On the Almost Intersections of Transient Brownian Motions

Let {B ₁ ^d (t)} and {B ^d ₂(t)} be independent Brownian motions in R ^d starting from 0 and nx respectively, and let w ^d _i (a,b) ={xR ^d : B ^d _i (t)=x for some t(a,b)}, i=1,2. Asymptotic expressions as n for the probability of dist(w ^d ₁(n ² t ₁, n ² t ₂), w ₂ ^d (0,n ² t ₃))1 with d4, respectively for the probability of dist(w ₁ ⁴(n ² t ₁,n ² t ₂),w ₂ ⁴(0,n ² t ₃))1 are obtained. As an application, an improvement of a result due to M. Aizenman concerning the intersections of Wiener sausages in R ⁴ is presented.     

Asymptotics for the Wiener Sausage among Poissonian Obstacles

We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a ball near its starting point. We show the weak law of large numbers, large deviation principle in special cases and the moment asymptotics for the volume of the corresponding Wiener sausage. One of the consequence of our results is that the trajectory of Brownian motion almost fills the confinement ball.     

下临界维数Wiener sausage相交时间的中偏差

本文研究在下临界维数情形下Wiener sausage 的相交时间, 应用新近提出的高阶矩方法和经典的Feynman-Kac 半群方法, 得到该情况下Wiener sausage 相交时间的中偏差.     

On the Boolean Model of Wiener Sausages

The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the capacity functional of this Boolean model is given. Moreover, the one- and two-point coverage probabilities as well as the contact distribution function and the specific surface area are studied. In and , the one- and two-point coverage probabilities are calculated numerically by Monte Carlo simulations and as a solution of the heat conduction problem. The corresponding approximation formulae are given and the error of approximation is analyzed. Research supported by the grant GACR 201/06/0302.     

On the expected surface area of the Wiener sausage

For parallel neighborhoods of the paths of the d ‐dimensional Brownian motion, so‐called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by means of geometric arguments that the expected surface area is equal to the first derivative of the mean volume of the Wiener sausage with respect to its radius (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Expected Volume of Intersection of Pinned Wiener Sausages and Heat Kernel Norms on Compact Riemannian Manifolds with Boundary

Estimates are obtained for the expected volume of intersection of independent pinned Wiener sausages in Euclidean space in the limit of small pinning time.      

双水相萃取法从风干香肠中分离提取蛋白酶

双水相萃取(ATPS)是近年来发展起来的蛋白纯化方法。为了扩展该方法适应领域,同时为风干香肠形成过程酶系的研究提供具体方法。本实验研究了运用双水相技术分离提取风干香肠中蛋白酶,对构成双水相体系中的PEG分子量、浓度和类型以及盐浓度的影响进行了分析。确定了双水相组成体系为20%PEG1000(m/m)和25%MgSO4(m/m),在此体系中风干香肠的蛋白酶主要分布在上相,最高酶活12.37U/μg;纯化倍数为4.61;回收率为85%。通过分子筛层析对比,表明风干香肠经过双水相分离提取杂蛋白峰被除去,而蛋白酶峰几乎未受到影响,说明该双水相体系萃取香肠中蛋白酶具有良好的专一性。调解双水相pH值对蛋白酶的萃取没有影响,而添加电解质NaCl反而产生不利影响。     

腌肉制品发色剂的研究

腌肉制品发色剂历来均用硝盐,但最近发现亚硝基对人体健康有害。我们采用GDL为主作香肠的发色剂,发色效果理想,有一定实用价值。     

氩气Z箍缩内爆动力学过程实验研究

在太瓦级脉冲功率装置“阳”加速器上开展了一系列氩气Z箍缩内爆实验研究.利用了高时空分辨的X射线纳秒分幅相机、可见光高速扫描相机、激光剪切差分干涉系统、X射线针孔相机和软X射线功率谱仪对内爆动力学过程进行了诊断.观测到了内爆中的“拉链”效应、“颈缩”效应、腊肠不稳定性等现象，获得了等离子体温度变化和内爆速度变化等典型结果，并分析了电流上升时间等因素对等离子体内爆过程的影响，给出了相关结论. 关键词： Z箍缩 等离子体 “拉链"效应 腊肠不稳定性     

Z箍缩等离子体不稳定性的数值研究

利用二维辐射磁流体程序模拟了钨丝阵Z箍缩等离子体腊肠不稳定性的演化：分析了存在不稳定性与没有不稳定性条件下等离子体内爆的差异；研究了不同初始密度扰动对x射线输出 功率和能量的影响.数值结果表明，在一定初始密度扰动范围内，这种不稳定性对x射线输 出的总能量影响不显著，但对x射线功率随时间变化的曲线有明显的影响.此外，还探讨了Z 箍缩等离子体数值模拟中低密度区的数值处理对数值结果的影响. 关键词： Z箍缩 腊肠不稳定性 数值模拟