超薄膜磁性材料上XY模型的临界现象

采用经典XY模型，阐明了三角格子上层状超薄膜磁性材料的相变和临界现象.并用Monte-Carlo方法对该模型的内部能量、比热、chirality等热力学量进行了计算.使用finite-size scaling 分析法对临界现象的性质进行了论述.通过上述分析和计算，发现该模型在反强磁性层与强磁性层内的chirality在一定范围内随温度的变化急剧增加，这是一种新的chirality相变；而在另一范围内存在Kosterliz-Thouless相变和通常的chirality相变.这种新的chirality相变的 关键词： 层状XY模型 临界现象 Monte-Carlo模拟 磁性薄膜     

一类具功能反应的食饵——捕食者系统定性分析

研究一类具功能反应的食饵-捕食者系统:x=xg(x)-y(?)(x),y=y(-d+e(?)(x)．在g(x)=α-bxm,(?)(x)=cxθ及m+θ=1,m=1/n,n>2为正整数情形下,分析了该系统的平衡点性态,并得到了系统在正平衡点外围的极限环的不存在性、存在性与唯一性的相关条件．     

Adaptive synchronization of a critical chaotic system

This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory, a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters. Theoretical analysis and numerical simulations show the effectiveness and feasibility of the proposed schemes.     

Line group theory of commensurate and incommensurate modulations

It is shown that the line group formalism proposed is suitable to describe both commensurate and incommensurate modulations. Symmetry groups of modulated crystal lattices can completely be characterized by symmetry transformations existing in real space, without any application of the formalism based on reciprocal space. As typical examples of the method elaborated, the fundamental invariance and symmetry properties of spin density functions and the soliton lattice are determined. Received: 20 July 1997 / Accepted: 25 August 1997     

Stable complete minimal surfaces in hyperkähler manifolds

In this paper we prove that an isometric stable minimal immersion of a complete oriented surface into a hyperkähler 4-manifold is holomorphic with respect to an orthogonal complex structure, if it satisfies a Bernstein-type assumption on the Gauss-lift. This result generalizes a theorem of Micallef for minimal surfaces in the euclidean 4-space. An example found by Atiyah and Hitchin shows that the assumption on the Gauss-lift is necessary.     

新的适用于整个热力面的1,1,1,2-四氟乙烷(R134a)跨接状态方程

1前言作者建立了一个新型的符合临界重整化群理论的跨接状态方程，能够描述物质的整个区域热力性质山。鉴于R134a是R12的新的主要替代制冷剂，为了计算其整个区域的热力性质，本文将新跨接状态方程应用于R134a，以便提供一个能在整个区域计算R134a热力性质的状态方程。2新跨接状态方程作者建立了以下型式的新跨接状态方程l‘］：上式中，西方一r一IDZ户一p巾c；，一DI—TD；T—To／T；产为密度；pc为临界密度；T为温度；To为临界温度；矿对比过余Helmholtz自由能；A是Helmholtz自由能。新函数中，a。一30，a，一10；0—0．325和西一…     

Critical points of two-dimensional bootstrap percolation-like cellular automata

Cellular automata in two dimensions that generalize the bootstrap percolation dynamics are considered, focusing on the thresholdp _c of the initial density for convergence to total occupancy to occur; these models are classified according top _c being 0, 1, or strictly between these extreme values. Explicit upper and lower bounds are provided in the third case.     

空间轴对称变形界面裂纹尖端的应力奇异性分析

假定位移场,并将位移势函数展开成一系列的特征函数,代入空间轴对称变形的基本方程,推得界面裂纹的特征值理论。把这一理论应用到单向增强的连续纤维复合材料上,建立了纤维断裂、基体开裂等模型下应力奇异性的特征方程,分析了界面裂纹尖端的应力奇异性。     

The lamellar-disorder interface: one-dimensional modulated profiles

We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a wide interfacial region involving a large number of lamellae. Our analytical results apply to systems with one dimensional symmetry in true thermodynamical equilibrium and are of relevance to metastable interfaces between lamellar and disordered phases in two and three dimensions. In addition, good agreement is found with numerical minimization schemes of the full free energy functional having the same one dimensional symmetry. The interfacial energy for the lamellar to disordered transition is obtained in accord with mean field scaling laws of tricritical points. Received: 28 March 1997 / Revised: 6 February 1998 / Accepted: 16 February 1998     

Critical value sets and dynamical systems

Elementary applications of singularity theory to dynamical systems are outlined. The main idea is to consider the geometry of the wrinkled surface generated by the time development of a one variable solution as a function of initial conditions or system parameters. Applications of singularity theory to vibro-impacting systems are discussed in some detail and further applications to dynamics are briefly reviewed.