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.     

An artificial ionophore based on a polyhydroxylated steroid dimer

The Na+ transporting properties of the first member of a new class of artificial ionophores, based on a C2-symmetric polyhydroxylated steroid dimer, are described.     

Solubilization of homopolymers in a solution of diblock copolymers

We study theoretically mixed solutions of homopolymer and diblock copolymer chains. The solvent is a poor solvent for the homopolymers and a selective solvent for the copolymers. We find that the formation of copolymer micelles containing also the insoluble chains allows for an increased solubility of the homopolymers in the solution. In agreement with experiments, we find also that the solubilization power of the micelles, that is, the maximum amount of total homopolymer weight solubilized per unit weight of copolymers in solution, decreases strongly with the homopolymer index of polymerization.     

Studies towards the total synthesis of contignasterol

The (17R,20S,22S,24S) C₂₀-C₂₉ segment of contignasterol has been stereoselectively prepared in 8 steps and 40% overall yield from (S)-carvone. Synthetic studies towards contignasterol's C/D ring functionalization/isomerization are also reported.     

Landau theory for isotropic,nematic, smectic-A,and smectic-C phases

ABSTRACT

We use the Landau theory of phase transitions to describe the phase diagram of a liquid crystal displaying the isotropic (i), nematic (N), smectic-A and smectic-C phases. The order parameter of the smectic-C phase is defined as the projection of the director on the plane of the smectic layers, vanishing in the smectic-A phase. We present a detailed phase diagram that shows transition between any two of these phases, containing a triple point INA, a Lifshitz point NAC, a tricritical at the NA line, and a critical end point IAC. As one approaches the NC line from the smectic-C phase, the tilt angle approaches a nonzero value, but if the AC line is approached, the tilt angle vanishes according to the distance to the AC line to the power 1/2.     

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.     

Enantioselective synthesis of 3(S)-hydroxy polygodial derivatives and evaluation of their vanilloid activity

The enantioselective synthesis of 3(S)-hydroxy polygodial and its acetyl derivative is described. The construction of the 3-hydroxy drimane skeleton was based on the titanium-catalyzed radical cyclization of (10S)-10, 11-epoxy-farnesyl acetate. Only underivatized 3(S)-hydroxy polygodial showed activity in assays on VR1 vanilloid receptor in HEK cells transfected with the human VR1.     

Search space pruning and global optimisation of multiple gravity assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation. This work was partially funded under the Ariadna scheme of the European Space Agency, contract number 18138/04/NL/MV.     

Algebras generated by the disc algebra and bounded harmonic functions

Let denote the open unit disc, and let denote the disc algebra. The subsets of such that the inclusion holds for every nonconstant continuous on , or the inclusion holds for every bounded harmonic nonholomorphic function on continuous on , are characterized. In the first case the condition is that has positive measure, and in the second case that has full measure in .