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.     

Role of ion ligands in the attachment of poly(ethylene oxide) to a charged surface

Using a surface force balance we demonstrate unambiguously that high-molecular-weight poly(ethylene oxide) (PEO) does not adsorb onto mica from purified water with no added salt, a surprising observation in view of its strong adsorption on mica from aqueous 0.1 M KNO3 solution. Analysis of the force profiles, together with the known complexation of PEO with metal ions, suggests that the polymer attachment to the negatively charged surface is mediated by the hydrated potassium ion acting as a ligand.     

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.     

Urea oxidation electrocatalysis on nickel hydroxide: the role of disorder

Journal of Solid State Electrochemistry - The urea oxidation reaction (UOR) is an important challenge in electrocatalysis, in the context of electrolyzers, fuel cells, medical sensing, and...     

Forcing matchings on square grids

Let G be a graph that admits a perfect matching. The forcing number of a perfect matching M of G is defined as the smallest number of edges in a subset S M, such that S is in no other perfect matching. We show that for the 2n × 2n square grid, the forcing number of any perfect matching is bounded below by n and above by n². Both bounds are sharp. We also establish a connection between the forcing problem and the minimum feedback set problem. Finally, we present some conjectures about forcing numbers in other graphs.     

Efficient current-induced domain-wall displacement in SrRuO3

We demonstrate current-induced displacement of ferromagnetic domain walls in submicrometer fabricated patterns of SrRuO3 films. The displacement, monitored by measuring the extraordinary Hall effect, is induced at zero applied magnetic field and its direction is reversed when the current is reversed. We find that current density in the range of 10(9)-10(10) A/m2 is sufficient for domain-wall displacement when the depinning field varies between 50 to 500 Oe. These results indicate relatively high efficiency of the current in displacing domain walls which we believe is related to the narrow width (approximately 3 nm) of domain walls in this compound.     

The dependence of the electronic conductivity of carbon molecular sieve electrodes on their charging states

The dependence of the electronic conductivity of activated carbon electrodes on their potential in electrolyte solutions was examined. Kapton polymer films underwent carbonization (1000 degrees C), followed by a mild oxidation process (CO(2) at 900 degrees C) for various periods of time, to obtain carbons of different pore structures. A specially designed cell was assembled in order to measure the conductivity of carbon electrodes at different potentials in solutions. When the carbon electrodes possessed molecular sieving properties, a remarkable dependence of their conductivity on their charging state was observed. Aqueous electrolyte solutions containing ions of different sizes were used in order to demonstrate this phenomenon. As the average pore size of the activated carbons was larger, their molecular sieving ability was lower, and the dependence of their conductivity on their charging state regained its classical form. This behavior is discussed herein.     

Rulesets for Beatty games

We describe a ruleset for a 2-pile subtraction game with P-positions \(\{(\lfloor \alpha n \rfloor ,\lfloor \beta n \rfloor ) : n \in \mathbb Z_{\ge 0} \}\) for any irrational \(1< \alpha < 2\), and \(\beta \) such that \(1/\alpha +1/\beta = 1\). We determine the \(\alpha \)’s for which the game can be represented as a finite modification of t-Wythoff (Holladay, Math Mag 41:7–13, 1968; Fraenkel, Am Math Mon 89(6):353–361, 1982) and describe this modification.