A stream tube model for miscible flow

A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.Nomenclature A total cross-section area of the sample - C (resident) concentration of tracer - D,D ^* dispersion coefficient - F flux of tracer - G probability distribution function for permeability in the stream-tube segments - I tracer intensity (mass crossing a surface per unit time) - K permeability - L length of the medium - M number of stream tubes in the medium - N number of segments along a stream tube - P pressure - Q total flow rate in the sample - a length of an elementary stream-tube segment - g probability distribution function for permeability in the space - i, j indices, tube numbers - q flow rate in each stream tube - s variable cross-section area of a stream tube - t, t time - u front velocity - x space variable in the flow direction - small local variation in time - , _t longitudinal, transverse dispersivity - porosity of the porous medium - correlation length in the permeability field - viscosity of the fluid - time for filling an elementary stream tube segment - standard deviation of a stochastic variable - probability distribution of arrival times (Gaussian)     

ContinuousK-theory

We study arithmetical properties of homotopy groups of thel-adic completion of Quillen'sK-theory space of number field, with a view on the Dwyer-Friedlander comparison map into étaleK-theory. The relation of these groups toK-theory is a complete analogy to the relation of continuous étale cohomology to étale cohomology. We identify the torsion subgroup of the resulting term with the subgroup of divisible elements inK _2n (F). We prove that this term is sent isomorphically into étaleK-theory, giving some further evidence for the Lichtenbaum-Quillen conjectures.     

Chains of strongly non-reflexive dual groups of integer-valued continuous functions

Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.

     

Cartesian closedness of categories of completely distributive lattices

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category of completely distributive lattices with nonempty union preserving mappings is cartesian closed.     

结晶器内连铸坯热弹塑性应力的有限元分析

建立了结晶器内连铸坯热弹塑性应力有限元分析模型,在推导的热弹塑性本构方程中考虑了材料力学性能,屈服函数随温度和应变速率的变化,模拟计算了结晶器内连铸坏应力分布。模拟结果表明,在铸坯的热节约内,高温坯壳受到拉应力的作用,易于产生裂纹,从而说明铸坯偏角区形成的热节约是连铸坯裂纹缺陷乃至漏钢事故发生的诱因。     

∑N_im_i强子产生过程中质量增加的经验公式和(英文)

强子质量ｍｉ和强子的平均数〈Ｎｉ〉遵从公式（βｍｍｉ／〈ｍ〉）μ＋νＫν（βｍｍｉ／〈ｍ〉）．自旋、奇异数压低和大产生截面（σ（Ｄ）,σ（Ｂ）,σ（Λ０））都是质量效应．质量产生过程受到在扩散方程和相对论波动方程之间连续变化所决定的连续阶导数（／ｔ）μＧＸα（ｘ,ｔ）控制．     

Improved oxygen delivery in a continuous-roller-bottle reactor

Variations to the original aeration system in a continuous roller bottle reactor of novel design have been tested and compared for optimal oxygen (O) delivery. Reactor operating parameters that affect O transfer are rotation rate, liquid-volume level, fresh-feed rate, and supplementary-aeration rate. Design modifications to enhance gas-liquid O transfer include the addition of wall baffles and center baffles. The number and location of each of these baffles are compared for their effect on k_La values in the reaction chamber. The liquid feed into the system has been modified to improve the axial liquid mixing and O transfer.     

Continuous chromatographic separation of glucose-fructose mixtures using anion-exchange resins

Summary A semi-continuous, counter-current chromatographic refiner (SCCR) was packed with an anion resin in the bisulphite form and used to separate mixtures of sugars from different feedstocks. Products with purities of more than 99% were achieved and solid concentrations of the fructose products of 12% w/v were possible. The deterioration of the anion resin was controlled by simple precautions and thus its useful life was substantially prolonged.     

Continuous determination of carbon dioxide evolved during thermal decomposition reactions

A simple device suitable for continuous monitoring of carbon dioxide evolved during thermal decomposition reactions is described. Carbon dioxide is transported by a carrier gas through the device connected to thermoanalytical equipment and absorbed by soda lime reagent. The reaction heat released is linearly proportional to the amount of carbon dioxide absorbed.     

A MORPHOLOGICAL STUDY OF POLY（DIVINYLBENZENE-co-ACRYLIC ACID） IN CROSSLINKING PRECIPITATION POLYMERIZATION

Divinylbenzene-80 （DVB-80） and polar monomer acrylic acid （AA） having hydrogen bonding at a total monomer loading of 5 vol% were precipitated-copolymerized in a variety of organic solvents with 2,2＇-azobis（isobutyronitrile） （AIBN） as initiator. The experiments were investigated from a two-dimensional matrix, i.e., the actual crosslinking degree of DVB varying from 0 to 80% and the solvent composition varying from 0 to 100% of toluene mixture with acetonitrile, when the mixture of acetonitrile and toluene was used as the reaction solvent. Under various reaction conditions, six distinct morphologies including soluble polymers, swellable microgels, coagulum, irregular microparticles, and nano-/micrometer microspheres were formed and the structures of these polymer architectures were described. A morphological map was utilized to discuss the effects of both crosslinking degree of DVB and composition of solvent on the transitions between morphology domains. The results demonstrated that the microspheres are formed by an internal contraction due to the marginal solvency of the continuous phase and the crosslinking of the polymer network through the covalent bonding from DVB as well as the interchain hydrogen-bonding between the carboxylic acid units.