On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer

New Mn II energy levels from STIS-HST spectrum of the HgMn star HD 175640

The NIST database lists several Mn II lines that were observed in the laboratory but not classified. They cannot be used in spectrum synthesis because their atomic line data are unknown. These lines are concentrated in the 2380-2700 A interval. We aimed to assign energy levels and log gf values to these lines. Semi-empirical line data for Mn II computed by Kurucz were used to synthesize the ultraviolet spectrum of the slow-rotating, HgMn star HD 175640. The spectrum was compared with the high-resolution spectrum observed with the HST-STIS equipment. A UVES spectrum covering the 3050-10000 A region was also examined. We determined a total of 73 new energy levels, 58 from the STIS spectrum of HD 175640 and another 15 from the UVES spectrum. The new energy levels give rise to numerous new computed lines. We have identified more than 50% of the unclassified lines listed in the NIST database and have changed the assignement of another 24 lines. An abundance analysis of the star HD 175640, based on the comparison of observed and computed ultraviolet spectra in the 1250-3040 A interval, is the by-product of this study on Mn II.Comment: Paper accepted by Astronomy & Astrophysic

The Healing Cane

Evaluating the concept of church and patriarchy within the Mormon (LDS) church, raises many questions about how such practices shape or mold attitudes and perceptions of environment. A close examination of a male-dominated authority system within a cultural context creates many underlying negative effects such as loss of self-esteem, powerlessness and the facilitation of abuse within relationships. A closed system of faith and support of leaders creates a great deal of personal conflict without granting any avenues to explore or rectify such conflicts. The Healing Cane is aimed at raising the level of consciousness towards church and patriarchy. We live in a society where race discrimination is not tolerated, but gender discrimination remains accepted and in some cultures, even encouraged. A large reason the LDS church has been unable to grow doctrinally as an organization is because there is no context in which their practices can be challenged. The novel also deals with forms of magic and mystical experience. In the latter years, the church has tried to cover and minimize their usage of magic, but it is part of what makes the LDS church so strong. The concept of priesthood is immensely empowering to those who hold belief in its authenticity. The interpretation of the healing cane possessed by the family in this story is left ambiguous just as all mystical experiences are left to sole interpretation. It is that ambiguity that gives this story its power

Temperature Evolution of the Quantum Gap in CsNiCl3

Neutron scattering measurements on the one-dimensional gapped S=1 antiferromagnet, CsNiCl3, have shown that the excitation corresponding to the Haldane mass gap Delta at low temperatures persists as a resonant feature to high temperatures. We find that the strong upward renormalisation of the gap excitation, by a factor of three between 5 and 70K, is more than enough to overcome its decreasing lifetime. We find that the gap lifetime is substantially shorter than that predicted by the scaling theory of Damle and Sachdev in its low temperature range of validity. The upward gap renormalisation agrees with the non-linear sigma model at low temperatures and even up to T of order 2Delta provided an upper mass cutoff is included.Comment: Latex, 3 figures, accepted by Pysical Review

Synthesis, Crystal Structure and Photophysical Properties of Lanthanide Coordination Polymers of 4- 4-(9H-Carbazol-9-Yl)Butoxy Benzoate: The Effect of Bidentate Nitrogen Donors on Luminescence

A new aromatic carboxylate ligand, 4-[4-(9H-carbazol-9-yl)butoxy]benzoic acid (HL), has been synthesized by the replacement of the hydroxyl hydrogen of 4-hydroxy benzoic acid with a 9-butyl-9H-carbazole moiety. The anion derived from HL has been used for the support of a series of lanthanide coordination compounds [Ln = Eu (1), Gd (2) and Tb (3)]. The new lanthanide complexes have been characterized by a variety of spectroscopic techniques. Complex 3 was structurally authenticated by single-crystal X-ray diffraction and found to exist as a solvent-free 1D coordination polymer with the formula [Tb(L)(3)](n). The structural data reveal that the terbium atoms in compound 3 reside in an octahedral ligand environment that is somewhat unusual for a lanthanide. It is interesting to note that each carboxylate group exhibits only a bridging-bidentate mode, with a complete lack of more complex connectivities that are commonly observed for extended lanthanide-containing solid-state structures. Examination of the packing diagram for 3 revealed the existence of two-dimensional molecular arrays held together by means of CH-pi interactions. Aromatic carboxylates of the lanthanides are known to exhibit highly efficient luminescence, thus offering the promise of applicability as optical devices. However, due to difficulties that arise on account of their polymeric nature, their practical application is somewhat limited. Accordingly, synthetic routes to discrete molecular species are highly desirable. For this purpose, a series of ternary lanthanide complexes was designed, synthesized and characterized, namely [Eu(L)(3)(phen)] (4), [Eu(L)(3)(tmphen)] (5), [Tb(L)(3)(phen)] (6) and [Tb(L)(3)(tmphen)] (7) (phen = 1,10-phenanthroline and tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline). The photophysical properties of the foregoing complexes in the solid state at room temperature have been investigated. The quantum yields of the ternary complexes 4 (9.65%), 5 (21.00%), 6 (14.07%) and 7 (32.42%), were found to be significantly enhanced in the presence of bidentate nitrogen donors when compared with those of the corresponding binary compounds 1 (0.11%) and 3 (1.45%). Presumably this is due to effective energy transfer from the ancillary ligands.Council of Scientific and Industrial Research (CSIR-TAPSUN Project) SSL, NWP-55CSIR, New DelhiRobert A. Welch Foundation F-0003Chemistr

LOW-MASS X-RAY BINARIES AND THEIR RELATION TO THE NON-X-RAY SOURCES

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73252/1/j.1749-6632.1977.tb37032.x.pd

Group 13 Decamethylmetallocenium Cations

Salts containing the decamethylmetallocenium cations, [( C5Me5) M-2](+) ( or Cp*M-2(+)) of the group 13 "metals" B, Al and Ga have been prepared using a variety of synthetic routes. Precursor molecules of the type Cp*2MX ( X = Cl, Br, Me) exhibit structural features that vary significantly depending on the size and electronegativity of the central atom. While salt metathesis, halide abstraction and methanide abstraction methods represent viable routes for the preparation of salts of Cp*B-2(+) and Cp*Al-2(+), acidolysis of a Cp* group from Cp*Ga-3 is the most reliable method for the synthesis of the analogous gallium cation. Gallocenium cations are less stable than either of the lighter congeneric cations since they prove to be susceptible to decomposition reactions involving the "back-transfer" of ligands from the counter anion. Density functional theory (DFT) calculations revealed that, whereas Cp*Ga-2(+) is predicted to adopt a molecular structure more similar to that of Cp*B-2(+), the electronic structure of the gallium cation bears a greater resemblance to that of Cp*Al-2(+).Chemistr

From Small-Scale Dynamo to Isotropic MHD Turbulence

We consider the problem of incompressible, forced, nonhelical, homogeneous, isotropic MHD turbulence with no mean magnetic field. This problem is essentially different from the case with externally imposed uniform mean field. There is no scale-by-scale equipartition between magnetic and kinetic energies as would be the case for the Alfven-wave turbulence. The isotropic MHD turbulence is the end state of the turbulent dynamo which generates folded fields with small-scale direction reversals. We propose that the statistics seen in numerical simulations of isotropic MHD turbulence could be explained as a superposition of these folded fields and Alfven-like waves that propagate along the folds.Comment: kluwer latex, 7 pages, 7 figures; Proceedings of the International Workshop "Magnetic Fields and Star Formation: Theory vs. Observations", Madrid, 21-25 April 2003 -- published version (but the e-print is free of numerous typos introduced by the publisher