Statistical properties of turbulence: An overview

We present an introductory overview of several challenging problems in the statistical characterization of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Weak discontinuities in relativisitic MHD

By using singular surface theory and ray theory the speeds of propagation of fast and slow waves, propagating into a medium in arbitrary motion, have been obtained in relativistic magnetohydrodynamics. The differential equation governing the growth of these waves along the rays has been derived and the solution has been presented in integral form.

Valence fluctuation in some Yb intermetallics by X-ray photoemission and X-ray absorption

The valence state of Yb in some of its intermetallics, YbNi2Ge2, YbCu2Si2 and YbPd2Si2 has been investigated by LIII(Yb) absorption edges and X-ray pnotoelectron spectra in the 4f and 4d regions. These studies establish the presence of mixed valence in all three systems and illustrate the utility of 4f and 4d spectra in the study of mixed valence in Yb compounds.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Crystallization and preliminary X-ray studies of the anti-T lectin from peanut (Arachis hypogaea)

The anti-T lectin from peanut (Arachis hypogaea) crystallizes in the orthorhombic space group P21212 with one tetrameric molecule (Mr 110,000) in the asymmetric unit in a cell of dimensions a = 129.3 Å, B = 126.9 Å and C = 76.9 Å. The crystals are suitable for high resolution work.

Chlorination of silver dosed with potassium and barium in presence of oxygen: An X-ray photoelectron spectroscopy study

XPS studies show that the presence of chemisorbed chlorine stabilizes and also enhances molecular dioxygen species on Ag surfaces dosed with either K or Ba. The surface atomic oxygen is found to become depleted on chlorination. The variation in the nature of surface species with respect to temperature shows chlorine-induced diffusion of atomic oxygen into the subsurface region at 300 K. For coverages of potassium up to 8 × 1014 atoms/cm2, preferential chloridation of Ag occurs while at higher potassium coverages, KCl formation is distinctly observed on the surface. In the case of barium, two types of adsorbed chlorine species, Cl(α) and Cl(β), associated with Ag and Ba, respectively, are clearly seen even at low barium coverages. This is believed to be due to the higher valence occupation of barium compared to potassium. The Cl(α) species associated with Ag is found to occupy a preferred site on both K- and Ba-dosed surfaces, involving chemisorptive replacement of O(α) to the subsurface region.

Spinorial relativistic rotator: The transformation from quasi-Newtonian to Minkowski coordinates

There exists a remarkably close relationship between the operator algebra of the Dirac equation and the corresponding operators of the spinorial relativistic rotator (an indecomposable object lying on a mass-spin Regge trajectory). The analog of the Foldy-Wouthuysen transformation (more generally, the transformation between quasi-Newtonian and Minkowski coordinates) is constructed and explicit results are discussed for the spin and position operators. Zitterbewegung is shown to exist for a system having only positive energies.

Novel Oxidation of Pyridoxal in Ternary Metal Complexes. An X-Ray Study of the Products

Attempts to prepare ternary metal complexes of pyridoxylidene-amino acid Schiff bases culminated in the oxidation of pyridoxal to pyridoxic acid or to its lactone and their complex formation, as evidenced from an X-ray study.

Tautomeric forms of hydroxycyclotriphosphazatrienes; X-ray crystal structure of N3P3Ph2(OMe)3OH

The prefered tautomer(s) of hydroxycyclotriphosphazatrienes and prototropic exchange in solution have been established by 31P n.m.r. spectroscopy, thus confirming predictions deduced from basicity calculations; the X-ray structure of N3P3Ph2(OMe)3OH shows that it exists as the hydrogen-bonded dimer of the oxophosphazadiene tautomer in which a proton is adjacent to the PPh2 group.

X-Ray Spectroscopic Studies of the Surface Species in Co-Mo-Al2O3 Hydrodesulphurization Catalysts

Octahedrally coordinated CoII and MoIV species are present on the surfaces of sulfided Co-Mo-Al2O3 catalysts used for hydrodesulfurization. They were characterized by XPE, EXAFS and XANES data. An excess of sulfur in the surface species can be explained in terms of the presence of S[stack 22 ] ions. Disulfide bridges could play a role in the hydrodesulfurization.

X-Ray Studies On Crystalline Complexes Involving Amino-Acids And Peptides .11. Peptide Aggregation And Water-Structure In The Crystals Of A Hydrated 1-1 Complex Between L-Histidyl-L-Serine And Glycyl-L-Glutamic Acid

The hexahydrate of a 1:1 complex between L-histidyl-L-serine and glycyl-L-glutamic acid crystallizes in space group P1 with a = 4.706(1), b= 8.578(2), c= 16.521(3) ÅA; α= 85.9(1), β= 89.7(1)°, = 77.4(1). The crystal structure, solved by direct methods, has been refined to an R value of 0.046 for 2150 observed reflections. The two peptide molecules in the structure have somewhat extended conformations. The unlike molecules aggregate into separate alternating layers. Each layer is stabilized by hydrogen bonded head-to-tail sequences as well as sequences of hydrogen bonds involving peptide groups. The arrangement of molecules in each layer is similar to one of the plausible idealized arrangements of L-alanyl-L-alanine worked out from simple geometrical considerations. Adjacent layers in the structure are held together by interactions involving side chains as well as water molecules. The water structure observed in the complex provides a good model, at atomic resolution, for that in protein crystals. An interesting feature of the crystal structure is the existence of two water channels in the interfaces between adjacent peptide layers.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation