Large Deviations of Local Times of Lévy Processes

For X(t) a real-valued symmetric Lévy process, its characteristic function is E(e ^{ilarge955.gif" alt="lambda" align="BASELINE" BORDER="0">X(t)})=exp(–tlarge968.gif" alt="psgr" align="MIDDLE" BORDER="0">(large955.gif" alt="lambda" align="BASELINE" BORDER="0">)). Assume that large968.gif" alt="psgr" align="MIDDLE" BORDER="0"> is regularly varying at infinity with index 1<large946.gif" alt="beta" align="MIDDLE" BORDER="0">large8804.gif" alt="le" align="MIDDLE" BORDER="0">2. Let L ^x _t denote the local time of X(t) and L* _t =sup _{xlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">R} L ^x _t . Estimates are obtained for P(L ⁰ _t large8805.gif" alt="ge" align="MIDDLE" BORDER="0">y) and P(L* _t large8805.gif" alt="ge" align="MIDDLE" BORDER="0">y) as ylarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">large8734.gif" alt="infin" align="MIDDLE" BORDER="0"> and t fixed.     

Komlós Theorem for Unbounded Random Sets

We present the Komlós theorem for multivalued functions whose values are closed (possibly unbounded) convex subsets of a separable Banach space. Komlós theorem can be seen as a generalization of the SLLN for it deals with a sequence of integrable multivalued functions that do not have to be identically distributed nor independent. The Artstein–Hart SLLN for random sets with values in Euclidean spaces is derived from the main result. Finally, since the main theorem concerns multifunctions whose values are allowed to be unbounded, we can restate it in terms of normal integrands (random lower semicontinuous functions).     

Large volume growth and finite topological type

It is shown in this paper that a complete noncompact -dimensional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than .

     

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as nlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">large8734.gif" alt="infin" align="MIDDLE" BORDER="0"> to a value large968.gif" alt="psgr" align="MIDDLE" BORDER="0"> _t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of large968.gif" alt="psgr" align="MIDDLE" BORDER="0"> _t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence.     

Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the nlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">large8734.gif" alt="infin" align="MIDDLE" BORDER="0"> limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

强外加电场与大调制度下光折变动力学光栅形成研究

强外加电场与大调制度在光折变效应的研究中已经得到了广泛应用。采用PDECOL算法,严格求解光折变带输运方程,得到外加电场时不同调制度下光折变晶体中随时间变化的空间电荷场、载流子浓度,并讨论了外加电场对它们的影响。通过将物质方程与耦合波方程联立数值求解,可得到光折变光栅形成过程中两波耦合增益系数以及光束条纹相位的变化。模拟结果表明,在强外加电场作用下,两束记录光之间的光强与相位耦合都得到了增强,而原有的解析式忽视了强外加电场与大调制度对空间电荷场相位耦合的影响,此时不再适用。同时发现折射率光栅与记录光束条纹均发生弯曲,并不再保持平行。     

气管支气管树内气流和颗粒运动的大涡模拟

为更精确地描述真实人体呼吸道内的空气流动,明晰颗粒的运动沉积规律,本文从直接医学CT扫描得到的原始数据出发,利用图像辨识技术,重构了一个男性真人气管支气管树前三级的三维几何模型.采用大涡模拟的方法计算了非规则几何曲面结构内的气体流动现象,并在拉格朗日框架下跟踪颗粒的运动规律.数值计算得到了气流场的三维分布,以及颗粒的运动轨迹情况,结果表明现有基于Weibel的对称模型与真实人体的几何结构有较大的差异,而几何结构对流动影响较大;受非对称复杂结构影响,在不同截面的二次气流速度的分布规律不同;分叉后颗粒进入左右支气管的数量有明显的不同.     

用于脉冲γ强度测量的Ф60,1000μmPIN探测器

采用电阻率为10000—20000Ω.cm的高阻单晶硅材料,研制成功灵敏区尺寸为60mm,耗尽层厚度~1000μm的大面积厚PIN半导体探测器.设计了该类探测器厚度测量专用的反冲质子测量系统,对探测器的时间响应、γ灵敏度、漏电流、γ/n分辨等物理参数进行了测量和分析,结果表明,这类探测器可满足低强度裂变n/γ混合场中脉冲γ强度测量的需要.     

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.