Epimeric 2-norbornyl cations in the solvolysis of 6-exo- and 6-endo-substituted 2-exo-norbornyl p-toluenesulfonates

Solvolysis of 6-exo- and 6-endo-substituted 2-exo-norbornyl tosylates $\text{1}$ and $\text{3}$, respectively, yields identical or different product mixtures depending on the inductive effect of the substituent, indicating that induction involves graded σ-participation.     

Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.     

Facile synthesis of @-tide beta-strand peptidomimetics: improved assembly in solution and on solid phase

The synthesis of @-tide beta-strand peptidomimetics has been improved such that oligomers now can be obtained from solution- and solid-phase synthesis protocols approaching the efficiency and flexibility of peptide chemistry. These methods enable the synthesis of @-tide oligomers with a variety of amino acids and with lengths up to 13 units. [reaction: see text]     

The quickest flow problem

Consider a network =(G, c, ) whereG=(N, A) is a directed graph andc _ij and _ij , respectively, denote the capacity and the transmission time of arc (i, j) A. The quickest flow problem is then to determine for a given value the minimum numberT() of time units that are necessary to transmit (send) units of flow in from a given sources to a given sinks.In this paper we show that the quickest flow problem is closely related to the maximum dynamic flow problem and to linear fractional programming problems. Based on these relationships we develop several polynomial algorithms and a strongly polynomial algorithm for the quickest flow problem.Finally we report computational results on the practical behaviour of our metholds. It turns out that some of them are practically very efficient and well-suited for solving large problem instances.Partial financial support by the Air Force Office of Scientific Research under grants AFOSR-89-0512 and AFOSR-90-0008 is gratefully acknowledged by the first author.     

The Separation of Zirconium and Hafnium by Liquid-Liquid Partition of their Thiocyanates

The partition equilibria of zirconium and hafnium thiocyanates between water and methyl isobutyl ketone have been studied under various conditions. Since the system shows extremely marked deviations from Nernst's distribution law, the two elements cannot be prepared in a very pure state by a simple multi-stage partition. By the use of suitable additives and a new scheme of material flow, however, a continuous process using 23 mixer settlers has been developed, by means of which ZrO₂ containing less than 10 p.p.m. of HfO₂ and HfO₂ containing only 0.3% of ZrO₂ can be obtained from a zirconium-hafnium mixture (hafnium content: 1 to 2%).     

Uncertainty Analysis of Radionuclide Transport in a Fractured Coastal Aquifer with Geothermal Effects

Groundwater flow and radionuclide transport at the Milrow underground nuclear test site on Amchitka Island are modeled using two-dimensional numerical simulations. A multi-parameter uncertainty analysis is adapted and used to address the effects of uncertainties associated with the definition of the modeled processes and the values of the parameters governing these processes. In particular, we focus on the effects on radioactive transport of uncertainties associated with conduction and convection of heat relative to the uncertainties associated with other flow and transport parameters. These include recharge, hydraulic conductivity, fracture porosity, dispersivity and strength of matrix diffusion. The flow model is conceptualized to address the problem of density-driven flow under conditions of variable salinity and geothermal gradient. The conceptual transport model simulates the advection–dispersion process, the diffusion process from the high-velocity fractures into the porous matrix blocks, and radioactive decay.For this case study, the uncertainty of the recharge-conductivity ratio contributes the most to the output uncertainty (standard deviation of mass flux across the seafloor). The location of the freshwater–saltwater transition zone changes dramatically as this ratio changes with the thickness of the freshwater lens and the location of the seepage face changing as well. In the context of radionuclide transport from the nuclear test cavity that is located in the area where the transition zone is uncertain, travel times of radionuclide mass from the cavity to the seepage face along the seafloor are significantly impacted. The variation in transition zone location changes the velocity magnitude at the cavity location by a large factor (probably an order of magnitude). When this effect is combined with porosity and matrix diffusion uncertainty, the uncertainty of transport results becomes large. Although thermal parameters have an effect on the solution of the flow problem and also on travel times of radionuclides, the effect is relatively small compared to other flow and transport parameters.     

On minimum weight pseudo-triangulations

In this note we discuss some structural properties of minimum weight pseudo-triangulations of point sets.