Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop

This paper considers the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. It continues recent work by Bräsel et al. [H. Bräsel, A. Herms, M. Mörig, T. Tautenhahn, T. Tusch, F. Werner, Heuristic constructive algorithms for open shop scheduling to minmize mean flow time, European J. Oper. Res., in press (doi.10.1016/j.ejor.2007.02.057)] on constructive algorithms. For this strongly NP-hard problem, we present two iterative algorithms, namely a simulated annealing and a genetic algorithm. For the simulated annealing algorithm, several neighborhoods are suggested and tested together with the control parameters of the algorithm. For the genetic algorithm, new genetic operators are suggested based on the representation of a solution by the rank matrix describing the job and machine orders. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The algorithms are compared relative to each other, and the quality of the results is also estimated partially by a lower bound for the corresponding preemptive open shop problem. For most of the problems, the genetic algorithm is superior when fixing the same number of 30 000 generated solutions for each algorithm. However, in contrast to makespan minimization problems, where the focus is on problems with an equal number of jobs and machines, it turns out that problems with a larger number of jobs than machines are the hardest problems.     

Stabilizing the monodromy of an open book decomposition

We prove that any mapping class on a compact oriented surface with non-empty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.      

On the Analysis of the Virtual Waiting Time in Open Queueing Networks

The model of an open queueing network in heavy traffic has been developed. These models are mathematical models of computer networks in heavy traffic. A limit theorem has been presented for the virtual waiting time of a customer in heavy traffic in open queueing networks. Finally, we present an application of the theorem—a reliability model from computer network practice.     

Open tubular columns and non-porous packings in copolymer HPLC analysis

Summary The separation of poly(styrene-co-acrylonitrile) is presented in open tubular stainless steel columns and columns packed with non-porous glass beads. Furthermore separation on a short silica packed column proved to be better than on a similar longer column. A definition of the term high performance precipitation liquid chromatography is suggested for gradient elution with sample injection into a starting eluent which is a nonsolvent for the copolymer under investigation. The choice of a suitable solvent-nonsolvent combination is of essential importance.     

Open boundary condition symposium benchmark solution: Stratified flow over a backward-facing step

This paper presents a detailed numerical solution to a simplified version of two-dimensional stratified flow over a backward-facing step with a Froude number of 16/9, a Reynolds number of 800 and a Prandtl number of 1—one of the Open Boundary Condition Symposium test problems. The steady state solution was derived by integrating the time-dependent Boussinesq equations forward in time using a semi-implicit finite-element-based model on a 38400-element mesh. In addition to presenting the results derived on this grid, the paper also presents the results of a Richardson extrapolation calculation for a set of ‘key’ parameters. It is hoped that this solution can be used as a baseline to compare the performance of the various techniques discussed at the Open Boundary Condition Symposium.     

Residual stress field and reduction of stress intensity factors in cold-worked holes

Closed-form and semi-analytical solutions are obtained for the residual stress distributions in a plate caused by pressure acting on a central circular hole, representing the cold-work process. The material is elastic–perfectly plastic. Both Tresca and von Mises yield criteria are used and the corresponding residual stress distributions are compared. The relation between the dimension of the plastic zone and the value of internal pressure is presented. The relation between the magnitude of the residual stresses and the remote uniform tensile stress required to open symmetrical radial cracks is also presented. The reduction of the stress intensity factors of cracked open and riveted holes as a function of the internal pressure applied (or mandrel radial displacement) is investigated using numerical models for both an elastic–perfectly plastic material and for an Al 2024-T3 Alclad aluminum alloy.     

Achiral and chiral separations using MEKC,polyelectrolyte multilayer coatings,and mixed mode separation techniques with molecular micelles

Mixed mode (MM) separation using a combination of MEKC and polyelectrolyte multilayer (PEM) coatings is herein reported for the separation of achiral and chiral analytes. Many analytes are difficult to separate by MEKC and PEM coatings alone. Therefore, the implementation of a MM separation provides several advantages for overcoming the limitations of these well‐established methods. In this study, it was observed that achiral separations using MEKC and PEM coatings individually resulted in partial resolution of eight very similar aryl ketones when the molecular micelle (sodium poly(N‐undecanoyl‐L ‐glycinate)) concentration was varied from 0.25 to 1.00% w/v and the bilayer number varied from 2 to 4. However, when MM separation was introduced, baseline resolution was achieved for all eight analytes. In the case of chiral separations, temazepam, aminoglutethimide, benzoin, benzoin methyl ether, and coumachlor were separated using the three separation techniques. For chiral separations, the chiral molecular micelle, sodium poly(N‐undecanoyl‐L ‐leucylvalinate), was employed at concentrations of 0.25–1.50% w/v for both MEKC and PEM coatings. Overall, the results revealed partial separation with MEKC and PEM coatings individually. However, MM separation enabled baseline separation of each chiral mixture. The separation of achiral and chiral compounds from different compound classes demonstrates the versatility of this MM approach.     

Separation of intact proteins on porous layer open tubular (PLOT) columns

Porous layer open tubular (PLOT) polystyrene divinylbenzene columns have been used for separating intact proteins with gradient elution. The 10 μm I.D. × 3 m columns were easily coupled to standard liquid chromatography–mass spectrometry (LC–MS) instrumentation with commercially available fittings. Standard proteins separated on PLOT columns appeared as narrow and symmetrical peaks with good resolution. Average peak width increased linearly with gradient time (t_G) from 0.14 to 0.33 min (t_G 20 and 120 min, respectively) using a 3 m column. With shorter columns, peak widths were larger and increased more steeply with gradient time. Theoretical peak capacity (n_c) increased with column length (tested up to 3 m). The n_c increased with t_G until a plateau was reached. The highest peak capacity achieved (n_c = 185) was obtained with a 3 m column, where a plateau was reached with t_G 90 min. The within- and between column retention time repeatabilities were below 0.6% and below 2.5% (relative standard deviation, RSD), respectively. The carry-over following injection of 0.5 ng per protein was less than 1.1%. The retention time dependence on column temperature was investigated in the range 20–50 °C. Proteins in a skimmed milk sample were separated using the method.