Approximate ab initio calculations and the method of molecular fragments

A two stage approach to performing ab initio calculations on medium and large sized molecules is described. The first step is to perform SCF calculations on small molecules or molecular fragments using the OPIT Program. This employs a small basis set of spherical and p-type Gaussian functions. The Gaussian functions can be identified very closely with atomic cores, bond pairs, lone pairs, etc. The position and exponent of any of the Gaussian functions can be varied by OPIT to produce a small but fully optimised basis set. The second stage is the molecular fragments method. As an example of this, Gaussian exponents and distances are taken from an OPIT calculation on ethylene and used unchanged in a single SCF calculation on benzene. Approximate ab initio calculations of this type give much useful information and are often preferable to semi-empirical approaches, since the nature of the approximations involved is much better defined.

Fast assembly of fock matrices utilising symmetry properties of the basis set

A method of assembling the elements of the Fock matrix is described which is a modification of that due to Dacre. Lists of symmetry equivalent one-electron integrals are used as pointers to abbreviate the process of collecting two-electron integrals into the Fock matrix.

Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length - the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.

A Component Based Heuristic Search Method with AdaptivePerturbations for Hospital Personnel Scheduling

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with adaptive perturbations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then mimic a natural evolutionary process on these components to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs a dynamic evaluation function which evaluates how well each component contributes towards the final objective. Two perturbation steps are then applied: the first perturbation eliminates a number of components that are deemed not worthy to stay in the current schedule; the second perturbation may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems.

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.