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.     

Structural Stability Theory and Phase Transitions Models

Global stability theory is introduced as a tool allowing the classification of mathematical models of phase transitions. The point of view is that a topological structure whose stability controls the transition, can be identified in the process of computation of the partition function. In particular we discuss mean field theories and the two dimensional Ising model. Interesting features are disclosed concerning the classification of the instabilities, such as the number of parameters and possible approximations.     

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.     

Topology, Formal Languages and Quantum Information

The paper provides a critical overview of the basic conceptual tools and algorithms of quantum information theory underlying the construction of quantum invariants of links and 3-manifolds as well as of their connections with algorithms and algorithmic complexity questions that arise in geometry and quantum gravity models.     

Quantum knitting

We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of “knot invariants,” among which the Jones polynomial plays a prominent role, since it can be associated with observables in topological quantum field theory. Although the problem of computing the Jones polynomial is intractable in the framework of classical complexity theory, it has been recently recognized that a quantum computer is capable of approximating it in an efficient way. The quantum algorithms discussed here represent a breakthrough for quantum computation, since approximating the Jones polynomial is actually a “universal problem,” namely, the hardest problem that a quantum computer can efficiently handle.