On a combinatorial problem in geometry

Denote by g(n) the cardinality of a minimal subset C of an n × n square array of lattice points which does not contain the vertices of a square with sides parallel to the axes, but which is such that the addition of any new point to C forces the appearance of such a square. It is proved that g(n) < n^α for some α < 2.     

Application of the Galerkin-Kantorovich-Dorodnitsyn method of integral relations to the solution of steady laminar boundary layers

Summary The Galerkin-Kantorovich-Dorodnitsyn N-parameter method of integral relations belongs in the same general category as those of Ritz and Galerkin. The method is employed to solve the steady, incompressible, two-dimensional flow of a laminar boundary layer. General Nth-order solutions are obtained for regions of accelerated flow and, with a modification to account for a possible separation point, for regions of retarded flow. The convergence and accuracy of the method are evaluated by comparing the solutions with a large number of similar and nonsimilar flow problems. The method permits a separation point to be approached as closely as desired without encountering numerical difficulties or requiring special continuation techniques.

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Übersicht Die N-Parameter-Methode der Integralbeziehungen von Galerkin, Kantorovich und Dorodnitsyn gehört zur gleichen Klasse wie die Verfahren von Ritz und Galerkin. Diese Methode wird benützt, um Lösungen für die stationäre, inkompressible, zwei-dimensionale Strömung einer laminaren Grenzschicht zu finden. Allgemeine Lösungen N. Ordnung werden für Gebiete mit beschleunigter Strömung erhalten und, mit gewissen Abänderungen zur Berücksichtigung eines möglichen Ablösepunktes, auch für Gebiete einer verzögerten Strömung. Die Konvergenz und die Genauigkeit der Methode werden durch Vergleich der Lösungen mit zahlreichen ähnlichen und nicht-ähnlichen Strömungsproblemen untersucht. Die Methode erlaubt eine beliebig weitgehende Annäherung an den Ablösepunkt, ohne daß numerische Schwierigkeiten auftreten oder besondere Grenzwertbetrachtungen erforderlich wären.

     

Gravitational effects on the SU(5) breaking phase transition for a Coleman-Weinberg potential

The gravitational coupling Rφ² plays a crucial role in determining the fate of the symmetric, high temperature state in a graud unified model with Coleman-Weinberg type symmetry breaking. If this term enters in the lagrangian with a negative sign, it drives the SU(5) breaking phase transition at a temperature of about 10¹⁰ GeV. If it enters with a positive sign, and in particular with the coefficient $\text{1}\text{12}$ which is required for a conformally invariant classical theory, this term prevents the phase transition from being completed, at least until temperatures are reached for which the SU(5) coupling becomes large.     

Estimating ground-state energies in supersymmetric quantum mechanics: (1) Broken case

For a class of the dynamically broken supersymmetric quantum-mechanical models proposed by Witten, we examine various methods of estimating the ground-state energy, including the instanton method developed by Salomonson and van Holten. We show that no existing method is entirely satisfactory, and develop a method using all stationary points of the Schrödinger potential (including those in the complex plane) in conjunction with the Rayleigh-Ritz variational method, thus combining perturbative and nonperturbative effects. Generalisations to more than one degree of freedom and to field theory are discussed.     

Selective extraction of metals from mixed oxide matrixes using choline-based ionic liquids

The solubility of a range of metal oxides in a eutectic mixture of urea/choline chloride is quantified, and it is shown that the dissolved metals can be reclaimed from a mixed metal oxide matrix using electrodeposition.     

On Ramsey numbers for circuits

Denote by r_k(n) the largest integer for which there exists some way of coloring the edges of a complete graph on r_k(n) vertices in k colors without forcing the appearance of a monochromatic simple circuit of length n. A new lower bound for r_k(5) is obtained.     

The collapse of an anti-de sitter bubble

We prove that the ultimate fate of a bubble of negative energy density which forms in a metastable universe of zero energy density is gravitational collapse. We improve on previous treatments in that we allow for departures from O(3, 1) symmetry in the initial state, so long as they are not too great.     

Effusive molecular beam study of C2H6 dissociation on Pt(111)

The dissociative sticking coefficient for C2H6 on Pt(111) has been measured as a function of both gas temperature (Tg) and surface temperature (Ts) using effusive molecular beam and angle-integrated ambient gas dosing methods. A microcanonical unimolecular rate theory (MURT) model of the reactive system is used to extract transition state properties from the data as well as to compare our data directly with supersonic molecular beam and thermal equilibrium sticking measurements. We report for the first time the threshold energy for dissociation, E0 = 26.5 +/- 3 kJ mol(-1). This value is only weakly dependent on the other two parameters of the model. A strong surface temperature dependence in the initial sticking coefficient is observed; however, the relatively weak dependence on gas temperature indicates some combination of the following (i) not all molecular excitations are contributing equally to the enhancement of sticking, (ii) that strong entropic effects in the dissociative transition state are leading to unusually high vibrational frequencies in the transition state, and (iii) energy transfer from gas-phase rovibrational modes to the surface is surprisingly efficient. In other words, it appears that vibrational mode-specific behavior and/or molecular rotations may play stronger roles in the dissociative adsorption of C2H6 than they do for CH4. The MURT with an optimized parameter set provides for a predictive understanding of the kinetics of this C-H bond activation reaction, that is, it allows us to predict the dissociative sticking coefficient of C2H6 on Pt(111) for any combination of Ts and Tg even if the two are not equal to one another.     

Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at sqrt[S(NN)] =2.76 TeV with the ATLAS detector at the LHC

By using the ATLAS detector, observations have been made of a centrality-dependent dijet asymmetry in the collisions of lead ions at the Large Hadron Collider. In a sample of lead-lead events with a per-nucleon center of mass energy of 2.76 TeV, selected with a minimum bias trigger, jets are reconstructed in fine-grained, longitudinally segmented electromagnetic and hadronic calorimeters. The transverse energies of dijets in opposite hemispheres are observed to become systematically more unbalanced with increasing event centrality leading to a large number of events which contain highly asymmetric dijets. This is the first observation of an enhancement of events with such large dijet asymmetries, not observed in proton-proton collisions, which may point to an interpretation in terms of strong jet energy loss in a hot, dense medium.