The structure of the hard sphere solid

We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the HCP structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.Comment: For related papers see: http://www.ma.utexas.edu/users/radin/papers.htm

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

Stability and post critical behavior of supported panel in supersonic gas jet

Flat panel stability, partially supported on the elastic base and located in a supersonic gas flow is considered on the basis of the dynamic method. We study an influence of base’s stiffness on the position of the stability region’s boundaries in the plane of loading parameters. For the case of displaceable supports a study of supercritical behavior of the panel is conducted taking into account the additional longitudinal force. Different cases of stability loss of the panel and its behavior in the near and distant supercritical regions are considered

A New Class of Monoamine Oxidase Inhibitors

Newly synthesized compounds have been found to inhibit mitochondrial monoamine oxidase (MAO) in mouse brain and rat liver. A series of 2-acylamino-3- tert -aminopropiophenones acted preferentially against MAO type B (2-phenylethylamine as substrate), apparently irreversibly. 2-Decanoylamino-3-morpholinopropiophenone acted similarly in vivo toward the cerebral MAO, producing a dose-related inhibition. At high dose levels, MAO type A was also severely inhibited. The effects were produced rapidly and restoration of enzyme activity also appeared rapidly. The half-life for MAO type A could be estimated from the rate of enzyme reappearance to be 13 h. It is suggested that the amino ketones undergo a Β-elimination reaction at the enzyme's active site, forming a reactive species (an Α,Β-unsaturated ketone), which reacts covalently with a nucleophilic group of the enzyme by a Michael addition. Some other related compounds, derivatives of phenylpropane, also showed inhibitory activity against MAO, particularly against type A (serotonin as substrate). The morpholino compound might have promise as a quickly effective, short-acting inhibitor of MAO type B.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66333/1/j.1471-4159.1980.tb06611.x.pd

PV cohomology of pinwheel tilings, their integer group of coinvariants and gap-labelling

In this paper, we first remind how we can see the "hull" of the pinwheel tiling as an inverse limit of simplicial complexes (Anderson and Putnam) and we then adapt the PV cohomology introduced in a paper of Bellissard and Savinien to define it for pinwheel tilings. We then prove that this cohomology is isomorphic to the integer \v{C}ech cohomology of the quotient of the hull by $S^1$ which let us prove that the top integer \v{C}ech cohomology of the hull is in fact the integer group of coinvariants on some transversal of the hull. The gap-labelling for pinwheel tilings is then proved and we end this article by an explicit computation of this gap-labelling, showing that \mu^t \big(C(\Xi,\ZZ) \big) = \dfrac{1}{264} \ZZ [\dfrac{1}{5}].Comment: Problems of compilation by arxiv for figures on p.6 and p.7. I have only changed these figure

How model sets can be determined by their two-point and three-point correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

Recurrence in 2D Inviscid Channel Flow

I will prove a recurrence theorem which says that any $H^s$ ($s>2$) solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small $H^0$ neighborhood. Periodic boundary condition is imposed along the stream-wise direction. The result is an extension of an early result of the author [Li, 09] on 2D Euler equation under periodic boundary conditions along both directions

Flatness is a Criterion for Selection of Maximizing Measures

For a full shift with Np+1 symbols and for a non-positive potential, locally proportional to the distance to one of N disjoint full shifts with p symbols, we prove that the equilibrium state converges as the temperature goes to 0. The main result is that the limit is a convex combination of the two ergodic measures with maximal entropy among maximizing measures and whose supports are the two shifts where the potential is the flattest. In particular, this is a hint to solve the open problem of selection, and this indicates that flatness is probably a/the criterion for selection as it was conjectured by A.O. Lopes. As a by product we get convergence of the eigenfunction at the log-scale to a unique calibrated subaction