Allocating energy in a first-to-n match

This paper models a decision where a player must allocate limitedenergy over a contest of uncertain length. The motivating exampleis a squash match where one of the players is not as fit asthe other. Should a player's energy be concentrated in the earlygames of the match? Should it be spread evenly over all possiblegames? Or should it be conserved for the end of the match? Wemodel this as a decision problem where, in each game, the decision-makermust determine how much energy to expend. We assume that thereare only a small number of discrete energy choices for eachgame and that the more energy the decision-maker expends, themore likely he is to win that game. We solve for the optimaldecision with dynamic programming. With only two possible energychoices for each game, we show that it does not matter how energyis expended. In the case where there are three or more energychoices, we show how to take advantage of the structure of theproblem to determine the optimal sequence of decisions. As forpractical advice, the model suggests that when the decision-makerfalls behind in a match, he ought to switch to a more conservativeapproach by dividing his remaining energy evenly among all thepossible remaining games. Received 14 May 2003. Revised 5 January 2004.     

Simple Analytical Model Predicting Some Features of the Electrolytic Steel-Pickling Process

Electrolytic pickling of steel with neutral solutions, to remove the surface scale, reduces the need for the use of strong acids as needed in conventional pickling. This study is a step towards a more in-depth understanding of the factors affecting the former process. A theoretical model, sufficiently simplified to allow analytical solution, is developed and evaluated to provide a first approximation of the potential and current distributions in the electrolyte and steel band. To gain knowledge and validate the model, a small electrolytic pickling cell is constructed, and experiments, including bubble generation and motion observation, are conducted. The experimental work has shown the remarkable bubble production and adherence to the surfaces, and its effects on reducing pickling efficiency and uniformity. The pickling efficiency is about 30%, confirming other researchers" results. The analytical model shows trends very similar to those observed in the experiments, and provides very valuable guidance. It shows, for example, that the current efficiency decreases as the electrode–band distance increases, and it increases with the band thickness and the band-to-electrolyte conductivity ratio. The energy efficiency decreases by orders of magnitude faster than the current efficiency with all of the above-mentioned parameters, because of the correspondingly strong drop in the band–surface potential. A large amount of current is lost due to interelectrode short circuiting.     

Variable coordination geometries at the diiron(II) active site of ribonucleotide reductase R2

The R2 subunit of Escherichia coli ribonucleotide reductase contains a dinuclear iron center that generates a catalytically essential stable tyrosyl radical by one electron oxidation of a nearby tyrosine residue. After acquisition of Fe(II) ions by the apo protein, the resulting diiron(II) center reacts with O(2) to initiate formation of the radical. Knowledge of the structure of the reactant diiron(II) form of R2 is a prerequisite for a detailed understanding of the O(2) activation mechanism. Whereas kinetic and spectroscopic studies of the reaction have generally been conducted at pH 7.6 with reactant produced by the addition of Fe(II) ions to the apo protein, the available crystal structures of diferrous R2 have been obtained by chemical or photoreduction of the oxidized diiron(III) protein at pH 5-6. To address this discrepancy, we have generated the diiron(II) states of wildtype R2 (R2-wt), R2-D84E, and R2-D84E/W48F by infusion of Fe(II) ions into crystals of the apo proteins at neutral pH. The structures of diferrous R2-wt and R2-D48E determined from these crystals reveal diiron(II) centers with active site geometries that differ significantly from those observed in either chemically or photoreduced crystals. Structures of R2-wt and R2-D48E/W48F determined at both neutral and low pH are very similar, suggesting that the differences are not due solely to pH effects. The structures of these "ferrous soaked" forms are more consistent with circular dichroism (CD) and magnetic circular dichroism (MCD) spectroscopic data and provide alternate starting points for consideration of possible O(2) activation mechanisms.     

Stöber synthesis of monodispersed luminescent silica nanoparticles for bioanalytical assays

We have developed a simple method to prepare bright and photostable luminescent silica nanoparticles of different sizes and narrow size distribution in high yield. The method is based on the use of St?ber synthesis in the presence of a fluorophore to form bright silica nanoparticles. Unlike micro-emulsion-based methods often used to prepare luminescent silica particles, the St?ber method is a one-pot synthesis that is carried out at room temperature under alkaline conditions in ethanol:water mixtures and avoids the use of potentially toxic organic solvents and surfactants. Our luminescent particles contained the transition metal complex tris(1,10-phenanthroline) ruthenium(II) chloride, [Ru(phen)3]Cl2. They showed higher photostability and a longer fluorescence lifetime compared to free Ru(phen)3 solutions. Leakage of dye molecules from the silica particles was negligible, which was attributed to strong electrostatic attractions between the positively charged ruthenium complex and the negatively charged silica. To demonstrate the utility of the highly luminescent silica nanoparticles in bioassays, we further modified their surface with streptavidin and demonstrated their binding to biotinylated glass slides. The study showed that digital counting of the luminescent nanoparticles could be used as an attractive alternative to detection techniques involving analogue luminescence detection in bioanalytical assays.     

Achiral Calcium‐Oxalate Crystals with Chiral Morphology from the Leaves of Some Solanacea Plants

The leaves of some plants, particularly among the Solanacea, contain crystals of calcium oxalate with a peculiar chiral pseudo‐tetrahedral morphology, even though the calcium oxalate crystal structure is centrosymmetric, hence achiral. We studied the morphology of these crystals extracted from the leaves of three Solanacea plants: the potato, the hot pepper, and a species of wild Solanum. The crystal morphology was the same in all three species. Based on the examination of more than 100 crystals from each plant, we showed that the crystal morphology is chiral with invariant chirality. We suggest that morphological chirality is induced by macromolecules during nucleation from a specific, genetically encoded crystal plane, and is further established during subsequent controlled crystal growth. This is one of few examples where it is possible to deduce a molecular mechanism for biologically induced breaking of morphological symmetry in organisms. A very high level of recognition is required by the macromolecules to allow them to distinguish between symmetry‐related crystal planes. It is also surprising that this finely controlled mechanism of crystal formation, including the chiral morphology, has been conserved during evolution.     

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed ‘splitting.’ We discuss far-field ‘splitting’ in the full field and near-horizon ‘splitting’ in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the ‘splitting’ behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field ‘splitting’ is explained by competition between projected modes. The near-horizon ‘splitting’ is due to excitation of lower multipole modes that back excite the multipole mode for which ‘splitting’ is observed. In both cases ‘splitting’ is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter-mode excitation effect that we study.