Conformations of cycloundecane

Cycloundecane (1) was shown to exist at -183.1 degrees C as a mixture of the [12323] (approximately 59%) and [335] (approximately 41%) conformations. Populations were determined from the (13)C NMR spectrum, and assignments were based on the (13)C spectra, calculated free energies and chemical shifts, and information from the literature, including X-ray studies of solid derivatives and calculated barriers.     

Polling systems with state-dependent setup times

We analyze a polling system with multiple stations (queues) attended by a cycling server, in which a setup occurs only when the queue that is polled by the server has one or more customers present. Although such systems are appropriate for modeling numerous manufacturing and telecommunication systems, their analysis is not well developed in the literature. We provide an exact analysis for the 2 station model and present two approximation schemes to determine the mean station waiting times for models with 3 or more stations. We show that some approximate models which have been proposed in the literature for providing upper bounds on the mean station waiting times do not always yield upper bounds. Extensive numerical tests indicate that a simple average of the two approximation schemes yields a close estimate of the true mean station waiting time. This average-of-approximations procedure appears to be robust for a large range of parameter values.Research supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP0045904.Research supported in part by the National Science Foundation under grant DMI-9500471.     

Conformational study of cis-1,4-di-tert-butylcyclohexane by dynamic NMR spectroscopy and computational methods. Observation of chair and twist-boat conformations

[reaction: see text] Low-temperature 13C NMR spectra of cis-1,4-di-tert-butylcyclohexane (1) showed signals for the twist-boat (1a) and chair (1b) conformations. 13C NMR signals were assigned to specific carbons based on the different populations, different symmetries (time-averaged C(2v) for 1a and time-averaged C(s) for 1b), and calculated chemical shifts (GIAO, HF/6-311+G*). In addition to slow ring inversion and interconversion of the chair and twist-boat conformations, slow rotation of the tert-butyl groups was found. Most of the expected 13C peaks were observed. Free-energy barriers of 6.83 and 6.35 kcal/mol were found for interconversion of 1a (major) and 1b (minor) at -148.1 degrees C. Conformational space was searched with Allinger's MM3 and MM4 programs, and free energies were obtained for several low-energy conformations 1a-c. Calculations were repeated with ab initio methods up to the HF/6-311+G* level. Molecular symmetries, relative free energies, relative enthalpies and entropies, frequencies, and NMR chemical shifts were obtained. A boat conformation (1d; C(2v) symmetry) was generated and optimized as a transition state by ab initio, MM3, and MM4 calculations.     

A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor–corrector operations enforcing function (C⁰) and derivative (C¹) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.     

Threshold start-up control policy for polling systems

A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine (server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal threshold level can be restricted to a finite set of possibilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cyclopentadecanone 2,4‐dinitrophenylhydrazone

In the title compound, C₂₁H₃₂N₄O₄, no disorder is present in the 15‐membered hydrocarbon ring, which exists in an unsymmetrical quinquangular [12345] conformation. The 2,4‐dinitrophenylhydrazone group is approximately perpendicular to the C₁₅ ring, with a dihedral angle of 84.66 (1)° between their best planes.     

Inorganic particulates in removal of heavy metal toxic ions IX. Rapid and efficient removal of Hg(II) by hydrous manganese and tin oxides

Batch studies have been carried out in the removal of Hg(II) from aqueous solutions by using well-synthesized and -characterized hydrous manganese oxide (HMO) and hydrous tin oxide (HTO) employing a radiotracer technique. Results obtained reveal that increased sorptive concentration (10(-8)-10(-2) mol dm(-3)), temperature (298-328 K), and pH (ca. 2.0-10.5) enhance the removal efficiency of these solids. First-order uptake of Hg(II) on HMO and HTO follows the Freundlich adsorption isotherm for entire concentration range. Positive values of DeltaH0 for the uptake process on both solids indicate endothermic uptake and desorption experiments point to irreversible uptake. Radiation stability of the adsorbents has also been assessed using a 300-mCi (Ra-Be) neutron source having an integral neutron flux of 3.85 x 10(6) N cm(-2) s(-1) and associated with a nominal gamma-dose of ca. 1.72 Gy/h.