缠结高分子链的Brown运动模型及其解缠弛豫时间的计算机模拟

以缠结高分子链的质心在约束管子中作Brown运动为基本假定,在忽略有效管长的涨落下,得到解缠弛豫时间τ链长N的渐近依赖关系τ^_N3。在有限链长及约束管长涨落的条件下,采用计算机模拟得到关系式τ^_N3.40±0.16。这一结论合理地解释了缠结高分子链动力学的实验结果。     

拼合扩散过程最小解的构造及其不变测度、可逆性与遍历性

§1.引言 本文讨论由算子Ω= (c_(ij)(x))生成的相空间为E=R~1×Z的马氏过程,其中且系数满足下列条件:     

三维随机Ising模型的亚稳态性(Ⅱ)

讨论三维格点环面上随机Ising模型当温度趋向零时的亚稳态性,确定从自旋全为-1的组态到自旋全为+1的组态的最大似然路径和临界组态,并计算出从自旋全为-1的组态出发首次到达自旋全为+1的组态的首达时间的渐近对数估计。证明利用一族带指数扰动的Markov链的大偏差估计。     

环面上具有间断梯度的势函数的模拟退火

本文证明了环面上具有间断梯度的势函数的模拟退火过程：dXt=-VU(Xt)dt √2dWt概率收敛到势函数的全局极小集附近。     

杰出的成就严谨的学风--贺江泽培教授80华诞

今年是江泽培教授八十华诞.值此,我们由衷地祝愿这位敬爱的老师、国际概率界的知名学者、我国著名的概率统计学家健康长寿.回顾江先生八十年的生活,不仅可以使我们深入地认识这位学精德馨的前辈,更能使我们从他的学识、为人、治学、育才的高尚风范与情操中获得宝贵的精神财富.江泽培先生1923年10月4日于上海市出生,3岁随家移居南京,在那里度过了小学和二年初中生活.     

马尔可夫过程的熵产生率与不可逆性

§1 引言在非平衡态统计物理中,统计不可逆性与熵产生率是两个十分重要的概念.在[1]、[2]、[3]中,我们讨论了可以用马氏链描写的系统的可逆性与熵产生率,并证明一个平稳马氏链可逆的充分必要条件是熵产生率为零,进而又说明熵产生率是系统对时间的统计不可逆程度的一个刻划指标.但是,由于马氏链的状态空间的局限性,上述结果不能适应大量连续状态空间的物理问题研究的需要.为此,本文设法对一般的随机过程给出熵产生率的概率定义,并进而     

非紧Riemann流形上平稳扩散过程的熵产生率

给出了具有有界Nelson速度流的平稳扩散过程的熵产生率的封闭形式,讨论了一列反射扩散的熵产生率的极限。     

ON THE LARGE DEVIATION FUNCTIONS OF MARKOV CHAINS

In this paper, we consider that how much information the large deviation rate functions contain. Namely, let us observe two processes Ⅹ~(1) and Ⅹ~(2) with the same large deviation function Ⅰ(μ), for all μ with compact support, and ask what the relation should have between Ⅹ~(1) and Ⅹ(~). In [1], Donsker and Varadhan gave the answer for the case of diffusion as the following theorem.     

The Metastable Behavior of the Two Dimensional Ising Model

There are continuous efforts in recent years in order to have a better understan-ding of metastable bekavior of a statistical mechanics system. We consider it in twodimensions, solve problems proposed in [Sch]. By the idea of [FW] we are able toshapen the previous results [NS], and to identify the critical droplet naturally.Let Λ be a 2-dimensional lattice torus, and X = { - 1, + 1}~Λ. For η∈X assignthe Hamiltonian     

The Metastable Behavior of the Three Dimensional Ising Model

The problem of metastability has attracted a great attention in the recent decade.In particular, it has been extensively investigated the 2-dimensional Ising model ina finite torus [CFQ]、[NS]、[Sch]. In this paper, the 3-dimensional Ising model withGlauber dynamics under a positive magnetic field is considered. We characterize themetastable behavior in the pathwise approacb, find out all metastable states, anddetermine naturally the critical droplet. We give a general and clear view of the sub-stance of the passage from all spins down (- 1) to all spins up (+ 1). For a largeclass of initial states, the logarithmic asymptotics of the hitting time of - 1 or + 1 areaccurately estimated, and the shrink and growth of droplets are described.