Bilevel optimization applied to strategic pricing in competitive electricity markets

In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures is illustrated in case studies with configurations derived from the Brazilian power system.     

Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model

We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [Speetjens M, Reusken A, Marquardt W. Steady-state solutions in a nonlinear pool-boiling model. IGPM report 256, RWTH Aachen. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.11.002] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. (doi:10.1016/j.cnsns.2006.11.002) can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study.     

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.     

New method for determination of trihalomethanes in exhaled breath: Applications to swimming pool and bath environments

A method for the estimation of the human intake of trihalomethanes (THMs), namely chloroform, bromodichloromethane, dibromochloromethane and bromoform, during showering and bathing is reported. The method is based on the determination of these compounds in exhaled breath that is collected by solid adsorption on Tenax using a device specifically designed for this purpose. Instrumental measurements were performed by automatic thermal desorption coupled to gas chromatography with electron capture detection. THMs in exhaled breath samples were determined during showering and swimming pool attendance. The levels of these compounds in indoor air and water were also determined as reference for interpretation of the exhaled breath results. The THM concentrations in exhaled breath of the volunteers measured before the exposure experiments showed a close correspondence with the THMs levels in indoor air where the sampler was located. Limits of detection in exhaled breath were dependent on THM analytes and experimental sites. They ranged between 170 and 710 ng m⁻³ in the swimming pool studies and between 97 and 460 ng m⁻³ in the showering studies. Application of this method to THMs determination during showering and swimming pool activities revealed statistically significant increases in THMs concentrations when comparing exhaled breath before and after exposure.