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.     

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.     

On the reachable sets in linear systems

We consider the finite-dimensional linear control system, with minimal assumptions concerning the control restraint set . Specifically, we consider the set of reachable states and conclude that as far as controllability is concerned, can be replaced by convhull().     

On state restrained linear-quadratic control problems

A finite dimensional linear autonomous control process with subspace state restraint is considered from the controllability and minimum quadratic cost points of view. The problem of holding in a subspace on an infinite time interval with finite total control energy is also considered.     

TDDFT study of one- and two-photon absorption properties: donor-pi-acceptor chromophores

We report a comprehensive time-dependent density functional theory (TDDFT) study of one-photon and two-photon absorption (OPA and TPA, respectively) spectra for donor-pi-acceptor molecules. The calculated excitation energies were generally shown to be in good agreement with experiment, particularly when compared to results from measurements carried out in a nonpolar solvent, although the oscillator strengths were overestimated in some cases. Calculated TPA cross sections applying the two-state approximation were shown to be highly dependent on the form of the line-shape function used. Although a good agreement with experimental TPA spectra was generally observed, the wide range in the experimentally measured values and lack of systematic experimental data on solvent effects limited a detailed comparison as yet.