The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

On Inequalities with Measures of Sobolev Type Embedding Theorems on Open Sets of the Real Axis

We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space.     

Cosmic dust and our origins

The small solid particles in the space between the stars provide the surfaces for the production of many simple and complex molecules. Processes involving the effects of ultraviolet irradiation of the thin (hundredth micron) mantles are shown to produce a wide range of molecules and ions also seen in comets. Some of the more complex ones inferred from laboratory experiments are expected to play an important role in the origin of life. An outline of the chemical evolution of interstellar dust as observed and as studied in the laboratory is presented. Observations of comets are shown to provide substantial evidence for their being fluffy aggregates of interstellar dust as it was in the protosolar nebula, i.e. the interstellar cloud which collapsed to form the solar system. The theory that comets may have brought the progenitors of life to the earth is summarized.     

约束层对激光驱动冲击波压力影响机理的理论研究

针对刚性约束层、柔性约束层以及液体约束层，从激光诱导冲击波阵面状态、汽化物(包括气体和等离子体)扩散以及冲击波的反射进行分析，发现对于脉宽小于冲击波通过汽化物层的时间间隔的短脉冲激光，约束层并不能直接提高冲击波的冲量，而对于脉宽大于冲击波通过汽化层时间间隔的激光，其增强冲击效果是通过约束汽化物的扩散，提高压力幅值和由于冲击波在约束层与工件表面的多次反射而延长对工件的作用时间来实现的.刚性约束层能最大地增加冲击冲量，而柔性约束层和液体约束层的主要优点是其形状可与非平面形工件表面符合. 关键词： 激光 约束层 扩散 反射波     

TOF-SIMS imaging of chlorhexidine-digluconate transport in frozen hydrated biofilms of the fungus Candida albicans

The diffusion of the anti-microbial chlorhexidine digluconate (CHG) has been studied in C. albicans biofilms by time-of-flight secondary-ion mass spectrometry (TOF-SIMS). C. albicans has been shown to become resistant to common anti-microbial agents, including CHG, when growing as a biofilm. Mass transport resistance within biofilms has commonly been suggested as a resistance mechanism, but measurement of transport for most anti-microbial agents in biofilms has proven extremely difficult because of the heterogeneity of the biofilms and the difficulty in detecting these agents within an intact biofilm. In this study, TOF-SIMS has been used to study the transport of CHG and glucose in a frozen hydrated biofilm. The TOF-SIMS images reveal a progression of CHG from the top of the biofilm to its base with time. Images suggest that there are channels within the biofilm and show preferential binding of CHG to cellular components of the biofilm. Additionally, both living and dead cells can be identified in the TOF-SIMS images by the sequestration of K⁺ and the presence of cell markers. This study demonstrates that TOF-SIMS has the unique potential to simultaneously observe the presence of an antimicrobial agent, concentration of nutrients, and the viability of the cell population.     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

基因芯片荧光图象采集与分析

描述了基因芯片荧光图象的光学共聚焦成象,大范围高速扫描与控制,数据采集的原理和方法.并讨论了基因芯片荧光图象的分析算法,即模板定位与阈值分割相结合的半自动算法,并将其计算结果与完全采用人工分割算法的结果进行了比较.     

Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps

We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’ – and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Kolmogorov Width of Classes of Smooth Functions on the Sphere

Let ^d−1{(x₁,…,x_d) ^d:x²₁+···+x²_d=1} be the unit sphere of the d-dimensional Euclidean space ^d. For r>0, we denote by B^r_p (1p∞) the class of functions f on ^d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on ^d−1, and P^λ_k(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of B^r_p in L^q( ^d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces X_N of L^q( ^d−1).The main result in this paper is that for r2(d−1)²,where A_NB_N means that there exists a positive constant C, independent of N, such that C⁻¹A_NB_NCA_N.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions.