Studies of phosphazenes. Part 14. The tautomerism of oxocyclotriphosphazadienes

The tautomeric behaviour of monohydroxycyclotriphosphazatrienes has been investigated by 31P n.m.r. spectroscopy. These derivatives exist as oxocyclotriphosphazadiene tautomers in which the hydrogen atom is attached to a ring nitrogen atom to the phosphoryl group. Three types of prototropic behaviour are observed : (a) no exchange is detected and only one tautomer is present [e.g. N3HP3(NHBut)2R3O (R = OMe or OEt)]; (b) exchange takes place between two equivalent sites and only one tautomer is observed [e.g. N3HP3R5O (R = OMe or OPh); N3HP3Ph4RO (R = OMe or OEt)]; and (c) exchange occurs between two non-equivalent sites and two tautomers are present [e.g. N3HP3Ph2R3O (R = OMe, OEt, or OPrn)]. It is shown that basicity calculations using substituent constants have predictive value since they are in good agreement with the spectroscopic observations.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Bearing capacity factor N-c under phi=0 condition for piles in clays

Bearing capacity factor N-c for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (phi=0) condition. The Study follows the lower bound limit analysis in conjunction With finite elements and linear programming. A new formulation is proposed for solving an axisymmetric geotechnical stability problem. The variation of N-c with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed on the stiff clay stratum overlaid by a soft clay layer. It was noticed that the magnitude of N-c reaches almost a constant value for embedment ratio greater than unity. The roughness of the pile base and shaft affects marginally the magnitudes of N-c. The results obtained from the present study are found to compare quite well with the different numerical solutions reported in the literature.

On the origin of the inflectional instability of a laminar separation bubble

This is an experimental and theoretical Study of a laminar separation bubble and the associated linear stability mechanisms. Experiments were performed over a flat plate kept in a wind tunnel, with an imposed pressure gradient typical of an aerofoil that would involve a laminar separation bubble. The separation bubble was characterized by measurement of surface-pressure distribution and streamwise velocity using hot-wire anemometry. Single component hot-wire anemometry was also used for a detailed study of the transition dynamics. It was foundthat the so-called dead-air region in the front portion of the bubble corresponded to a region of small disturbance amplitudes, with the amplitude reaching a maximum value close to the reattachment point. An exponential growth rate of the disturbance was seen in the region upstream of the mean maximum height of the bubble, and this was indicative of a linear instability mechanism at work. An infinitesimal disturbance was impulsively introduced into the boundary layer upstream of separation location, and the wave packet was tracked (in an ensemble-averaged sense) while it was getting advected downstream. The disturbance was found to be convective in nature. Linear stability analyses (both the Orr-Sommerfeld and Rayleigh calculations) were performed for mean velocity profiles, starting from an attached adverse-pressure-gradient boundary layer all the way up to the front portion of the separation-bubble region (i.e. up to the end of the dead-air region in which linear evolution of the disturbance could be expected). The conclusion from the present work is that the primary instability mechanism in a separation bubble is inflectional in nature, and its origin can be traced back to upstream of the separation location. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the detached shear layer Outside the bubble, with its associated Kelvin-Helmholtz mechanism. We contendthat only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum-height location of the mean bubble), a description by the Kelvin-Helmholtz instability paradigm, with its associated scaling principles, Could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection-point height and the vorticity thickness and show it to be universal.

Chemical changes during the aging and decomposition of composite solid propellants

During the thermal decomposition of orthorhombic ammonium perchlorate (AP) at 230°C, where the decomposition is only up to 30 wt %, there is an accumulation in the solid of acids, the concentration of which increases up to 15% decomposition, after which it decreases till it reaches the original value. Similar observations have been made in the polystyrene (PS)/AP propellant systems. Aging studies of PS/AP propellants have been carried out earlier [1], where it has been shown that for the aged propellants the thermal decomposition (TD) rate at 230°C and 260°C and ambient pressure burning rate (Image ) both increase and this increase is due to the formation of reactive intermediate “polystyrene peroxide (PSP).” In the present studies it has been observed that during the aging of the propellant at 150°C, the acid is formed and gets accumulated in the propellant, which may also be responsible for the increase in TD rate and perhaps may be more effective than PSP.

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.

Stimulation of liver tryptophan pyrrolase during heat exposure

Exposure of rats to heat (39 +/- 1 degree C) stimulated liver tryptophan pyrrolase 2-fold between 3 and 48 h. Plasma corticosterone increased 2-fold after 1 h of heat exposure and decreased to a low value of 50% by 16 h. The effect of heat exposure on the enzyme was obtained in adrenalectomized animals. Stimulation by cortisol and tryptophan of the enzyme was also obtained in heat exposure, and the effects seemed to be additive. The concentration of tryptophan in the liver remained unchanged, and that in the plasma decreased to about 50% at 8 h exposure to heat and reverted to normal by 46 h. Simultaneous administration of noradrenaline to heat-exposed rats had no effect, whereas that of thyroxine partly prevented the stimulation of the enzyme activity. Hypothyroid conditions obtained by thyroidectomy or treatment with propylthiouracil significantly stimulated the enzyme activity. Cycloheximide treatment of heat-exposed rats did not prevent the stimulation of the enzyme activity. The results indicate that the effect of heat exposure on liver tryptophan pyrrolase is obtained, due to the accompanying hypothyroid condition, by increasing the activity of the existing protein by a mechanism possibly different from those known at present.