Statistical properties of shocks in Burgers turbulence

We consider the statistical properties of solutions of Burgers' equation in the limit of vanishing viscosity, , with Gaussian whitenoise initial data. This system was originally proposed by Burgers^[1] as a crude model of hydrodynamic turbulence, and more recently by Zel'dovichet al..^[12] to describe the evolution of gravitational matter at large spatio-temporal scales, with shocks playing the role of mass clusters. We present here a rigorous proof of the scaling relationP(s)s ^1/2,s1 whereP(s) is the cumulative probability distribution of shock strengths. We also show that the set of spatial locations of shocks is discrete, i.e. has no accumulation points; and establish an upper bound on the tails of the shock-strength distribution, namely 1–P(s)exp{–Cs ³} fors1. Our method draws on a remarkable connection existing between the structure of Burgers turbulence and classical probabilistic work on the convex envelope of Brownian motion and related diffusion processes.Inadvertently the sequel to this article, Statistical Properties of Shocks in Burgers Turbulence, II. Tail Probabilities for Velocities, Shock-Strengths and Rarefaction Intervals has already appeared in an earlier issue of Commun. Math. Phys. (Commun. Math. Phys.169, 45–59 (1995).     

Practical aspects of Mössbauer spectroscopy instrumentation

The setting up and updating of a Mössbauer laboratory imply the acquisition and assembling of different units. Guidelines concerning either the construction or the acquisition of the various parts which compose a Mössbauer spectrometer are given in this paper.     

Iron-57 Mössbauer spectroscopic studies of materials of composition Fe x NbTiP3O12: materials with low concentrations of iron and the effects of treatment in air

The⁵⁷Fe Mössbauer spectrum recorded from the material of composition Fe_0.25NbTiP₃O₁₂ shows the presence of Fe²⁺ in a distribution of approximately octahedral type I sites within the channels of the NbTiP₃O₁₂ structure. A comparison of the results with those recorded from the material Fe_0.33NbTiP₃O₁₂ demonstrates the existence of an upper limit to the occupation by the Fe²⁺ species of the type I sites. Lattice parameter measurements and⁵⁷Fe Mössbauer spectroscopy show that treatment of Fe_0.25NbTiP₃O₁₂ in air induces the migration of the incorporated iron from the channels to form macroscopic -Fe₂O₃.     

The rate difference between the weak decays of t and in supersymmetry

We find that the CP-violating asymmetry

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at the one-loop order within the minimal supersymmetric extension of the standard model is of the order of few percent for maximal CP violation. It could be measured by considering the rate difference in the one-lepton events.     

WKB-type approximations for second-order differential equations in -algebras

Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to in the framework of -algebras. Both cases and are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.

     

Reactions of Substituted Boryl Radicals with Nitroalkanes. EPR, Kinetic, and Product Studies

The radical-initiated reaction of amine-boranes and phosphine-boranes, LBH(3) (L = R(3)N, R(3)P) with aliphatic nitro compounds has been investigated in order to explore the possibility of reducing tertiary nitroalkanes to the corresponding hydrocarbons. In all the examined cases boroxy nitroxides, RN(O(*))OBLH(2), resulting from the addition of ligated boryl radicals, LBH(2)(*), to an oxygen atom of the nitro group were detected and characterized by EPR spectroscopy. This reaction occurs at room temperature with a rate constant of 1.5 x 10(7) M(-)(1) s(-)(1) for LBH(2)(*) = Me(3)NBH(2)(*) and RNO(2) = Me(3)CNO(2). The boroxy nitroxides from tertiary nitroalkanes decay by a fragmentation reaction occurring with cleavage of the nitrogen-oxygen bond, rather than of the carbon-nitrogen bond as would be required for the reduction to the corresponding alkane to take place. The Arrhenius parameters for this fragmentation have been determined in few cases.     

Formation of ferrocyanides-IV Th(IV), Nd(III), UO(2)(II) and Hg(II)

The stoichiometry of the reaction between ferrocyanide and thorium, neodymium, uranyl ion and mercury(II) has been investigated. The first three give single products irrespective of the order of addition of the reagents, but the last does not. If mercury(II) is added to ferrocyanide Hg(2)Fe(CN)(6) is obtained, but if ferrocyanide is added to mercury(II) various cyanide complexes of mercury are formed. The K(sp) values for the precipitates are reported.     

Domino metathesis of 2-azanorbornenones: a new strategy for the enatioselective synthesis of 1-azabicyclic compounds

Domino metathesis of N-alkylated derivatives of (1S)-2-azanorborn-5-en-3-one allowed for the enantioselective synthesis of pyrrolizidine, quinolizidine, pyrrolidinoazepine, and pyrrolidinoazocine derivatives in a straightforward process.     

The reactions of some halogenated pyridines with methoxide and methanethiolate ions in dimethylformamide

The reactions of 2,6- and 2,5-dibromopyridines and of 2,3- and 3,5-dichloropyridines with sodium isopropanethiolate and methanethiolate afforded the products of mono- or of bis-substitution depending on the experimental conditions. The same pyridines reacted with sodium methoxide to give good yields of the mono-substituted products; bis-substitution occurred easily only in the case of the 2,6-dibromo- and of the 3,5-dichloropyridine. The syntheses of some methoxy thiomethoxypyridine, starting from the halogeno methoxypyridines or from the halogeno thiomethoxypyhdines are also described. The bis-(alkylthio)pyridines can be fragmented by sodium in HMPA to give the bis(mercapto)pyridines.     

Thermally activated conduction in molecular junctions

We report temperature dependence measurements on the conductance of individual molecular wires. The results show for the first time in a molecular junction the theoretically predicted transition from coherent superexchange tunneling conductance to an activated hopping mechanism as temperature is increased.