Calculation of electric field strengths at a sharp edge

Sharp edges were first used for field ionisation mass spectrometry by Beckey. Although Cross and Robertson found that etched metal foils were more effective than razor blades for field ionisation, blades are very convenient for determination of field ionisation mass spectra, as reported by Robertson and Viney. The electric field at the vertex of a sharp edge can be calculated by the method of the conformal transformation. Here we give some equations for the field deduced with the assumption that the edge surface can be approximated by a hyperbola. We also compare two hyperbolae with radii of curvature at the vertex of 500 Angstrom and 1000 Angstrom with the profile of a commercial carbon-steel razor blade.

Calculated ionization potentials of the linear alkanes

The equivalent orbital (EO) method is investigated and used for predicting outer and inner ionization potentials of the linear alkanes. The calculated ionization potentials are in good agreement with those observed in photoelectron spectra provided that a set of 12 parameters is used in the theory. An optimization technique is used to find the best values for thle parameters and a single transferable parameter set can be found which is applicable to all the n-alkanes. A good fit to the experimental results can only be obtained if the uppermost molecular orbital of the n-alkanes is an antisymmetrical orbital built up from CH equivalent orbitals.

A new method for conditioning stochastic groundwater flow models in fractured media

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposal of radioactive waste in underground repositories. A specific area of interest is the conditioning of fracture transmissivities on measured values of pressure in these formations. This is the process where the values of fracture transmissivities in a model are adjusted to obtain a good fit of the calculated pressures to measured pressure values. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium there is little literature on conditioning fracture networks. Conditioning fracture transmissivities on pressure or flow values is a complex problem because the measurements are not linearly related to the fracture transmissivities and they are also dependent on all the fracture transmissivities in the network. We present a new method for conditioning fracture transmissivities on measured pressure values based on the calculation of certain basis vectors; each basis vector represents the change to the log transmissivity of the fractures in the network that results in a unit increase in the pressure at one measurement point whilst keeping the pressure at the remaining measurement points constant. The fracture transmissivities are updated by adding a linear combination of basis vectors and coefficients, where the coefficients are obtained by minimizing an error function. A mathematical summary of the method is given. This algorithm is implemented in the existing finite element code ConnectFlow developed and marketed by Serco Technical Services, which models groundwater flow in a fracture network. Results of the conditioning are shown for a number of simple test problems as well as for a realistic large scale test case.