Showing papers in "Philosophical Transactions of the Royal Society A in 1979"

The Elliptic Umbilic Diffraction Catastrophe

Abstract: We have made a detailed theoretical and experimental study of the three-dimensional diffraction pattern decorating the geometrical-optics caustic surface whose form is the elliptic umbilic catastrophe in Thom’s classification. This caustic has three sheets joined along three parabolic cusped edges (‘ribs’) which touch at one singular point (the ‘focus’). Experimentally, the diffraction catastrophe was studied in light refracted by a water droplet 9lens’ with triangular perimeter, and photographed in sections perpendicular to the symmetry axis of the pattern. Theoretically, the pattern was represented by a diffraction integral E(x,y,z) , which was studied numerically through computer simulations and analytically by the method of stationary phase. Particular attention was concentrated on the ‘dislocation lines’ where | E | vanishes, since these can be considered as a skeleton on which the whole diffraction pattern is built. Within the region bounded by the caustic surface the interference of four rays produces hexagonal diffraction maxima stacked in space like the atoms of a distorted crystal with space group R3m. The dislocation lines not too close to the ribs form hexagonally puckered rings. On receding from the focus and approaching the ribs, these rings approach one another and eventually join to form ‘hairpins’, each arm of which is a tightly wound sheared helix that develops asymptotically into one of the dislocations of the cusp diffraction catastrophe previously studied by Pearcey. Outside the caustic there are also helical dislocation lines, this time formed by interference involving a complex ray. There is close agreement, down to the finest details, between observation, exact computation of E(x,y,z) , and the four-wave stationary-phase approximation.

K-Ar geochronology and palaeomagnetism of volcanic rocks in the Lesser Antilles island arc

Abstract: K-Ar age determinations, mainly whole rock, with some corroboration from mineral separates, are presented for lava flows, domes, minor intrusives and blocks in tuffs from 95 localities in the Lesser Antilles. Together with the much smaller number of previously published data, these show a distinction between a range 38-10 million years (Ma) in the outer arc (Limestone Caribbees) and less than 7.7 Ma in the inner arc (Volcanic Caribbees). From southern Martinique southwards, the two arcs are superposed, and the whole range is fragmentarily represented. The observed age ranges in the outer and inner arcs fit between discontinuities in sea floor spreading in the North Atlantic at ca. 38 and ca. 9 Ma and a causal connection between spreading change and relocation of arc volcanicity is suggested. Palaeomagnetic directions at 108 localities in ten of the islands fall into normal ( N = 56, k = 13.8, D = 359°, I = + 22°, pole position 229° E, 89° N with drjr = 3°, d X = 6°) and reversed groups ( N = 41, k = 14.1, D = 178°, I = -22°, pole position 18° E, 88° S with d xjr = 3°, dx = 6°) plus six sites of intermediate polarity and five sites indeterminate. The mean dipole axis is within 2° of the present rotation axis and is likely to be identical with it with a probability of 99%. The data are generally in accord with the established geomagnetic polarity time scale, but there is some suggestion of a normal polarity event at ca. 1.18 Ma within the Matuyama Reversed Epoch. The palaeomagnetic data relate mainly to be past 10 Ma and suggest that within that time the Lesser Antilles have not changed their latitude or geographic orientation, and that the geomagnetic field has averaged that of a centred axial dipole. The few older palaeomagnetic data are consistent with these same conclusions (though with less certainty) back to ca. 20 Ma ago. There is no evidence for oroclinal bending of the arc since then.

The symmetry and interfacial structure of bicrystals

Abstract: It is shown that the point and space symmetry of bicrystals can be classified according to established schemes of symmetry groups. The symmetry of the pattern created by the lattices of two crystals comprising a bicrystal is considered first. This symmetry depends on the symmetry of the component lattices and their relative orientation and position. A space group can be assigned to such a pattern by using the schemes of crystallographic rods, crystallographic layers, or conventional space groups (Shubnikov & Koptsik 1974) respectively, according to whether one, two or three non-collinear translation symmetry axes are present in the pattern. Patterns are considered to be dichromatic by regarding one lattice arbitrarily as white and the other black; space groups can then be expressed by using colour symmetry formulation. The variation of the symmetry of dichromatic patterns as the component lattices are displaced relatively is discussed. For a pattern with fixed relative orientation of the component lattices the number of non-collinear translation axes is invariant to changes of relative position. However, the point symmetry of the pattern varies according to a conservation rule; the product n $\_{j}$ r $\_{j}$ is invariant with relative displacement where n $\_{j}$ is the numerical expression of the point symmetry for the pattern created by a given relative displacement away from a holosymmetric pattern and r $\_{j}$ is the number of crystallographically equivalent patterns obtained by symmetry related displacements. The product is equal to n $\_{\text{h}}$ , the numerical expression of the point symmetry of the holosymmetric pattern, i.e. n $\_{j}$ r $\_{j}$ = n $\_{\text{h}}$ . Bicrystals are supposed to be obtained from dichromatic patterns by choosing the orientation and location of an interface plane and locating white bases at white lattice points on one side of the interface and black bases at black sites on the other. Bicrystals are therefore regarded as three-dimensional objects containing a unique plane, the interface, and the adjacent crystals can have different compositions and structures. Depending on the symmetry of a dichromatic pattern and the choice of interface plane there can be two, one or no translation symmetry axes in the interface plane, and colour symmetry groups can be assigned to bicrystals according to the schemes of two sided layers, bands or rosettes (Shubnikov & Koptsik 1974) respectively. The variation of bicrystal point symmetry with relative displacement of the adjacent crystals follows a conservation rule analogous to that for the case of dichromatic patterns. The symmetry of the physical properties of bicrystals is considered by invoking Neumann's principle. Computer calculations indicate that the relative displacements of adjacent crystals in mechanically stable polymeric and metallic bicrystals are such that bicrystal symmetry is often lower than holosymmetric. The relative position of adjacent crystals in a bicrystal is an important additional degree of freedom compared to a single crystal. For bicrystals which have at least one-dimensional translation symmetry and point symmetry higher than 1, equivalent bicrystal structures can exist corresponding to crystallographically equivalent relative displacements away from a holosymmetric structure. The number of equivalent bicrystals in a set, r $\_{j}$ , depends on the symmetry of these bicrystals and the holosymmetric form, and is given by the rule r $\_{j}$ = n $\_{\text{h}}$ /n $\_{j}$ . Such equivalent bicrystals have degenerate energy, and it is possible for domains of equivalent structures, separated by special interfacial dislocations, to exist in a physical bicrystal. The Burgers vectors of these dislocations can have very small magnitudes and the dissociation of perfect interfacial dislocations into special dislocations is discussed.

Nonlinear wave packets in the Kelvin-Helmholtz instability

Abstract: The instability of two layers of immiscible inviscid and incompressible fluids in relative motion is studied with allowance for small, but finite, disturbances and for spatial as well as temporal development. By using the method of multiple scaling, a generalized formulation of the amplitude equation is obtained, applicable to both stable and marginally unstable regions of parameter space. Of principal concern is the neighbourhood of the critical point for instability, where weakly nonlinear solutions can be found for arbitrary initial conditions. Among the analytical results, it is shown that (1) the nonlinear effects can be stabilizing or destabilizing depending on the density ratio, (2) the existence of purely spatial instability depends upon the frame of reference, the density ratio, and whether the nonlinear effects are stabilizing, (3) exact nonlinear solutions of the amplitude equation exist representing modulations of permanent form travelling faster than the signal velocity of the linear equation (in particular, a solution is found that represents a solitary wave packet), and (4) the linear solution to the impulsive initial value problem has 9fronts’ which travel with the two (multiple) values of the group velocity (the packet as a whole moves with the mean of the two values). Numerical solutions of the amplitude equation (a nonlinear, unstable Klein-Gordon equation) are also presented for the case of nonlinear stabilization. These show that the development of a localized disturbance, in one or two dimensions, is highly dependent on the precise form of the initial conditions, even when the initial amplitude is very small. The exact solutions mentioned above play an important role in this development. The numerical experiments also show that the familiar uniform solution, an oscillatory function of time only, is unstable to spatial modulation if the amplitude of oscillation is large enough.

The Statistical Theory of Turbulent Flames

Abstract: The theory stemming from the statistical representation of turbulent flames is presented and developed, the major aim being to describe the basic processes in relatively simple flames. Starting from conservation equations, with the assumption of low Mach number and high Reynolds number, it is shown that the properties at any point in the flame can be determined from the transport equations for the velocity U and a set of scalars : represents the species mass fractions and enthalpy. However, the solution of these equations with initial conditions and boundary conditions appropriate to turbulent flames is prohibitively difficult. Statistical theories attempt to describe the behaviour of averaged quantities in terms of averaged quantities. This requires the introduction of closure approximations, but renders a more readily soluble set of equations. A closure of the Reynolds-stress equations and the equation for the joint probability density function of is considered. The use of the joint probability density function (p.d.f.) equation removes the difficulties that are otherwise encountered due to non-linear functions of the scalars (such as reaction rates). While the transport equation for the joint p.d.f. provides a useful description of the physics, its solution is feasible only for simple cases. As a practical alternative, a general method is presented for estimating the joint p.d.f. from its first and second moments: transport equations for these quantities are also considered therefore. Modelled transport equations for the Reynolds stresses, the dissipation rate, scalar moments and scalar fluxes are discussed, including the effects of reaction and density variations. A physical interpretation of the joint p.d.f. equation is given and the modelling of the unknown terms is considered. A general method for estimating the joint p.d.f. is presented. It assumes that the joint p.d.f. is the statistically most likely distribution with the same first and second moments. This distribution is determined for any number of reactive or non-reactive scalars.

Photochemical and biological implications of the atmospheric reactions of amines and benzo(a)pyrene

Abstract: The discovery of direct mutagenic activity, as determined by the Ames Salmonella typhimurium reversion assay, in the organic fractions of ambient aerosols collected throughout Southern California, led us to investigate the reactions of benzo(a)pyrene (BaP) deposited on glass fibre filters with ambient photochemical smog, as well as with O$\_{3}$, NO$\_{2}$, and peroxyacetyl nitrate (PAN) in simulated atmospheres. A variety of products are readily formed, including phenols, diphenols, dihydrodiols, etc. Directly mutagenic nitroderivatives are formed upon exposure of BaP (a carcinogen and pro-mutagen) and of perylene and pyrene (non-mutagens) to 1 part/10$^{6}$ of NO$\_{2}$ and a trace of HNO$\_{3}$ in air. If such reactions occur in urban atmospheres they may account in part for the 'excess' carcinogenicity (over BaP and certain other polycyclics) observed in organic particulates collected from smog and exhausts of spark ignition and diesel engines. However, such gas-solid interface processes may also have occurred on the filters commonly used in particulate sampling. Thus the possibility of 'filter artefacts' must be recognized. Carcinogenic N-nitrosamines have been detected in air at or near several industrial plants. Therefore, reactions of their possible precursors, e.g. secondary and tertiary methyl and ethylamines with NO$\_{x}$-HONO were studied both at levels of less than 1 part/10$^{6}$ in air in a 50 m$^{3}$ outdoor chamber and at levels around 4 parts/10$^{6}$ in a long path (720 m) outdoor infrared cell with the use of Fourier transform spectroscopic techniques. At concentrations less than 1 part/10$^{6}$ diethyl and triethylamine readily form photochemical smog (O$\_{3}$, PAN, aerosols, etc.). Additionally, small but significant amounts of diethylnitrosamine (C$\_{2}$H$\_{5}$)$\_{2}$NNO are formed in the dark from diethylamine (DEA) but destroyed in sunlight. In contrast, (C$\_{2}$H$\_{5}$)$\_{2}$NNO is initially formed on irradiation of triethylamine (TEA)-NO$\_{x}$ mixtures, then photodecomposed. Other significant nitrogenous compounds formed in sunlight include dialkylnitramines (R$\_{2}$NNO$\_{2}$, a major product) and substituted amides; small amounts of acetamide are present in the particulate phase from DEA and TEA. Both (CH$\_{3}$)$\_{2}$NNO$\_{2}$ and CH$\_{3}$CONH$\_{2}$ are carcinogens in animals, though less potent than nitrosamines; the activity of (C$\_{2}$H$\_{5}$)$\_{2}$NNO$\_{2}$ is not known. Environmental implications of both systems are discussed.

Discrete Symmetric Dynamical Systems at the Main Resonances with Applications to Axi-Symmetric Galaxies

Abstract: A study of two-degrees-of-freedom systems with a potential which is discrete-symmetric (even in one of the position variables) is carried out for the resonance cases 1:2, 1:1, 2:1 and 1:3. To produce both qualitative and quantitative results, we obtain in each resonance case normal forms by higher order averaging procedures. This method is related to Birkhoff normalization and provides us with rigorous asymptotic estimates for the approximate solutions. The normal forms have been used to obtain a classification of possible local and global bifurcations for these dynamical systems. One of the applications here is to describe the two-parameter family of bifurcations obtained by detuning a one-parameter family studied by Braun. In all the resonances discussed an approximate integral of the motion other than the total energy exists, but in the 2:1 and 1:3 resonance cases this degenerates into the partial energy of the z motion. In conclusion some remarks are made on the relation between two-degrees-of-freedom systems and solutions of the collisionless Boltzmann equation. Moreover we are able to make some observations on the Henon-Heiles problem and certain classical examples of potentials.

Acoustic destabilization of vortices

Abstract: A line vortex which has uniform vorticity 2$\Omega \_{0}$ in its core is subjected to a small two-dimensional disturbance whose dependence on polar angle is e$^{\text{i}m\theta}$. The stability is examined according to the equations of compressible, inviscid flow in a homentropic medium. The boundary condition at infinity is that of outgoing acoustic waves, and it is found that this capacity to radiate leads to a slow instability by comparison with the corresponding incompressible vortex which is stable. Numerical eigenvalues are computed as functions of the mode number m and the Mach number M based on the circumferential speed of the vortex. These are compared with an asymptotic analysis for the m = 2 mode at low Mach number in which it is found that the growth rate is ($\pi $/32)M$^{4}\Omega \_{0}$ in good agreement with the numerical results.

Uranium mineralization and granite magmatism in the British Isles

Abstract: Uranium mineralization associated with granites in the Caledonian and Hercynian provinces of the British Isles is shown to be genetically related to the uranium content and distribution, age, and structural setting of these granites. The uranium content of whole rock samples, analysed by the delayed neutron method, is used to demonstrate that mineralization is associated with intrusive complexes with a high mean content of uranium which also exhibit a high concentration of incompatible elements, low K/Rb ratio, low total Sr, low initial $^{87}$Sr/$^{86}$Sr ratio and high geothermal gradient. The standard deviation for uranium is greater where such intrusives are mineralized but the mean value is relatively unaltered. Therefore mineralization is the result of uranium redistribution, and does not involve further introduction of uranium. Fission track studies indicate that the high 'background' uranium content of granites, away from mineralization, is due to the occurrence of uranium in resistate primary phases such as zircon. Uranium is released by the dissolution of these resistate minerals. The processes of greisenization and tourmalinization which have been shown by oxygen isotope studies to involve massive interaction with meteoric water all extract uranium, which is redeposited down the PT gradient as 'primary' uraniferous ore minerals in vein-type mineralization. It is suggested, therefore, that mineralization involves leaching of granite magma enriched in metals and fluorine by water of meteoric origin containing dissolved carbonate. The breakdown of primary zircon is attributed to a phase of short duration of high temperature interaction of granite magma with meteoric water, and uranium mineralization is thought to have occurred at this time. However, the high concentration of uranium, thorium and potassium of the 'background' granite which produce hot rock districts may cause redistribution of uranium by hydrothermal mineralization during periods of high average heat flow from the mantle (as in the Tertiary of southwest England) or during dyke emplacement. An extensive system of channels for heating and circulating water is necessary for this system to function, and faults in granite would be particularly favourable. The regional trend of uranium and incompatible elements shown by late Caledonian (Devonian) and Hercynian granites in Britain is related to dehydration reactions during subduction of oceanic crust. The importance of phlogopite breakdown in accounting for the characteristics of uraniferous granites is discussed in relation to magma generation, with the use of closed and open system models with partial fusion of ocean crust or upper mantle. Uranium enrichment by scavenging of subcontinental lithosphere is considered important, but late stage assimilation of uranium from higher levels in the crust is relatively insignificant. The applications of the models for uranium mineralization to exploration at a regional and local scale are discussed.

Nonlinear effects upon waves near caustics

Abstract: According to linear theory the wave intensity of a slowly varying wave train becomes particularly large near caustics. In this paper it is shown how the waves are modified when the wave intensity is sufficient for nonlinear effects to begin to be important. Two types of near-linear caustics can arise in which nonlinearity either tends to advance or to retard the reflexion of waves from the caustic. General examples are given in terms of one-dimensional wave propagation, and of propagation in a uniform medium. Detailed consideration is given to a particular example: small-amplitude water waves on deep currents. This helps to provide an interpretative framework for the large-amplitude results presented in the companion paper (Peregrine & Thomas 1979). For the more exceptional case of triple roots, or cusped caustics, the increase in wave intensity is even more dramatic. In three appendices the analysis for caustics is extended to some higher-order cases.

A Study of 5p Excitation in Atomic Barium I. The 5p Absorption Spectra of Ba I, Cs I and Related Elements

Abstract: New observations of the 5p spectra of Cs I and Ba I are reported. The extreme complexity of the structure does not permit precise configuration labels to be attached to all the excited levels. Nevertheless, more than 160 transitions in Ba I have been ordered into 14 series converging on experimentally known levels of the parent ion. An attempt has been made to analyse the limit structure by comparison with the data for Cs I and Hartree-Fock atomic structure calculations. The results obtained are consistent with previous interpretations of the double ionization anomaly in Ba I. Further comments are made on the comparison between experiment and the predictions of the r.p.a.e. theory for 5p excitation in Ba I. It is shown that the 5p$^{6}$ 6s $^{2}$S$\_{\frac{1}{2}}\rightarrow $ 5p$^{5}$ 6s$^{2}$ $^{2}$P$\_{\frac{1}{2}}$ and $^{2}$P$_{\frac{3}{2}}$ transitions of Cs I have been incorrectly identified and new assignments are proposed.

The shape of a pendent liquid drop

Abstract: Formal solutions of the static equilibrium equations for the form of the outer surface of a pendent liquid drop are studied. An approach is adopted in which only the one-parameter family determined by vertex height (u sub 0) need be described. Attention is restricted to rotationally symmetric configurations, and all symmetric solutions are characterized for the case where the Lagrange parameter lambda is equal to zero. It is shown that for any u sub 0 the function u(r; u sub 0) can be extended as a parametric solution of a system of equations for all arc lengths, yielding a curve without limit sets or double points, and that the resulting capillary rotation surface spreads out indefinitely away from the axis r = 0. The asymptotic form of the surface in the case of large absolute values of u sub 0 is characterized quantitatively, along with the global structure of all such surfaces.

The dispersion of lead from motor exhausts

Abstract: Lead is added to petrol as organic tetraethyl or tetramethyl lead but is emitted as inorganic oxides, sulphides, halides and carbonates. From vehicles cruising at high speed on motorways, the lead is emitted as very small (ca. 0.02 $\mu $m) discrete particles. In city streets, where there is also a background aerosol, coagulated chain-aggregate particles are found. The concentration of lead in air downwind of a road can be calculated theoretically, and measured concentrations agree fairly well. Within a few metres of the carriageways of motorways carrying heavy traffic, concentrations as high as 10 $\mu $g/m$^{3}$ are found, but the concentration falls rapidly with distance owing mainly to the upward diffusion of the plume. Measurements of the rate of deposition to surfaces near the M 4 motorway show that an appreciable, but not large, fraction of the lead is deposited within 100 m of the motorway. Near towns, the contribution from a given highway merges rapidly into the background due to emissions from other roads. The dispersion is countrywide and probably some cross-frontier transfer occurs.

Stability predictions through a succession of folds

Abstract: For a discrete, or discretized, conservative gradient system, such as is envisaged in catastrophe theory and arises throughout the physical sciences, it is often necessary to assess the stable regions of an equilibrium path that exhibits a succession of folds. At each fold the degree of instability changes by one, so that as the system evolves from a region of known stability the first fold must represent a loss of stability. At a second fold, however, it is not clear whether the system is suffering a further loss, as we shall see in some examples, or is regaining its original stability as is more common in elasticity. A new theorem involving a conjugate parameter allows all such stability changes to be readily assessed on the basis of the form of the equilibrium paths themselves. The application of the general theory to the external and internal stabilities of an elastic structure under dead and rigid loading is demonstrated. Under the former, the load is the control parameter and the corresponding deflection plays the role of the conjugate parameter, while in a direct analysis of rigid loading these roles are reversed. A supplementary study of rigid loading which uses Lagrange multipliers supplies further theorems relating the dual concepts of external and internal stability. The use of the theorems is demonstrated in the buckling of elastic arches and shallow domes, and in the incipient gravitational collapse of a massive cold star. The possible stabilization of bifurcations by rigid loading is examined, and shows how the results can also be of value in bifurcational instabilities.

Finite-Amplitude Deep-Water Waves on Currents

Abstract: Accurate integral properties of plane periodic deep-water waves of amplitudes up to the steepest are tabulated by Longuet-Higgins (1975). These are used to define an averaged Lagrangian which, following Whitham, is used to describe the properties of slowly varying wave trains. Two examples of waves on large-scale currents are examined in detail. One flow is that of a shearing current, V ( x ) j , which causes waves to be refracted. The other flow, U ( x ) i , varies in the direction of wave propagation and causes waves to either steepen or become more gentle. Some surprising features are found.

The evolution of a uranium province in northern sweden

Abstract: The Arjeplog-Arvidsjaur uranium province contains epigenetic uranium deposits formed at the culmination of Svecofennian orogenesis at about 1750 Ma ago, stratabound deposits in subsequent volcanics and enhanced uranium contents in a wide variety of rock types. The province is situated along the southern margin of an early Proterozoic continent and may have been underlain both by older basement and, more speculatively, by a subduction zone. The movement of uranium is clearly related to processes of magmatism and metamorphism during the Svecofennian orogenesis. Pre-Svecofennian basement is a potential source of uranium.

The study of Brownian motion by intensity fluctuation spectroscopy

Abstract: The principles and methods of quasielastic light scattering and intensity fluctuation spectroscopy (i.f.s.) are reviewed briefly. Their application to the study of Brownian motion is discussed with emphasis on the behaviour of the velocity autocorrelation function $\phi (\tau)$ of a single particle. We consider: (i) The situation usually assumed where $\phi (\tau)$ decays rapidly compared with other timescales of interest; (ii) the modification of (i) due to the $\tau ^{-\frac{3}{2}}$ \`long-time tail' in $\phi (\tau)$ including the recent i.f.s experiment of Boon & Bouiller (1976) which confirms its existence, and finally (iii) systems of charged colloidal particles exhibiting \`liquid-like' spatial ordering due to long-range Coulombic interactions. Here $\phi (\tau)$ has a negative long-time tail. We also consider the many-body dynamics in these systems by exploiting the similarity with neutron scattering by simple atomic liquids. `Solid-like' systems are discussed briefly.

Some Aspects of Mass Spectrometry in Research on Steroids

Abstract: The application of mass spectrometry to steroids has been extensively developed since its inception in 1956. Detailed studies based on pure steroids and their isotope labelled analogues have established the major pathways of fragmentation under electron impact. The resulting correlations have been of great value in the analytical characterization of steroids and their metabolites. The combination of mass spectrometry with gas chromatography is particularly powerful: the latter technique reduces the complexity of samples, and provides independent characterization by virtue of retention regularities. These features are essential for distinguishing many stereoisomeric or otherwise closely related steroids. Modifications of functional groups can augment the utility of mass spectrometry in qualitative and quantitative analysis. Derivatives may be chosen to alter fragmentation modes, or to produce informative shifts in ion masses within an essentially unchanged fragmentation pattern. Enhancement of molecular ion abundance is usually achievable with derivatives, or by means of milder ionization techniques such as chemical ionization.

A comparison of one-, two- and three-dimensional model representations of stratospheric gases

Abstract: Three- and two-dimensional model results have been averaged to investigate conceptual errors in two- and one-dimensional models. Average dynamical quantities show inter-hemispheric asymmetries in both mean and eddy vertical motions, with anomalous behaviour of tracers near effective source and sink regions. Zonal, hemispheric and global means of the rates of gas reactions show large deviations between terms like $\overline{k\[\text{A}\]\[\text{B}\]}$ and $\overline{k}\overline{[\text{A}]}$ $\overline{[\text{B}]}$, causing significant errors in two- and one-dimensional model calculations. These errors are often associated with dynamical features such as jet streams or the tropopause, and affect the entire model atmospheres except in the summer mid-stratosphere. It is concluded that correlated measurements of atmospheric molecular number densities are urgently required to understand the deficiencies in models, which have been widely used to make perturbation calculations of the effects of aircraft and chlorofluoromethanes on stratospheric ozone. The sources of error described in this work arise from inadequacies in the formulation of one- and two-dimensional models, rather than from uncertainties in the input data, and have not been included in published error analyses.

Resonance Raman spectra

Abstract: Selection rules for resonance Raman spectra are given for several porphins of D 4h point group symmetry. A normal coordinate treatment is presented, based on a potential function for which stretching and bending force constants are related to bond lengths, and to the product of the bond lengths of the bonds defining the bending angle, respectively. The results can be correlated with the persistent frequencies observed in the resonance Raman spectra of haem proteins where the haem is an iron octasubstituted porphin.

Collisional Activation Mass Spectra

Abstract: Collision with gas molecules can be used to add internal energy to gaseous ions in transit through a mass spectrometer, causing their subsequent unimolecular decomposition. Mass analysis of the resulting fragment ions produces a collisional activation mass spectrum whose utility is basically similar to that of a normal mass spectrum. Promising applications to date have been found in ion structure characterization for fundamental studies and molecular structure determination, for which the insensitivity of the collisional activation mass spectrum to the ion’s internal energy is a unique advantage; examples are given for structure determination of C 7 H 7 + and CSH 3 + isomers. An additional application attracting increasing attention is as a separation/identification technique for complex mixtures; this involves mass spectrometric separation of the ionized mixture components followed by their identification from the corresponding collisional activation (or metastable ion) mass spectra. This two-dimensional mass spectrometry (‘m.s.-m.s.’) technique is complementary to g.c.-m.s. and liquid chromatography - mass spectrometry, and its use is illustrated by the determination of trace components in gasoline and the chirality of organophosphates.

The Surface Structure and Composition of Layered Silicate Minerals: Novel Insights from X-Ray Photoelectron Diffraction, K-Emission Spectroscopy and Cognate Techniques

Abstract: Angle-resolved X-ray photoelectron spectra of freshly exposed cleavage planes of muscovite, lepidolite, phlogopite, and both natural and Pb-exchanged vermiculite are interpreted to yield both quantitative elemental analyses relating to the outermost 100 A of the crystals and a wealth of structural information, the latter from consideration of phenomena resulting from diffraction of the photo-emitted electrons. It is demonstrated that X-ray photoelectron diffraction can be used to differentiate between equivalent, near-equivalent, and non-equivalent sites occupied by two (or more) elements either in one single crystal or in crystals of closely similar structure, even when the element(s) concerned comprise only a small fraction of the crystal and when the sub-lattice lacks both long- and short-range order. These studies are complemented by extensive chemical analyses, by energy-dispersive X-ray (K-emission) analyses performed in an electron microscope (an elementary calibration procedure for which is outlined) and by X-ray diffraction studies. The muscovite and lepidolite are shown to cleave in regions exhibiting typical bulk composition, whereas the phlogopite and vermiculite both cleave in regions rich in aluminium, and deficient in magnesium (relative to their silicon content). The principal interlayer cations in the vermiculite, potassium and calcium, could be entirely replaced with lead by prolonged refluxing in lead nitrate solution: the lead and calcium are shown to retain their hydration spheres whereas potassium coordinates directly (without hydration) to the layer oxygen, as in the true micas. Some structural implications of these data are evaluated and discussed.

The geochemical cycle of uranium

Abstract: If the uranium content of the mantle is based on data from basalts, a homogeneous mantle would contain about 10 parts U/10$^{9}$. This gives a similar mass of uranium in mantle and crust. Sea floor processes may enrich the surface layers of basalt in uranium but do not significantly change the mass of uranium subducted in basalts. If pelagic sediments are subducted, they contribute a significant mass of uranium to the mantle. Present rates of andesite production do not seem adequate to return all subducted uranium to the crust but andesites may make a significant contribution to uranium which eventually appears in granitic rocks. Uranium transport and accumulation in sediments may be dominantly biochemical. The problem of uranium distribution in the mantle during evolution of the Earth is unresolved. The main models of crustal evolution suggest continual depletion, early depletion, or early depletion followed by slow replenishment; a constant mantle composition seems unlikely.

Regional Geochemistry of Uranium as a Guide to Deposit Formation

Abstract: Geochemical maps of northern Scotland prepared by the Institute of Geological Sciences show the distribution of uranium based on the analysis of stream sediment and water samples by the delayed neutron method. These maps not only indicate the relative concentration of the element in the principal tectonic units but also identify areas of uranium mineralization in the bedrock. Evaluation of the geochemical maps in the light of known geophysical and geological data suggests that both the Galedonides of northern Scotland and the Hebridian craton to the west of the Caledonian orogenic front are underlain by a thick layer of basement depleted in uranium and other incompatible elements. Enrichment of uranium has occurred only where the basement has been disrupted either as a result of magmatism or by deep faulting. Thus, most granites in the area surveyed contain only average abundances of U, but large values characterize certain early Proterozoic and Caledonian granites which appear to have derived at least part of their substance from the mantle. Uranium enrichment in the non-marine Old Red Sandstone overlying the metamorphic Galedonides is most marked in the vicinity of deep faults which are thought to have separated areas of emergence from subsiding sedimentary basins in Old Red Sandstone times. The style of mineralization thus reflects both regional and local factors.

Brillouin Scattering Spectroscopy of Ferroelectric and Ferroelastic Phase Transitions

Abstract: Light scattering spectroscopy has played a crucial role in the study of numerous phase transitions and critical phenomena. In the case of structural phase transitions in crystalline solids, high resolution Raman and Brillouin scattering experiments have provided detailed information on the ‘soft modes’, the highly temperature-dependent lattice vibrations whose frequencies fall towards zero at the transition temperature. The condensation of the soft modes precipitates the spontaneous symmetry breaking which inevitably accompanies these transitions. Ferroelectrics comprise a particular class of crystals exhibiting structural phase transitions which have been investigated extensively by light scattering techniques. In addition to numerous soft mode studies, other subtle aspects of these transitions have been investigated by light scattering, including mode interactions and central peaks. In this presentation, the fundamental aspects of structural phase transitions and their relation to light scattering will be reviewed. A number of light scattering studies of ferroelectric crystals spanning the past decade will be summarized and used to illustrate the current level of understanding of these phenomena.

Significance of Diagenesis for the Origin of Witwatersrand-Type Uraniferous Conglomerates

Abstract: A petrographic study of pyrite may be the key to the understanding of the Witwatersrand (South Africa) gold-uranium deposits: the sediments of the Witwatersrand Supergroup contain at least nine types of pyrite, namely (1) Laminated pyrite seams; (2) pyrite nodules in shales; (3) pyrite nodules in quartzite and conglomerate; (4) pyrite as overgrowths on carbonaceous filaments; (5) pyrite filling pore spaces and replacing clasts; (6) pyrite replacing detrital magnetite; (7) allogenic fragments of laminated pyrite; (8) allogenic fragments of pyrite nodules; and (9) allogenic fragments of coarse-grained pyrite. Types 1-6 probably formed during diagenesis of the sediment due to the activity of sulphate-reducing bacteria; types 7 and 8 are transported fragments of diagentic pyrite; type 9 may be of diverse origin, but may also in part be transported fragments of diagenetic pyrite. Pyrite petrography suggests a multi-stage history of ore enrichment: diagenetic precipitation of gold, uraninite and pyrite in sediments containing organic matter, followed by erosion, transport of allogenic fragments of ore minerals for short distances, and concentration in lag gravels at channel bottoms and unconformities. Repeated cycles of weathering, diagenetic precipitation from weathering solutions, erosion, minor transport and redeposition may have caused the extraordinary enrichment of the ores on major unconformities in the Upper Witwatersrand Supergroup.

Research on peptides and glycopeptides

Abstract: The current state of methodology for protein sequence analysis is discussed with reference to the enzyme dihydrofolate reductase. Studies on biologically active compounds of unusual structure are shown, covering data on peptide hormones and factor X, the zymogen of a serine protease involved in blood coagulation. Recent research on glycopeptides from biological sources illustrates the development of chemical and mass spectrometric methods for concurrent determination of saccharide and peptide structure. Details of future trends are discussed by reference to present work in the areas of negative chemical ionization, computerized automation and high-field magnet studies.

The Crystal Structures of the Polyiodide Salts (phenacetin)$_{2}\cdot $HI$_{5}$ and (theobromine)$_{2}\cdot $H$_{2}$I$_{8}$

Abstract: The crystal structures of (phenacetin)$\_{2}\cdot $HI$\_{5}$ (triclinic, a = 12.44 angstrom, b = 10.67, c = 5.81, $\alpha $ = 103.3 degrees, $\beta $ = 103.7, $\gamma $ = 87.3, P$\overline{1}$, Z = 1) and (theobromine)$\_{2}\cdot $H$\_{2}$I$\_{8}$ (triclinic, a = 14.38 angstrom, b = 14.07, c = 7.75, $\alpha $ = 91.2 degrees, $\beta $ = 100.8, $\gamma $ = 91.0, P$\overline{1}$, Z = 2) have been solved by Patterson methods, using intensities measured by Weissenberg diffractometer with graphite-monochromated Mo K$\alpha $ radiation (2815 and 2827 intensities, R = 8.3% and 11.1% respectively). Both structures are polyiodide salts, with alternating cationic (organic) and anionic (polyiodide) layers. In (phenacetin)$\_{2}\cdot $HI$\_{5}$ the organic layers consist of hydrogen-bonded phenacetin 'dimers', with the proton bridging the oxygens of the carbonyl bonds in a short hydrogen bond (d(O...O) = 2.46 (2) angstrom); the polyiodide layers contain zigzag chains of alternating iodine molecules and triiodide ions, with secondary bonds (d(I...I) = 3.55 angstrom) between these moieties. There is only van der Waals bonding between parallel chains. This substance, bis-(phenacetin)hydrogen iodine triiodide, is a type A basic salt. In (theobromine)$\_{2}\cdot $H$\_{2}$I$\_{8}$ the organic layer consists of hydrogen-bonded theobrominium cations and the polyiodide layer of centrosymmetric S-shaped (I$\_{16}^{4-}$) ions, with the arrangement I$\_{3}^{-}\cdot $I$\_{2}\cdot $I$\_{3}^{-}\cdot $I$\_{3}^{-}\cdot $I$\_{2}\cdot $I$\_{3}^{-}$; there is secondary bonding between triiodide and iodine moieties within the hexadecaiodide ions. There are tertiary bonds (d(I...I) = 3.84 angstrom) between adjacent I$\_{16}^{4-}$ ions.

Uranium in South Africa and South West Africa (Namibia)[and Discussion]

Abstract: A number of genetically different uranium deposits occur in South Africa and South West Africa in rocks of widely differing ages. Early Proterozoic clastic rocks contain sedimentary uraninite, whose deposition in auriferous quartz-pebble conglomerates and carbon seams can be related to fluvial fans and algal mats. Recently discovered deposits of uranium in the Phanerozoic Karoo Supergroup occur as widespread but small bodies in channel sandstones of fluvial association. Carnotite deposits are developed in Cainozoic calcretes in the western, more arid, regions of southern Africa in which the uranium has been precipitated epigenetically from circulating groundwater. Uranium mineralization in magmatic rocks is present to a small extent in phoscorite and carbonatite of the middle Proterozoic Phalaborwa Igneous Complex, and is associated with alkaline lavas and intrusive rocks in the Pilanesberg alkaline complex of middle-late Proterozoic age. Multicyclic processes of ore formation have produced extensive deposits of uraninite-bearing alaskitic pegmatitic granites, of Phanerozoic age, in the Pan-African Damara metamorphic belt.

Photochemical oxidation of atmospheric sulphur dioxide

Abstract: Oxidation of atmospheric sulphur dioxide can occur by homogeneous photochemically initiated gas-phase reactions as well as by heterogeneous reactions in cloud and fog droplets. Gas phase oxidation can result from reactions of excited SO$\_{2}$ molecules formed by absorption of solar u.v. radiation by ground state SO$\_{2}$, from reactions of SO$\_{2}$ with photochemically generated OH and RO$\_{2}$ free radicals, and from its reaction with transient species produced in thermal ozone-alkene reactions. Evaluation of the available mechanistic and rate data reveals that, of these three processes, oxidation by free radicals, particularly OH, is likely to be the most important in the atmosphere. Oxidation rates of up to 4% h$^{-1}$ are predicted for a hydrocarbon-NO$_{x}$ polluted atmosphere under western European summertime conditions. This can lead to the formation of elevated concentrations of sulphuric acid and sulphate aerosol in polluted air. In the natural background troposphere oxidation rates are much less, ca. 0.3% h$^{-1}$ averaged over 24 h, but probably still significant as a source of atmospheric sulphates.