Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.     

The combinatorial game Nofil played on Steiner triple systems

We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions.     

Molecular dynamics of cyclic and linear poly(dimethylsiloxanes)

Dielectric spectroscopy (10^–1 Hz to 10⁷ Hz) has been employed to study the molecular dynamics of a series of cyclic and linear polydimethylsiloxanes (PDMS) of various molecular weights ranging from 300 to 10 000 g/mol in the temperature range above the glass transition (from 130 K to 190 K). The observed -relaxation depends strongly on both molecular weight and structure of the samples. For linear PDMS oligomers, the -relaxation shifts towards lower temperatures with decreasing molecular weight in good accordance with the Fox-Flory-model. Cyclic PDMS reveals a qualitatively different molecular weight dependence: for a given temperature the -relaxation time increases with decreasing ring length, but has a maximum for small oligomers (degree of polymerizationn6). The shape of relaxation curves and, with it, the relaxation time distribution is independent from length and architecture of the chains The observed experimental findings are in qualitative agreement with dynamic Monte-Carlo simulations.Dedicated to Prof. E.W. Fischer on the occasion of his 65th birthday Fast macht' das WLF ihn krank, jetzt raucht er wieder, Gott sei Dank! (frei nach Wilhelm Busch)     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

End-functionalized polyethylene oxide coated silica particles for packed capillary column supercritical fluid chromatography

Summary Polyethylene oxide (PEO)-based polymers with hydroxy, methoxy, and aminopropoxy terminal groups were coated on diol functionalized and hexamethyldisilazane end-capped silica particles. Proton-donor and proton-acceptor test solutes, including carboxylic acids, hydroxy-containing compounds, arylamines, and alkylamines were used to evaluate the chromatographic performances of these polymer coated particles under SFC conditions with neat CO₂ as mobile phase. It was found that the particles coated with hydroxy-terminated PEO were suitable for the separation of proton-donor compounds such as hydroxy-containing compounds and carboxylic acids, and the particles coated with aminopropoxy-terminated PEO could be used for the separation of amines. That is, the proton-accepting stationary phase is suitable for the separation of proton accepting solutes, including strong basic alkylamines (pK_b4), using neat CO₂ as mobile phase, while the protondonating stationary phase is suitable for the separation of proton-donating compounds such as carboxylic acids (pK_a4). Hydrogen bond basicity was found to be a critical factor for the chromatography of basic amines. Low volatility acidic and basic drugs were chromatographed using the new stationary phases. The stability of the PEO coated particles was determined by measuring the loss of organic carbon under SFC conditions. It was found that approximately 18 % of the coating (average molecular weight of 15,000) was washed out of the particles by supercritical CO₂ after 7 h at 350 atm and 50°C     

离线超临界流体萃取和气相色谱/质谱联用对实验室内空气中气相有机污染物的测试

通过团体吸附剂富集，再用超临界ＣＯ２脱附后用气相色谱及质谱技术对实验室内空气中气相有机污染物进行了考察。文中对采样和萃取条件进行了优化，并与热脱附所得结果做了比较。结果表明在２２ＭＰａ，８０℃时，用甲醇改性的超临界ＣＯ２进行萃取的结果优于热脱附法。该法鉴定出气相有机污染物中５２个组分，占色谱峰总面积的９９．６％。     

Supercritical fluid extraction-capillary gas chromatography: On-line coupling with a programmed temperature vaporizer

A simple and versatile system is described for the on-line coupling of SFE to capillary GC. The interfacing consists of a programmed temperature vaporizer (PTV) injector. With this injector it is possible to combine solute trapping, elimination of a high flow of extraction fluid, and quantitative transfer of solutes to the seperation column. The problems caused by impurities in the extraction fluid in on-line SFE-GC are discussed. Simple methods are described for the purification of commercially available carbon dioxide. The trapping efficiency of the PTV injector is studied. Applications of the SFE-PTV-GC system are given for the analysis of polymer anti-degradants, polar compounds, and samples with environmental relevance.     

聚苯醚砜在二甲基甲酰胺中稀溶液性质的研究(Ⅱ)

本文用广角及准弹性光散射法测定了聚苯醚砜各级分在DMF中和在θ溶剂中25℃时的均才半径R_G,第二维利系数A_2,流体力学半经R_H,扩散系数D_O,扩散系数的浓度依赖性k_F以及这些参数与分子量M的关系。它们的结果如下R_G=0.031MO~(0.55) D_O(θ)=0.906×10~(-4)M~(0.5) D_0=1.445×10~(-4)M~(0.55)A_2=0.033M~(-0.35) k_D(θ)=0.5M~(0.34) k_D=2.3×10~(-6)M~(1.36)α_H=R_H/R_H(θ)=0.63M~(0.05)R_H(θ)=0.0299M~(0.5)R_H=0.0188M~(0.55) 作者讨论了静态与动态两种高分子尺寸之间的关系;三种溶胀因子α_η和、α_H、α_G之间的关系;以及摩擦系数的浓度系数k_F与流体力学体积V_H之间的关系。它们的结果满足下面各关系式: R_H/R_G=[π(v+1)(2v+1)/3]~(1/2)(2-v)(1-v)/2, α_η~3=α_(G)~2α_H, k_F=1.2A_2M+N_AV_H/M,K_F(θ)=N_AV_H/M     

Analysis of grid file algorithms

Grid file algorithms were suggested in [12] to provide multi-key access to records in a dynamically growing file. We specify here two algorithms and derive the average sizes of the corresponding directories. We provide an asymptotic analysis. The growth of the indexes appears to be non-linear for uniform distributions:O(v ^c ) orO(v ), wherec=1+b^–1, =1+(s-1)/(sb+1),s is the number of attributes being used,v the file size, andb the page capacity of the system. Finally we give corresponding results for biased distributions and compare transient phases.     

A discrete method of optimal control based upon the cell state space concept

A discrete method of optimal control is proposed in this paper. The continuum state space of a system is discretized into a cell state space, and the cost function is discretized in a similar manner. Assuming intervalwise constant controls and using a finite set of admissible control levels (u) and a finite set of admissible time intervals (), the motion of the system under all possible interval controls (u, ) can then be expressed in terms of a family of cell-to-cell mappings. The proposed method extracts the optimal control results from these mappings by a systematic search, culminating in the construction of a discrete optimal control table.The possibility of expressing the optimal control results in the form of a control table seems to give this method a means to make systems real-time controllable.Dedicated to G. LeitmannThe material is based upon work supported by the National Science Foundation under Grant No. MEA-82-17471. The author is also indebted to Professor G. Leitmann for his many helpful comments.