Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.     

立井强化冻结施工理论分析

本文以谢桥主井为例,从冻结壁强度、变形、工作面底鼓和超前位移及冻胀压力等几方面.分析了深厚表土立井强化冻结施工对防止冻结管断裂和外层井壁破坏的机理.给出了强化冻结施工适用条件.并提出了按井帮温度进行强化冻结设计的方法.     

流动注射-氢化物发生-原子吸收光谱法测定雪中的微量铅

建立了测定雪中微量铅的流动注射-氢化物发生-原子吸收光谱法。在优化条件下。测定铅的线性范围为0～52．0ng／mL，线性回归方程为A=0．018c 0．016，相关系数r=0．9995，检出限为0．2ng／mL。用于雪中微量铅的测定，加标回收率为94．2％～107．3％，相对标准偏差为1．47％～3．22％。该方法的测定结果与标准加入法基本一致。     

Mössbauer Spectroscopic Studies of Chlorostannate(II) Complexes in Frozen Aqueous Solutions

Mössbauer parameters of frozen aqueous solutions of Sn(ClO₄)₂ in 0.5 M HClO₄ did not change with the concentration of NaClO₄, so that it was used to keep the ionic strength at the desired level. When NaCl was added into Sn(ClO₄)₂ solutions, isomer shift did not change, but quadrupole splitting did. Therefore, stability constants were calculated from the quadrupole splitting data, which were in good agreement with the published values. The observed spectra could be resolved into components.     

Sound velocity in different reacting thermal plasma systems

In most cases the energy dissipated in plasma jets used either,for heating or spraying is varied by changing the are current, the total gas floc+rate, and composition. However, when doing so, conditions are reached where the plasma jet may become supersonic. To predict such conditions or to characterize supersonic plasma jets the knowledge of the sound velocitya is mandatory The goal of this paper is to calculatea versus plasma forming gas composition, temperature, and pressure. Rigorous calculation would imply the knowledge of the chemical reaction kinetics, sound velocity depending strongly on this. Unfortunately such kinetics are generally lolknown for plasma jet floras and the only possibility is to determine the equilibrium sound velocitya calculated through the isentropic coefficient T. This coefficient has been calculated taking into account the dissociation and ionization reactions at equilibrium for temperatures ranging from 300 to 25,000 K and pressures between 0.1 and 1 Mpa for Ar, H₂, He, Ar-He, Ar-H₂, O₂, N₂, air, .steam, and methane.a often called the frozen sound velocity, was also calculated using (ratio of specific heats) instead of .     

水分在季节性冻土中的运动

季节性冻土是一种冰水共存的特殊土水体系,在分析冻土中水分运动的驱动力及其影响因素,冻土介质的物理特性（热特性和水力特性）及其参数测定方法的基础上,综述了水分在冻土中运动的基本规律及定量研究水分运动的试验与数值模拟方法。     

Effect of hydrocolloids on starch thermal transitions,as measured by DSC

Differential scanning calorimetry (DSC) was used to analyze the influence of different hydrocolloids (xanthan, guar, and locust bean gums, carboxymethylcellulose and sodium alginate) on the gelatinization of corn starch in systems with starch concentration ranging between 0.1 and 0.7 g starch/g mixture. The reduction of available water produced a shift in gelatinization temperature, especially of the conclusion temperature. The effect was more marked for ionic hydrocolloids. The influence of hydrocolloids on glass transition temperature (T _g) of gelatinized starch suspensions and on the glass transition temperature of the maximally freeze-concentrated solute/unfrozen water matrix (T _g) was also studied.T _g onset values ranged between –4.5 and –5.5C for corn starch pastes with and without hydrocolloids. Those hydrocolloids that increased the viscosity of the unfrozen matrix inhibited additional ice formation during thawing (devitrification).Starch concentration and final heating temperature were found to be relevant factors affecting the kinetics of amylopectin retrogradation during frozen storage at –4C. Xanthan gum failed to prevent amylopectin retrogradation; this observation could be attributed to the fact that gums act outside the starch granule, while amylopectin retrogradation takes place within the granule.     

微波加热技术在清除道路积冰中的应用

在我国北方寒冷地区的冬季,道路积冰严重妨碍交通,并且现有设备不能有效地对其清除.针对这种状况,提出了应用微波加热技术清除道路积冰的设想,并通过理论分析和实验证实了冰不易吸收微波,而路面材料能够吸收大量微波.因此,微波能够透过冰层加热路面,使贴近路面的冰层融化,消除冰层与路面之间的结合力,以便很容易地利用除冰机械对其清除.在参考了现有的各种清冰除雪机的基础上,设计出了专门用于清除道路积冰的微波除冰机原理图.     

冻土墙墙体时空扩展过程中热能消耗的有限元分析

用于人工冻土墙形成过程相关计算的Sanger—Sayles经验公式是，Fourier热传导方程在单值热物理参数轴对称条件下的求解结果，对结构形成过程中冻结管吸热的计算采用了不合理的温度分布假设，计算结果不能令人满意。运用有限元分析程序，完成了对热物理参数非线性变化土体材料的人工冻结过程的计算分析，模拟了冻土墙时空扩展过程，研究了土体内的温度分布以及能量消耗等问题，在此基础上推导出的关于冻结过程的能量消耗计算的一般形式，对人工冻土墙的工程设计具有重要的指导意义。     

北京一次降雪的云物理过程作用模拟

应用非静力平衡MM5 V3模式对2001年12月7日一次北京降雪过程进行了数值模拟试验，对云和降水物理过程的作用进行了初步分析。试验结果表明：本次降雪过程是从对流层上层形成冰核向下发展的，中高空的强低温和上升运动区与冰粒子及雪的分布基本吻合，为降雪的进一步发展提供了有利的条件。