Bifurcation analysis and amplitude equations for viscoelastic convective fluids

Summary The possible bifurcations of a convective instability in viscoelastic fluid are studied. The viscoelastic behaviour is modelized by means of the Oldroyd type fluid whose parameters can be adjusted to suit a large class of polymeric fluids. We analyse in some detail bifurcations of codimension one (stationary or oscillatory convection) and codimension two for such kind of fluids. By a weak nonlinear analysis, the coefficients of the amplitude equations corresponding to the different bifurcations are also determined. It has been found that the nature of the convective solution depends crucially on both the viscoelastic parameters and the constitutive equation used to describe the fluid.     

Dissipative solitons that cannot be trapped

We show that dissipative solitons in systems with high-order nonlinear dissipation cannot survive in the presence of trapping potentials of the rigid wall or asymptotically increasing type. Solitons in such systems can survive in the presence of a weak potential but only with energies out of the interval of existence of linear quantum mechanical stationary states.     

Driving defect modes of Bose-Einstein condensates in optical lattices

We present an approximate analytical theory and direct numerical computation of defect modes of a Bose-Einstein condensate loaded in an optical lattice and subject to an additional localized (defect) potential. Some of the modes are found to be remarkably stable and can be driven along the lattice by means of a defect moving following a steplike function defined by the period of Josephson oscillations and the macroscopic stability of the atoms.     

Supersolitons: solitonic excitations in atomic soliton chains

We show that, by tuning interactions in nonintegrable vector nonlinear Schr?dinger equations modeling Bose-Einstein condensates and other relevant physical systems, it is possible to achieve a regime of elastic particlelike collisions between solitons. This would allow one to construct a Newton's cradle with solitons and supersolitons: localized collective excitations in solitary-wave chains.     

Developmental gametophyte morphology of seven species of Thelypteris subg. Cyclosorus (Thelypteridaceae)

The morphogenesis of the sexual phase of seven species of Thelypteris subg. Cyclosorus (Thelypteridaceae) is described and compared. Spores of all species are monolete, ellipsoid and have positive photoblastism. They have Vittaria-type germination, germinal filaments are short and uniseriate, and Aspidium-type development. Adult gametophytes are spatulate-cordiform, and have wide wings with numerous glandular, marginal and superficial hairs. Antheridia have a narrow or widened basal cell, an undivided annular cell, and an opercular cell; antherozoids are liberated through three mechanisms. Archegonia have short necks and four triangular cells on the neck's mouth. The sporophyte's first leaf is lobed, with open dichotomous veins, glandular hairs similar to those of the gametophyte, and anomocytic stomata. Differences observed between the studied species are: spore size; ornamentation of the perispore; germination and emergence periods; size of hairs; developmental period of gametangia; and antherozoid liberation mechanisms through total detachment of the operculum, partial detachment of the operculum, and development of an apical pore through tearing of the operculum. These taxonomically valuable characters, combined with the sporophyte characteristics, can be useful tools in the identification of the species studied to the subg. Cyclosorus.     

Bohr’s strip for vector valued Dirichlet series

Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series , converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr’s strip for a Dirichlet series with coefficients a _n in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series. The first, second and third authors were supported by MEC and FEDER Project MTM2005-08210.     

Towards a tunable tautomeric switch in azobenzene biomimetics: implications for the binding affinity of 2-(4'-hydroxyphenylazo)benzoic acid to streptavidin

The tautomeric equilibria of 2-(4'-hydroxyphenylazo)benzoic acid (HABA) and 2-(3',5'-dimethyl-4'-hydroxyphenylazo)benzoic acid (3',5'-dimethyl-HABA) have been studied by a combination of spectroscopic and computational methods. For neutral HABA in solvents of different polarity (toluene, chloroform, DMSO, DMF, butanol, and ethanol) the azo tautomer (AT) is largely predominant. For monoanionic HABA, the hydrazone tautomer (HT) is the only detected species in apolar solvents such as toluene and chloroform, while the AT is the only detected species in water and a mixture of both tautomers is detected in ethanol. Comparison of the results obtained for HABA and its 3',5'-dimethylated derivative shows that dimethylation of the hydroxybenzene ring shifts the tautomeric preferences towards the hydrazone species. These findings have been used to examine the differences in binding affinity to streptavidin, as the lower affinity of HABA can be explained in terms of the larger energetic cost associated with the tautomeric shift to the bioactive hydrazone species. Overall, these results suggest that a balanced choice of chemical substituents, embedding environment, and pH can be valuable for exploitation of the azo-hydrazone tautomerism of HABA biomimetics in biotechnological applications.     

Multiple summing operators on<Emphasis Type="Italic">C(K)</Emphasis> spaces

In this paper, we characterize, for 1≤p<∞, the multiple (p, 1)-summing multilinear operators on the product ofC(K) spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of (p, 1)-summing linear operators onC(K) in terms of their representing measures and a new multilinear characterization ofL _∞ spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures. Both authors were partially supported by DGICYT grant BMF2001-1284.     

Structural studies of spiroarsoranes derived from 2-aminophenols

This paper describes the structural studies of 2-phenyl-9,9′-dimethyl-2,2′-spirobis(1,3,2-λ⁵-benzoxazarsoline) 5, 2-phenyl-8,8′-dimethyl-2,2′-spirobis(1,3,2-λ⁵-benzoxazarsoline) 6 by ¹H,¹³C,¹⁵N NMR in [²H₆]DMSO and CDCl₃. The solid state studies were made by X-ray experiments. Infrared spectroscopy was obtained in CDCl₃ and the vibrational signals were assigned using DFT calculations. The nature of the As–N, As–C and As–O bonds in these compounds was established by NBO studies.