The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

Puckering structure in the infrared spectrum of cyclobutane

The theory of rotational-pucker-vibrational transitions in the vibrational spectrum of cyclobutane is reviewed. Puckering sideband structure on the 1453 cm-1v14 infra-red fundamental of C4H8 has been observed and analysed, in terms of two slightly different puckering potential functions for the ground and the excited vibrational states. The results have been fitted to quartic-quadratic potential functions in the puckering coordinate, with a barrier to inversion of 503 cm-1 (1•44 kcal mole-1 = 6•02 kJ mole-1) in the ground state and 491 cm-1 in the excited state ν14 = 1. For reasonable assumptions about the reduced mass, the equilibrium dihedral angle of the C4 ring is determined to be about 35°, in agreement with previous estimates. Ueda and Shimanouchi's observations on the 2878 cm-1 C4H8 band have been re-analysed, and puckering sidebands have also been observed and analysed for the 1083 cm-1v14 infra-red fundamental of C4D8. Pure puckering transitions have been observed in the Raman spectrum of C4H8 vapour. All of these observations are shown to be consistent with the same ground state puckering potential function.

The structure of interrupted human AC microsatellites

Microsatellite lengths change over evolutionary time through a process of replication slippage. A recently proposed model of this process holds that the expansionary tendencies of slippage mutation are balanced by point mutations breaking longer microsatellites into smaller units and that this process gives rise to the observed frequency distributions of uninterrupted microsatellite lengths. We refer to this as the slippage/point-mutation theory. Here we derive the theory's predictions for interrupted microsatellites comprising regions of perfect repeats, labeled segments, separated by dinucleotide interruptions containing point mutations. These predictions are tested by reference to the frequency distributions of segments of AC microsatellite in the human genome, and several predictions are shown not to be supported by the data, as follows. The estimated slippage rates are relatively low for the first four repeats, and then rise initially linearly with length, in accordance with previous work. However, contrary to expectation and the experimental evidence, the inferred slippage rates decline in segments above 10 repeats. Point mutation rates are also found to be higher within microsatellites than elsewhere. The theory provides an excellent fit to the frequency distribution of peripheral segment lengths but fails to explain why internal segments are shorter. Furthermore, there are fewer microsatellites with many segments than predicted. The frequencies of interrupted microsatellites decline geometrically with microsatellite size measured in number of segments, so that for each additional segment, the number of microsatellites is 33.6% less. Overall we conclude that the detailed structure of interrupted microsatellites cannot be reconciled with the existing slippage/point-mutation theory of microsatellite evolution, and we suggest that microsatellites are stabilized by processes acting on interior rather than on peripheral segments.

Molecular structure of 2,5-dihydropyrrole (C4NH7), obtained by gas-phase electron diffraction and theoretical calculations

The structure of 2,5-dihydropyrrole (C4NH7) has been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing third-order Moller-Plesset (MP3) level of theory and the 6-311+G(d,p) basis set. Several theoretical calculations were performed. From theoretical calculations using MP3/6-311+G(d,p) evidence was obtained for the presence of an axial (63%) (N-H bond axial to the CNC plane) and an equatorial conformer (37%) (N-H bond equatorial to the CNC plane). The five-membered ring was found to be puckered with the CNC plane inclined at 21.8 (38)&DEG; to the plane of the four carbon atoms.

Anion-pi, Lone-Pair-pi, pi-pi and Hydrogen-Bonding Interactions in a Cu-II Complex of 2-Picolinate and Protonated 4,4 '-Bipyridine: Crystal Structure and Theoretical Studies

A Cu-II complex of protonated 4,4'-bipyridine (Hbyp) and 2-picolinate (pic), [Cu-2(pic)(3)(Hbyp)(H2O)(ClO4)(2)], has been synthesised and characterised by single-crystal X-ray analysis. The structure consists of two copper atoms that have different environments, bridged by a carboxylate group. The equatorial plane is formed by the two bidentate picolinate groups in one Cu-II, and one picolinate, one monodentate 4,4'-bipyridyl ligand and a water molecule in the other. Each copper atom is also weakly bonded to a perchlorate anion in an axial position. One of the coordinated perchlorate groups displays anion-pi interaction with the coordinated pyridine ring. The noncoordinated carboxylate oxygen is involved in lone-pair (l.p.)-pi interaction with the protonated pyridine ring. In addition there are pi-pi and H-bonding interactions in the structure. Bader's theory of "atoms in molecules" (AIM) is used to characterise the anion-pi and l.p.-pi interactions observed in the solid state. A high-level ab initio study (RI-MP2/aug-cc-pVTZ level of theory) has been performed to analyse the anion-pi binding affinity of the pyridine ring when it is coordinated to a transition metal and also when the other pyridine ring of the 4,4'-bipyridine moiety is protonated. Theoretical investigations support the experimental findings of an intricate network of intermolecular interactions, which is characterised in the studied complex, and also indicate that protonation as well as coordination to the transition metal have important roles in influencing the pi-binding properties of the aromatic ring. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009)

The local adsorption geometry and electronic structure of alanine on Cu{110}

The adsorption of alanine on Cu {110} was studied by a combination of near edge X-ray absorption fine structure (NEXAFS) spectroscopy, X-ray photoelectron spectroscopy (XPS) and density functional theory (DFT). Large chemical shifts in the C 1s, N 1s, and O 1s XP spectra were found between the alanine multilayer and the chemisorbed and pseudo-(3 x 2) alaninate layers. From C, N, and O K-shell NEXAFS spectra the tilt angles of the carboxylate group (approximate to 26 degrees in plane with respect to [1 (1) over bar0] and approximate to 45 degrees out of plane) and the C-N bond angle with respect to [1 (1) over bar0] could be determined for the pseudo-(3 x 2) overlayer. Using this information three adsorption geometries could be eliminated from five p(3 x 2) structures which lead to almost identical heats of adsorption in the DFT calculations between 1.40 and 1.47 eV/molecule. Due to the small energy difference between the remaining two structures it is not unlikely that these coexist on the surface at room temperature. (c) 2006 Elsevier B.V. All rights reserved.

Ag(I) and Cu(I) complexes of tetramethyldiphosphinedisulfide: synthesis and structure

Reaction of [M(NCCH3)(4)][PF6] (M = Ag, Cu) with the S2P2Me4 ligand in dichloromethane solution led to substitution of all the nitrile ligands by two molecules of the sulfur ligand, affording the new species [Ag(S2P2Me4)(2)][PF6] (1) and [Cu(S2P2Me4)(2)][PF6] (2). The structures of these complexes were determined by single crystal X-ray diffraction. showing the expected tetrahedral coordination around each metal. Density functional theory (DFT) calculations confirmed the different geometries and energies of the free and coordinated ligand, and provided a very good reproduction of the experimental structures, both for Ag and Cu. The lengths of the S=P bonds are barely affected by coordination, indicating that the pi bond is not important in binding to the metal. (C) 2002 Elsevier Science B.V. All rights reserved.

The factor structure of the Edinburgh postnatal depression scale in a South African peri-urban settlement

The factor structure of the Edinburgh Postnatal Depression scale (EPDS) and similar instruments have received little attention in the literature. The researchers set out to investigate the construct validity and reliability of the EPDS amongst impoverished South African women. The EPDS was translated into isiXhosa (using Brislin's back translation method) and administered by trained interviewers to 147 women in Khayelitsha, South Africa. Responses were subjected to maximum likelihood confirmatory factor analysis. A single factor structure was found, consistent with the theory on which the EPDS was based. Internal consistency was satisfactory (a = 0.89).

On the structure of Langmuir turbulence

The Stokes drift induced by surface waves distorts turbulence in the wind-driven mixed layer of the ocean, leading to the development of streamwise vortices, or Langmuir circulations, on a wide range of scales. We investigate the structure of the resulting Langmuir turbulence, and contrast it with the structure of shear turbulence, using rapid distortion theory (RDT) and kinematic simulation of turbulence. Firstly, these linear models show clearly why elongated streamwise vortices are produced in Langmuir turbulence, when Stokes drift tilts and stretches vertical vorticity into horizontal vorticity, whereas elongated streaky structures in streamwise velocity fluctuations (u) are produced in shear turbulence, because there is a cancellation in the streamwise vorticity equation and instead it is vertical vorticity that is amplified. Secondly, we develop scaling arguments, illustrated by analysing data from LES, that indicate that Langmuir turbulence is generated when the deformation of the turbulence by mean shear is much weaker than the deformation by the Stokes drift. These scalings motivate a quantitative RDT model of Langmuir turbulence that accounts for deformation of turbulence by Stokes drift and blocking by the air–sea interface that is shown to yield profiles of the velocity variances in good agreement with LES. The physical picture that emerges, at least in the LES, is as follows. Early in the life cycle of a Langmuir eddy initial turbulent disturbances of vertical vorticity are amplified algebraically by the Stokes drift into elongated streamwise vortices, the Langmuir eddies. The turbulence is thus in a near two-component state, with suppressed and . Near the surface, over a depth of order the integral length scale of the turbulence, the vertical velocity (w) is brought to zero by blocking of the air–sea interface. Since the turbulence is nearly two-component, this vertical energy is transferred into the spanwise fluctuations, considerably enhancing at the interface. After a time of order half the eddy decorrelation time the nonlinear processes, such as distortion by the strain field of the surrounding eddies, arrest the deformation and the Langmuir eddy decays. Presumably, Langmuir turbulence then consists of a statistically steady state of such Langmuir eddies. The analysis then provides a dynamical connection between the flow structures in LES of Langmuir turbulence and the dominant balance between Stokes production and dissipation in the turbulent kinetic energy budget, found by previous authors.

The Structure of the chiral Pt{531} surface: a combined LEED and DFT study

The structure of the chiral kinked Pt{531} surface has been determined by low-energy electron diffraction intensity-versus-energy (LEED-IV) analysis and density functional theory (DFT). Large contractions and expansions of the vertical interlayer distances with respect to the bulk-terminated surface geometry were found for the first six layers (LEED: d(12) = 0.44 angstrom, d(23) = 0.69 angstrom, d(34) = 0.49 angstrom, d(45) = 0.95 angstrom, d(56) = 0.56 angstrom; DFT: d(12) = 0.51 angstrom, d(23) = 0.55 angstrom, d(34) = 0.74 angstrom, d(45) = 0.78 angstrom, d(56) = 0.63 angstrom; d(bulk) = 0.66 angstrom). Energy-dependent cancellations of LEED spots over unusually large energy ranges, up to 100 eV, can be explained by surface roughness and reproduced by applying a model involving 0.25 ML of vacancies and adatoms in the scattering calculations. The agreement between the results from LEED and DFT is not as good as in other cases, which could be due to this roughness of the real surface.

Low-lying excited states and primary photoproducts of [Os-3(CO)(10)-(s-cis-L)] (L = cyclohexa-1,3-diene, buta-1,3-diene)] clusters studied by picosecond time-resolved UV/Vis and IR spectroscopy and by density functional theory

Combined picosecond transient absorption and time-resolved infrared studies were performed, aimed at characterising low-lying excited states of the cluster [Os-3(CO)(10)(s-cis-L)] (L= cyclohexa-1,3-diene, 1) and monitoring the formation of its photoproducts. Theoretical (DFT and TD-DFT) calculations on the closely related cluster with L=buta-1,3-diene (2') have revealed that the low-lying electronic transitions of these [Os-3(CO)(10)(s-cis-1,3-diene)] clusters have a predominant sigma(core)pi*(CO) character. From the lowest sigmapi* excited state, cluster 1 undergoes fast Os-Os(1,3-diene) bond cleavage (tau=3.3 ps) resulting in the formation of a coordinatively unsaturated primary photoproduct (1a) with a single CO bridge. A new insight into the structure of the transient has been obtained by DFT calculations. The cleaved Os-Os(1,3-diene) bond is bridged by the donor 1,3-diene ligand, compensating for the electron deficiency at the neighbouring Os centre. Because of the unequal distribution of the electron density in transient la, a second CO bridge is formed in 20 ps in the photoproduct [Os-3(CO)(8)(mu-CO)(2)- (cyclohexa-1,3-diene)] (1b). The latter compound, absorbing strongly around 630 nm, mainly regenerates the parent cluster with a lifetime of about 100 ns in hexane. Its structure, as suggested by the DFT calculations, again contains the 1,3-diene ligand coordinated in a bridging fashion. Photoproduct 1b can therefore be assigned as a high-energy coordination isomer of the parent cluster with all Os-Os bonds bridged.

Structure variation and evolution in microphase-separated grafted diblock copolymer films

The phase behavior of grafted d-polystyrene-block-poly(methyl methacrylate) diblock copolymer films is examined, with particular focus on the effect of solvent and annealing time. It was observed that the films undergo a two-step transformation from an initially disordered state, through an ordered metastable state, to the final equilibrium configuration. It was also found that altering the solvent used to wash the films, or complete removal of the solvent prior to thermal annealing using supercritical CO2, could influence the structure of the films in the metastable state, though the final equilibrium state was unaffected. To aid in the understanding to these experimental results, a series of self-consistent field theory calculations were done on a model diblock copolymer brush containing solvent. Of the different models examined, those which contained a solvent selective for the grafted polymer block most accurately matched the observed experimental behavior. We hypothesize that the structure of the films in the metastable state results from solvent enrichment of the film near the film/substrate interface in the case of films washed with solvent or faster relaxation of the nongrafted block for supercritical CO2 treated (solvent free) films. The persistence of the metastable structures was attributed to the slow reorganization of the polymer chains in the absence of solvent.

The correlation structure of spatial autoregressions

This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties ofW to correlation properties of SAR(1) models defined on irregular lattices.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).