上评价沉积盆地的油气资源远景的重要方法,它的产生标志着油气资源评价工作由传统的定性描述上升到定量描述的新高度。通过计算机技术把地质、地球物理、地球化学等多方面的概念模型变为数学模型,得到定量的结果。虽然由于石油地质理论尚有一些不成熟之处,获得参数的精度也存在一定问题,但它仍然是一种很有发展前景的定量评价方法。文中指出了这种方法的发展方向。