An introduction to Maslov's asymptotic method

Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.     

Multiple longshore sand bars in the upper Chesapeake Bay

In the upper Chesapeake Bay (Maryland, U.S.A.) field surveys were conducted at 18 multiple longshore sand bar sites. The multiple bar systems were found in water depths less than approximately 2 m (mean sea level), and exhibited mild bottom slopes of 0·0052 or less. The number of bars composing each system ranged from four to 17 and the spacing between the crests typically increased in the offshore direction, ranging from 12 to 70 m. Bar height also typically increased with distance offshore and ranged from 0·03 to 0·61 m. A grain size analysis of crest and trough sediment did not reveal any significant differences and the sediment was categorized as ‘fine sand’. A review of the literature data indicated that the Chesapeake Bay multiple bars possessed similar characteristics to those found in Gelding Bay (Baltic Sea); similarities in fetch, wave height and tidal range between the two bays may account for this finding. The surf-scaling parameter indicated that the multiple bar systems were extremely dissipative with regard to wave energy, and wave height appeared to be an important factor in controlling bar spacing and bar height. A multiple wave break point hypothesis was discussed as a possible mechanism for the formation of Chesapeake Bay multiple longshore bars, and limited observational evidence appeared to support such a mechanism.     

THE BLOOMINGTON (LL6) CHONDRITE AND ITS SHOCK MELT GLASSES

The Bloomington meteorite, a 67.8 gram veined, brecciated chondrite, fell during the summer of 1938 in Bloomington, Illinois. Its olivine, orthopyroxene and metal compositions (fo₆₉, en₇₄ and Fe₅₂ Ni₄₈ respectively) and its texture identify it as a brecciated LL6 chondrite of shock facies d. Shock melt glasses occur in Bloomington as sparse melt pockets and veins in clasts and as isolated masses in the black, clast-rich matrix. The vein glasses chemically resemble bulk LL-group chondrites and thus appear to reflect total melting of the host meteorite. The melt pocket and matrix glasses, like those described previously in L-group chondrites, have more varied compositions and are typically enriched in normative plagioclase. All glasses that we analyzed in Bloomington have FeO/MgO and Na/Al ratios similar to those of LL-group chondrites, indicating that melting of this meteorite involved neither a significant change in the oxidation state of iron nor loss of sodium to a vapor phase. Bloomington is a monomict breccia whose components formed in place as a result of a single episode of shock and attendant melting.     

Dynamics of the Nuclear Outflow in NGC 1068

A short survey is presented of dynamical (and thermodynamical) issues relevant to outflows in Seyfert galaxies like NGC 1068. Numerical simulations incorporating both realistic radiative heating and cooling, and angular momentum, show that the fraction of injected gas which escapes in a wind is very sensitive to both the injection pressure and the gas's angular momentum. Radiation pressure acting through a variety of atomic opacity processes may also be important. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Monahans chondrite and halite: Argon‐39/argon‐40 age,solar gases,cosmic‐ray exposure ages,and parent body regolith neutron flux and thickness

Abstract— The Monahans H‐chondrite is a regolith breccia containing light and dark phases and the first reported presence of small grains of halite. We made detailed noble gas analyses of each of these phases. The ³⁹Ar‐⁴⁰Ar age of Monahans light is 4.533 ± 0.006 Ma. Monahans dark and halite samples show greater amounts of diffusive loss of ⁴⁰Ar and the maximum ages are 4.50 and 4.33 Ga, respectively. Monahans dark phase contains significant concentrations of He, Ne and Ar implanted by the solar wind when this material was extant in a parent body regolith. Monahans light contains no solar gases. From the cosmogenic ³He, ²¹Ne, and ³⁸Ar in Monahans light we calculate a probable cosmic‐ray, space exposure age of 6.0 ± 0.5 Ma. Monahans dark contains twice as much cosmogenic ²¹Ne and ³⁸Ar as does the light and indicates early near‐surface exposure of 13–18 Ma in a H‐chondrite regolith. The existence of fragile halite grains in H‐chondrites suggests that this regolith irradiation occurred very early. Large concentrations of ³⁶Ar in the halite were produced during regolith exposure by neutron capture on ³⁵Cl, followed by decay to ³⁶Ar. The thermal neutron fluence seen by the halite was (2–4) × 10¹⁴ n/cm². The thermal neutron flux during regolith exposure was ～0.4‐0.7 n/cm²/s. The Monahans neutron fluence is more than an order of magnitude less than that acquired during space exposure of several large meteorites and of lunar soils, but the neutron flux is lower by a factor of ≤5. Comparison of the ³⁶Ar_n/²¹Ne_cos ratio in Monahans halite and silicate with the theoretically calculated ratio as a function of shielding depth in an H‐chondrite regolith suggests that irradiation of Monahans dark occurred under low shielding in a regolith that may have been relatively shallow. Late addition of halite to the regolith can be ruled out. However, irradiation of halite and silicate for different times at different depths in an extensive regolith cannot be excluded.     

Porphyroblast inclusion-trail orientation data: eppure non son girate*!

Extensive examination of large numbers of spatially orientated thin sections of orientated samples from orogens of all ages around the world has demonstrated that porphyroblasts do not rotate relative to geographical coordinates during highly non-coaxial ductile deformation of the matrix subsequent to their growth. This has been demonstrated for all tectonic environments so far investigated. The work also has provided new insights and data on metamorphic, structural and tectonic processes including: (1) the intimate control of deformation partitioning on metamorphic reactions; (2) solutions to the lack of correlation between lineations that indicate the direction of movement within thrusts and shear zones, and relative plate motion; and (3) a possible technique for determining the direction of relative plate motion that caused orogenesis in ancient orogens.     

Evolutionary state of W UMa-type systems

The evolutionary status of a sample of 31 W UMa-type systems (20 of W, 9 of A, and 2 of A/W sub-class) is examined and discussed on the basis of their positions in the H-R, mass-radius and mass-luminosity diagrams. The absolute elements of these systems have been evaluated by use of their spectroscopic and photometric data as they were found in the literature. Since different analysis methods have been used by the various investigators this gives the opportunity to make different H-R, mass-radius and mass-luminosity diagrams, according to the method used, and compare the results.Moreover, from the spectral type-period diagram of those systems that have spectral types from O to G2 it was found that all of them lie in the evolved region. Finally, the log (L _l/L _s) log (M _l/M _s) diagrams are presented and discussed.