Unsteady axisymmetric stagnation flow on a circular cylinder

Unsteady, axisymmetric stagnation flow about a circular cylinderis examined when the far-field flow is a periodic function oftime with a fixed time average and an oscillatory part of prescribedamplitude and frequency. Solutions are computed for arbitraryvalues of the Reynolds number, quantifying the effects of surfacecurvature, and a frequency parameter based on the period ofthe far-field flow. It is found that solutions remain regularand periodic provided that the far-field amplitude lies belowa critical value. Above this value, solutions terminate in afinite-time singularity. The blow-up time is delayed by increasingthe curvature of the surface. These results are corroboratedby asymptotic predictions valid in the limits of small and largeamplitude and frequency. For large Reynolds number, the problemreduces to the two-dimensional stagnation-point flow againsta plane wall studied by previous authors.     

Superbranching processes and projections of random Cantor sets

We study sequences (X ₀, X ₁, ...) of random variables, taking values in the positive integers, which grow faster than branching processes in the sense that , for m, n0, where the X _n (m, i) are distributed as X _n and have certain properties of independence. We prove that, under appropriate conditions, X _n ^1/n almost surely and in L ¹, where =sup E(X _n )^1/n . Our principal application of this result is to study the Lebesgue measure and (Hausdorff) dimension of certain projections of sets in a class of random Cantor sets, being those obtained by repeated random subdivisions of the M-adic subcubes of [0, 1] ^d . We establish a necessary and sufficient condition for the Lebesgue measure of a projection of such a random set to be non-zero, and determine the box dimension of this projection.Work done partly whilst visiting Cornell University with the aid of a Fulbright travel grant     

Random walk on the infinite cluster of the percolation model

Summary We consider random walk on the infinite cluster of bond percolation on ^d . We show that, in the supercritical regime whend3, this random walk is a.s. transient. This conclusion is achieved by considering the infinite percolation cluster as a random electrical network in which each open edge has unit resistance. It is proved that the effective resistance of this network between a nominated point and the points at infinity is almost surely finite.G.R.G. acknowledges support from Cornell University, and also partial support by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell UniversityH.K. was supported in part by the N.S.F. through a grant to Cornell University     

Percolation in half-spaces: equality of critical densities and continuity of the percolation probability

Renormalization arguments are developed and applied to independent nearest-neighbor percolation on various subsets of ^d ,d2, yielding:

Polyethylene glycol matrix reduces the rates of photochemical and thermal release of nitric oxide from S-nitroso-N-acetylcysteine

S -nitrosothiols have many biological activities and may act as nitric oxide (NO) carriers and donors, prolonging NO half-life in vivo. In spite of their great potential as therapeutic agents, most S -nitrosothiols are too unstable to isolate. We have shown that the S -nitroso adduct of N -acetylcysteine (SNAC) can be synthesized directly in aqueous and polyethylene glycol (PEG) 400 matrix by using a reactive gaseous (NO/O₂) mixture. Spectral monitoring of the S–N bond cleavage showed that SNAC, synthesized by this method, is relatively stable in nonbuf-fered aqueous solution at 25°C in the dark and that its stability is greatly increased in PEG matrix, resulting in a 28-fold decrease in its initial rate of thermal decomposition. Irradiation with UV light (λ= 333 nm) accelerated the rate of decomposition of SNAC to NO in both matrices, indicating that SNAC may find use for the photogeneration of NO. The quantum yield for SNAC decomposition decreased from 0.65 ± 0.15 in aqueous solution to 0.047 ± 0.005 in PEG 400 matrix. This increased stability in PEG matrix was assigned to a cage effect promoted by the PEG microenvironment that increases the rate of geminated radical pair recombination in the homolytic S–N bond cleavage process. This effect allowed for the storage of SNAC in PEG at −20°C in the dark for more than 10 weeks with negligible decomposition. Such stabilization may represent a viable option for the synthesis, storage and handling of S -nitrosothiol solutions for biomedical applications.     

Bond percolation on isoradial graphs: criticality and universality

In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the sense that the one-arm and $2j$ -alternating-arm critical exponents (and therefore also the connectivity and volume exponents) are constant across the family of such percolation processes. The isoradial graphs in question are those that satisfy certain weak conditions on their embedding and on their track system. This class of graphs includes, for example, isoradial embeddings of periodic graphs, and graphs derived from rhombic Penrose tilings.     

A linear cell-size dependent branching process

We consider a cell-size dependent branching process in which each cell grows at a linear rate and divides into a pair of daughter cells, preserving total size, at a rate proportional to its size. Such processes expand exponentially fast. If, on division, each possible combination of daughter sizes occurs with equal probability, then conventional analysis provides explicit values for the limiting distribution of the size of a typical cell, together with the distributions of its size just after its birth and just before its division.