Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

Variable step size destabilizes the Störmer/leapfrog/verlet method

For fixed step-sizeh the Störmer method is stable for the standard test equationÿ= ² y,>0, if and only ifh<2. We show that for variable step sizeh _n there does not exist a (positive) limit onh which ensures stability. Nor can we guarantee stability if, in addition, we limit the step size ratioh _n/h _n–1.This work was supported in part by National Science Foundation Grant DMS 90 15533.     

Study of cross-conjugated iso-polytriacetylenes and related oligoenynes

Two series of monodisperse cross-conjugated oligomers based on enyne repeat units have been realized. The first class of molecules, iso-polytriacetylenes (iso-PTAs, 2), was divergently synthesized using an iterative sequence of palladium-catalyzed cross-coupling reactions of vinyl triflate 5 with terminal alkynes. The second series of oligoenynes (17-20) are based on an octatetrayne backbone, and result from homocoupling of the differentially protected iso-PTA oligomers 8-11. The longest member of this series, 20, spans ca. 5.6 nm from Si atom to Si atom and is composed of a contiguous sequence of 44 sp and sp(2) carbons. The lowest energy electronic absorption band for iso-PTA dimers in the progression 13 --> 9 --> 16 is consistently red-shifted as a result of extending the cross-conjugated structure. A similar comparison within each series (i.e., 16, 6-7, or 17-20), however, suggests little effect on the electronic characteristics of these molecules as oligomer length is increased. The solid-state properties of one derivative, 17, are also described.     

Comparison of diatomics-in-molecules and simple valence-bond potential surfaces for FH2

The method of diatomics-in-molecules (DIM) is applied to the FH₂ system. With spin—orbit interaction neglected, all elements of the 24 × 24 hamiltonian matrix are tabulated as analytic functions of the six diatomic fragment potential curves. It is found that neglect of off-diagonal 8 × 8 blocks in the DIM hamiltonian matrix leads to an energy expression for the ground 1 ²A′ level which is identical to the valence-bond formula used by Blais and Truhlar in dynamical studies of the F + D₂ reaction. The ²A″ excited level from DIM theory is identical to the result derived by Blais and Truhlar, without neglect of the 8 × 8 off-diagonal blocks. The DIM and simple valence-bond energies are compared numerically for noncollinear geometries.     

Obtaining partial widths from siegert wavefunctions

It is shown that a simple expression for the partial widths in a multichannel decay problem can be readily obtained from a Siegert wavefunction.     

Electron pairing and chemical bonds. Molecular structure from the analysis of pair densities and related quantities

The Fermi holes are presented as a new means of analysis and visualisation of molecular structure. Based on these quantities it is possible to get clear and highly visual insight into the structure of molecular fragments (functional groups) even in molecules with complex bonding patterns like multicenter bonding, hypervalence, etc. In addition to allowing the detection and localization of multicenter bonding, the new approach also brings some new interesting possibilities for the quantitative evaluation of molecular similarity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Phase discrimination by automated BKD

Automated backscatter Kikuchi diffraction in the SEM enables rapid discrimination of phases and the automated acquisition of phase-distribution maps at sub-micron resolution, if the phases belong to different Laue groups and/or if their lattice constants are significantly different. The acquired database can be further used for quantitative determination of phase contents, for construction of crystal orientation maps, for characterization of grain and phase boundaries, for crystal texture analysis on a grain-specific level by calculating pole figures and orientation density functions separately for each phase, and for orientation stereology in general. Pattern-quality maps provide a clear reproduction of the microstructure on a meso-scale level.     

The arylation of nitroalkanes and nitronate salts with aryllead triacetates

Nitroalkanes and their nitronate salts undergo α-arylation in good yield when treated with an aryllead triacetate in dimethyl sulfoxide.     

Spatially constrained minimization of macromolecules

A structural minimization procedure which converges rapidly and restricts the atomic shifts is outlined. It is implemented by adding a harmonic penalty term for the displacements of atomic positions and resetting the reference coordinates with respect to which the constraints are computed during the minimization. The resetting serves to reduce the constraint energy of the minimized structure to negligible levels.