Many-body effects in diffusion-limited kinetics

We review a novel approach to treating many-body effects in diffusion-limited kinetics. The derivation of the general expression for the survival probability of a Brownian particle in the presence of randomly distributed traps is given. The reduction of this expression to both the Smoluchowski solultion and the wellknown asymptotic behavior is demonstrated. It is shown that the Smoluchowski solution gives a lower bound for the particle survival probability. The correction to the Smoluchowski solution which takes into account the particle death slowdown in the initial process stage is described. The steady-state rate-constant concentration dependence and the reflection of many-body effects in it are discussed in detail.     

三阶泛函微分方程的周期解的存在性

本文利用重合度理论研究了一类三阶泛函微分方程方程的2π-周期解的问题,获得了该方程存在2π-周期解的若干新结论,改进推广了有关文献中的已有结果．     

Diffusion in quasi-one-dimensional structures with a periodic sharp narrowing of the cross section

The problem of diffusion of particles in a tube with periodically positioned partitions with circular orifices at the center of each was considered. Using an approach based on the methods and results of the theory of diffusion-controlled reactions and the idea of homogenization of the permeability of partitions, we derived a formula for the effective diffusion coefficient for the steady-state regime of the process. The accuracy and applicability domain of the formula were determined by comparing its predictions with computer simulation results.     

Retardation of diffusion in porous media with stagnation zones

The problem of diffusion in a porous medium with stagnation zones, which reduce the rate of transport of particles, is considered. A method based on the concept of entropy barriers associated with the small size of inlets into the stagnation zone is used to solve the diffusion problem. This method made it possible to reduce the diffusion problem in 3D structures to a set of one-dimensional equations that can be solved analytically. The calculations yielded an exact value of the effective diffusion coefficient, which is reduced due to random delays in the stagnation zones, and the transition time required to attain this reduction.     

氢链系统中的非线性问题

考虑氢原子之间的非谐相互作用,分别用代数方法和变分法求得氢链系统中扭结与反扭结孤波解,解的特点是在非谐项的影响下,正孤波与反孤波不再对称,从而解释了实验中观察到的冰分子中L缺陷和D缺陷的对称性破缺现象,进一步的计算表明,由于非谐项的存在,正孤波与反孤波携带的能量也失去对称性,且代数方法和变分法给出一致的结果.     

基于联合变换相关器的像移测量仿真分析

对基于联合变换相关器的像移测量数学原理进行了说明,介绍了面阵CCD的安装位置以及输入图像的获取方法,分析了低信噪比输入图像、相对转动位移对测量精度的影响。应用MATLAB对输入图像进行傅里叶变换得到联合功率谱,对二值化处理的功率谱进行傅里叶变换得到相关输出,用质量中心算法计算出像移量。分析得出,输入图像信噪比大于5dB,测量均方误差小于0.05像素;输入图像相对转动位移在0.1°的范围内,转动位移对测量精度和峰噪比的影响可以忽略不计。综合分析表明像移测量均方误差小于0.05像素。     

超级微波消解-电感耦合等离子体发射光谱（ICP-OES）法测定土壤中18种元素

为提高土壤多元素同时检测的效率,采用超级微波消解-电感耦合等离子体发射光谱法测定土壤中钾、钠、钙、镁、铜、铁、锰、锌、磷、硫、硼、砷、镉、铬、铅、钴、镓、锂等18种元素含量。比较了超级微波消解、常规微波消解和电热板消解的处理效果,采用超级微波消解法对样品进行前处理,并优化了消解条件。在最优条件下,各元素的检出限在0.05~20 mg/kg,加标回收率在86.2%~107.5%,RSD在0.1%~3.0%,方法准确度及精密度可以满足多元素同时测定的需求,且该方法具有简单、快速、成本低、用酸量少、重现性好等特点。     

Reciprocating motion on the nanoscale

This paper analyzes the confined motion of a Brownian particle fluctuating between two conformational states with different potential profiles and different position-dependent rate constants of the transitions, the fluctuations arising from both thermal (equilibrium) and external (nonequilibrium) noise. The model illustrates a mechanism to transduce, on the nanoscale, the energy of nonequilibrium fluctuations into mechanical energy of reciprocating motion. Expressions for the reciprocating velocity and the efficiency of energy conversion are derived. These expressions are treated in more detail in the slow-fluctuation (quasi-equilibrium) regime, by simple perturbation theory arguments, and in the fast fluctuation limit, in terms of the potential of mean force. A notable observation is that the generalized driving force of the reciprocating motion is caused by two sources: the energy contribution due to the difference between the potential profiles of the states and the entropic contribution due to the difference between the position-dependent rate constants. Two illustrative examples are presented, where one of the two sources can be ignored and an exact solution is allowed. Among other aspects, we also discuss the ways to construct a molecular motor based on the reciprocating engine.     

A Thermal Non-Neutral Plasma Column and Its Dispersion Relation

In this paper we study the dispersion relation of thermal non-neutral plasma column by MHD theory. We use the dispersion relation to discuss the stability and dispersive properties in a non-neutral plasma-filled waveguide. The results are in agreement with those of cold non-neutral plasma.