Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.     

带有弹性碰撞的离散的凝结方程

带有弹性碰撞的离散的凝结方程是反映粒子增长动力学的数学模型，它刻划了这样一种粒子反应系统；系统中任意两个粒子碰撞后一定的概率或者凝结成为更大的粒子，或者发生弹性碰撞．本文研究了这一系统发生冻肢的可能性，并给出了一个充分条件．     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

乳状液法制备憎液溶胶Ⅰ.BaCO_3均匀粒子的制备

均匀胶体粒子的形成，除与反应条件（反应物浓度、陈化时间和温度、介质种类等）有关外，反应体系的环境也影响最终产物的形态，《至结晶结构．气溶胶法和微乳液法正是利用微环境中的‘水池效应”；分别制备出球形亚微米和纳米级的均匀粒子［‘－‘］、这些方法与水解法和相转化法等方法比较，反应物浓度要大几个数量级，而反应时间却短很多，因而受到研究人员的关注．乳状液也能提供亚微米、微米及以上级的微环境，因此，可以应用O／W乳状液乳液中的聚合反应制备亲液的分散体系．然而，极少有关利用w／O乳状液制备僧液溶胶的报导问；最近…     

Computer Simulation of the Structure of Porous Electrodes with an Immobilized Enzyme and Nanosized Support Particles

The efficiency of the operation of a porous electrode with an immobilized enzyme is defined, in particular, by a lucky structure of its active layer, which can contain nanosized particles of the support. The composites of such a kind are prepared with the aid of methods of colloidal chemistry. The aim of this particular investigation is to perform a computer simulation of processes of coagulation of particles of the support and their possible heterocoagulation with molecules of the enzyme. Algorithms of the formation of nanocomposite structures in solution are suggested. Calculations show that the concentration of the enzyme molecules in the nanocomposite structures cannot exceed a certain critical value. On the other hand, at a fixed value of the concentration of the enzyme molecules, the concentration of the support particles must not fall below a certain threshold quantity, which provides for the passing of current through the active layer. In order for all the enzyme molecules, rather than for a fraction of these, in the composite to take part in the process of bioelectrocatalysis, the concentration of support particles must be increased even higher, to an optimum value.__________Translated from Elektrokhimiya, Vol. 41, No. 6, 2005, pp. 738–747.Original Russian Text Copyright © 2005 by Chirkov, Rostokin.     

The size distribution for theA g RB f−g Model of polymerization

This paper gives the equilibrium distribution of polymer sizes for Flory'sA _g RB _f–g model of polymerization. In this model, the polymers are composed of structural units withg functional groups of the typeA and (f-g) functional groups of the typeB. Reaction is subject to three conditions: (1) Functional groups of the typeA react only with those of typeB, and vice versa. (2) Intramolecular reactions do not occur [and therefore only branched-chain (noncyclic) polymers and formed]. (3) Subject to conditions (1) and (2), all functional groups are equally reactive. The derivation employs Stockmayer's statistical mechanical method (first used on Flory'sRA _f model), coupled with a recursion giving the number of distinct polymers which may be assembled fromk units of theA _g RB _f–g type. We also give distributions for a limiting case of theA _g RB _f–g model, the so-calledA _g RB model. This paper completes the solution of the Smoluchowski coagulation equation (monodisperse case) for the kernelsa _ij =A + B(i +j)+ Cij. The proof will be given in another publication.     

Effects of citrate on the composition and enzymic coagulation of colloidal bovine casein aggregates

Colloidal casein aggregates (CCA) prepared from soluble whole bovine caseinates in the presence of Ca²⁺ and phosphate (Pi) ions by addition of different citrate (Cit) concentrations showed different mineral and proteic composition. Citrate concentration conditions the Ca and Pi concentrations incorporated into CCA, probably due to the complexing effect of this anion on calcium. A significant change in the incorporated Ca/Pi ratio at 8 mM citrate could very likely be associated to changes in CCA net charge. The incorporation of individual caseins to the colloidal particles obtained, as well as their average size and size distribution, depended also on the Cit concentration used [Cit]_P. α_S- and β-caseins assembled in the CCA structure sharply decreased at a [Cit]_P higher than 15 mM, i.e., at a low Ca²⁺ concentration in the aggregates, showing that the presence of this cation is necessary for the incorporation of these caseins. An inverse relationship between the aggregation step rate in CCA enzymic coagulation and their average size was observed. The aggregation rate vs the average size curve obtained at [Cit]_P 8 mM clearly differed from the curves obtained at 10 and 12 mM, respectively, a fact probably related to a change in the CCA net charge. This behavior showed the effect of citrate concentration on CCA functional properties.     

基于支持向量机的凝血功能诊断模型

使用凝血四项指标诊断凝血功能是临床的常规检查,但根据经验进行诊断正确率不高.剔除临床上最重要的指标FIB后,建立支持向量机模型诊断的正确率和根据凝血四项指标诊断的正确率没有显著差异,100次模拟的平均正确率分别达到了95.4496%和95.5039%.     

不同抗凝比例对凝血四项检测结果的影响

目的观察并分析凝血四项检测结果与不同比例下的全血与抗凝剂之间的关系。方法研究对象取2015年6月来湖北省宜昌市第二人民医院参加体检的110例健康人员,抽取全血血液样本后按照不同比例与抗凝剂混匀,常规分离血浆并测定受试者凝血酶时间(TT)、凝血酶原时间(PT)、激活部分促凝血酶原激酶时间(APTT)以及纤维蛋白原(FIB),并对研究结果相关数据作统计学处理。结果当血液量与抗凝剂比例为1∶5时,标本TT、PT、APTT以及FIB各项指标较1∶9时差异显著而具有统计学意义(P0.05);抗凝比例1∶7的情况下,TT指标差异与1∶9抗凝比例标本相比差异具有统计学意义(P0.05),而PT、FIB以及APTT三项指标差异并无统计学意义(P0.05);抗凝比例为1∶11与1∶13的情况下,TT指标与1∶9抗凝比例标本相比差异具有统计学意义(P0.05),而PT、FIB以及APTT三项指标差异并无统计学意义(P0.05)。结论凝血四项检测工作中,标本质量检测控制最关键的环节在于准确采集血液量,倘若采集血量过多或过少,导致与抗凝剂比例失调往往会影响测定结果准确性,检验科工作人员应予以重视。     

Raman spectroscopy and thermal analysis of gum and silica-filled NR/SBR blends prepared from latex system

Natural rubber/styrene-butadiene rubber (NR/SBR) blends, with and without silica, were prepared by co-coagulating the mixture of rubber latices and various amounts of well-dispersed silica suspension. An attempt to predict blend compositions was made using Raman spectroscopy in association with differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). It was found that the intensity of each Raman characteristic peak was strongly dependent on the blend composition, but there was no significant evolution with the presence of silica. Also, TGA results revealed an improvement in thermal stability of NR/SBR blends with increasing both SBR and silica contents due to the dilution effect. Two distinct glass transition temperatures (T_g) were observed in DSC thermograms of all blends, and their T_g values were independent on both blend composition and silica content. This indicated a physical blend formation, which agreed well with no shifts in Raman peaks of the blends in comparison with those of the individual rubbers. Linear regression with R² quality factor close to 0.99 was achieved when plotting intensity ratio at 1371/1302 cm^?1 versus blend ratios. On the other hand, the peak height ratio and heat capacity ratio from TGA and DSC analysis, respectively, yielded quadratic equations as a function of blend ratios.