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.     

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.     

Parameter dependence and outcome dependence in dynamical models for state vector reduction

We apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous state vector reduction. We show that in the nonlinear model there is a set of realizations of the stochastic process that drives the state vector reduction for which parameter independence is violated for parallel spin components in the EPR-Bohm setup. Such a set has an appreciable probability of occurrence ( 1/2). On the other hand, the linear model exhibits only extremely small parameter dependence effects. We investigate some specific features of the models and we recall that, as has been pointed out recently, if one wants to be able to speak of definite outcomes (or equivalently of possessed objective elements of reality) at finite times, one has to slightly change the criteria for their attribution to physical systems. The concluding section is devoted to a detailed discussion of the difficulties which one meets when one tries to take, as a starting point for the formulation of a relativistic theory, a nonrelativistic scheme which exhibits parameter dependence. Here we derive a theorem which identifies the precise sense in which the occurrence of parameter dependence forbids a genuinely relativistic generalization. Finally we show how the appreciable parameter dependence of the nonlinear model gives rise to problems with relativity, while the extremely weak parameter dependence of the linear model does not give rise to any difficulty, provided one takes into account the appropriate criteria for the attribution of definite outcomes.Work supported in part by the Trieste Section of the INFN.     

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.     

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.     

Investigations into the parallel kinetic resolution of 2-phenylpropanoyl chloride using quasi-enantiomeric oxazolidinones

The resolution of 2-phenylpropanoyl chloride using an equimolar combination of quasi-enantiomeric oxazolidinones is discussed. The levels of diastereoselectivity were found to be dependent upon the structural nature of the metallated oxazolidinone, temperature and metal counter-ion.