Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Type II beta-turn conformation of pivaloyl-L-prolyl-alpha-aminoisobutyryl-N-methylamide: Theoretical, spectroscopic, and X-ray studies

Pivaloyl-L-Pro-Aib-N-methylamide has been shown to possess one intramolecular hydrogen bond in (CD3)2SO solution, by 1H-nmr methods, suggesting the existence of beta -turns, with Pro-Aib as the corner residues. Theoretical conformational analysis suggests that Type II beta-turn conformations are about 2 kcal mol-1 more stable than Type III structures. A crystallographic study has established the Type II beta-turn in the solid state. The molecule crystallizes in the space group P21 with a = 5.865 Å, b = 11.421 Å, c = 12.966 Å, beta = 97.55°, and Z = 2. The structure has been refined to a final R value of 0.061. The Type II -turn conformation is stabilized by an intramolecular 4 1 hydrogen bond between the methylamide NH and the pivaloyl CO group. The conformational angles are Pro = -57.8°, Pro = 139.3°, Aib = 61.4°, and Aib = 25.1°. The Type II beta-turn conformation for Pro-Aib in this peptide is compared with the Type III structures observed for the same segment in larger peptides.

Interaction of manganese(II) with valinomycin: Observation of mixed complexes

The interaction of antibiotic valinomycin with manganese (II) has been studied using circular dichroism, electron spin resonance and infrared techniques. Results show that Mn(II) forms complexes with valinomycin in both 2:1 (valinomycin-ion-valinomycin sandwich) and 1:1 (equimolar) stoichiometries. The 1:1 type observed here is very different from the well known K+-valinomycin bracelet conformation.

Metal chelates in vinyl polymerization: Kinetics and mechanism of acrylonitrile polymerization initiated by Cu(II) imine complexes

The free radical polymerization of acrylonitrile (AN) initiated by Cu(II) 4-anilino 2-one [Cu(II) ANIPO] Cu(II), 4-p-toluedeno 3-pentene 2-one [Cu(II) TPO], and Cu(II) 4-p-nitroanilino 3-pentene 2-one [Cu(II) NAPO] was studied in benzene at 50 and 60°C and in carbon tetrachloride (CCl4), dimethyl sulfoxide (DMSO), and methanol (MeOH) at 60°C. Although the polymerization proceeded in a heterogeneous phase, it followed the kinetics of a homogeneous process. The monomer exponents were 2 at two different temperatures and in different solvents. The square-root dependence of Rp on initiator concentration and higher monomer exponents accounted for a 1:2 complex formation between the chelate and monomer. The complex formation was shown by ultraviolet (UV) study. The activation energies, kinetics, and chain transfer constants were also evaluated.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Coalescence of rigid droplets in a stirred dispersion-II. Band-limited force fluctuations

The coalescence of nearly rigid liquid droplets in a turbulent flow field is viewed as the drainage of a thin film of liquid under the action of a stochastic force representing the effect of turbulence. The force squeezing the drop pair is modelled as a correlated random function of time. The drops are assumed to coalesce once the film thickness becomes smaller than a critical thickness while they are regarded as separated if their distance of separation is larger than a prescribed distance. A semi-analytical solution is derived to determine the coalescence efficiency. The veracity of the solution procedure is established via a Monte-Carlo solution scheme. The model predicts a reversing trend of the dependence of the coalescence efficiency on the drop radii, the film liquid viscosity and the turbulence energy dissipation per unit mass, as the relative fluctuation increases. However, the dependence on physical parameters is weak (especially at high relative fluctuation) so that for the smallest droplets (which are nearly rigid) the coalescence efficiency may be treated as an empirical constant. The predictions of this model are compared with those of a white-noise force model. The results of this paper and those in Muralidhar and Ramkrishna (1986, Ind. Engng Chem. Fundam. 25, 554-56) suggest that dynamic drop deformation is the key factor that influences the coalescence efficiency.

X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

Synthesis and physico-chemical properties of diruthenium(III, II) tetra-aryl carboxylato compounds

Monochloro-tetra-μ-aryl-carboxylatodiruthenium(III, II) compounds Ru2Cl (O2CAr)4 (Ar = -C6H5; -C6H4-p-OCH3), are prepared and characterized. The compounds have magnetic moments that correspond to three unpaired spins per dimer. The Rusingle bondRu bond order is 2.5 and the ground electronic configuration is σ2π4δ2(δ*π*)3. The visible spectral band is observed at ca 450 nm along with a shoulder near 580 nm in DMF solution. The compounds undergo a one-electron Ru(III)Ru(II) → Ru(II)Ru(II) quasi-reversible reduction in DMF near 0.0 V vs sce.

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.

Ternary metal complexes of anionic and neutral pyridoxine (vitamin B6) with 2,2'-bipyridine. Syntheses and x-ray structures of (pyridoxinato)bis(2,2'-bipyridyl)cobalt(III) perchlorate and chloro(2,2'-bipyridyl)(pyridoxine)copper(II) perchlorate hydrate

Ternary metal complexes involving vitamin B6 with formulas [CO",(PN-H)](anCdI [OC)'(bpy)(PN)Cl]C10(.bpHy 0 = 2,2'-bipyridine, PN = neutral pyridoxine, PN-H = anionic pyridoxine) have been prepared for the first time and characterized by means of magnetic and spectroscopic measurements. The crystal structures of the compounds have also been determined. [CO(PN-H)](CcryIsOta,l)lize s in the space group P2,/c with a = 18.900 (3) A, b = 8.764 (1) A, c = 20.041 (2) A,p = 116.05 (l)', and Z = 4 and [Cu(bpy)(PN)C1]C104-H20in the space group Pi with a = 12.136 (5) A, b = 13.283 (4) A,c = 7.195 (2) A, a = 96.91 (Z)', 0 = 91.25 (3)', y = 71.63 (3)', and Z = 2. The structures were solved by the heavy-atom method and refined by least-squares techniques to R values of 0.080 and 0.042 for 3401 and 2094 independent reflections, respectively. Both structures consist of monomeric units. The geometry around Co(II1) is octahedral and around Cu(I1) is distorted square pyramidal. In [CO(PN-H)]t(wCo IoxOy~ge)n~s ,fro m phenolic and 4-(hydroxymethyl) groups of PN-H and two nitrogens from each of two bpy's form the coordination sphere. In [Cu(bpy)(PN)C1]C104.H20o ne PN and one bpy, with the same donor sites, act as bidentate chelates in the basal plane, with a chloride ion occupying the apical position. In both structures PN and PN-H exist in the tautomeric form wherein pyridine N is protonated and phenolic 0 is deprotonated. However, a novel feature of the cobalt compound is that PN-H is anionic due to the deprotonation of the 4-(hydroxymethyl) group. The packing in both structures is governed by hydrogen bonds, and in the copper compound partial stacking of bpy's at a distance of -3.55 also adds to the stability of the system. Infrared, NMR, and ligand field spectroscopic results and magnetic measurements are interpreted in light of the structures.

Modification of chemical reactivity by cyclodextrins. Observation of moderate effects on Norrish type I and type II photobehavior

The photochemistry and photophysics of organic molecules in organized assemblies are being studied with great interest in order to understand the features controlling the selectivity in the photoreactions brought about by these media.l These studies have paved the way to an intriguing number of possibilities by which photoreactivity can be modified. In this connection, we have investigated the photobehavior of a number of phenyl alkyl ketones and cu,cu-dimethylphenyl alkyl ketones (Scheme I) incorporated in the hydrophobic interior of cyclodextrin cavities.

Mixed ligand complexes in vinyl polymerization-II: [NN-ethylenebis(salicylideneiminato)] (benzoylacetonato)cobalt(III) as an initiator

The polymerization of methyl methacrylate initiated by a mixed ligand complex. [NN-ethylenebis(salicylideneiminato)](benzoylacetonato)cobalt(III) has been studied in bulk and in benzene at 70° and 80°. The rate of polymerization is proportional to (concentration of the chelate)Image and the monomer exponent is close to 1.5. The activation energy and the kinetic and transfer constants are evaluated. A free radical mechanism has been proposed.

Preparation and properties of nickel(II) complex dyes

The preparation and properties of five new dyes derived from nickel(I1) ions and aromatic azo derivatives of ethylenebls(P-ketoesters) are reported.

Mononitrosated and phenylamido substituted chelate linkage isomers of quadridentate Schiff base copper(II) complexes

The nitrosation of monophenylamido substituted quadridentate Schiff base complexes of copper(II) are observed to adopt N-bonded isonitroso coordination whereas the phenylisocyanation of the corresponding mononitrosated quadridentate complexes are found to prefer O-bonded isonitroso coordination.