Neutron quasi-elastic scattering in disordered solids: a Monte Carlo study of metal-hydrogen systems

The dynamic structure factor of neutron quasi-elastic scattering has been calculated by Monte Carlo methods for atoms diffusing on a disordered lattice. The disorder includes not only variation in the distances between neighbouring atomic sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent intermediate scattering function which translate into a significant increase in the intensity in the wings of the quasi-elastic spectrum as compared with the Lorentzian form. The effect is particularly marked at high values of the momentum transfer and at site occupancies of the order of unity. The MC calculations demonstrate how the degree of disorder may be derived from experimental measurements of the quasi-elastic scattering. The model structure factors are compared with the experimental quasi-elastic spectrum of an amorphous metal-hydrogen alloy.

Case base adaptation using solution-space metrics

In this paper we propose a generalisation of the k-nearest neighbour (k-NN) retrieval method based on an error function using distance metrics in the solution and problem space. It is an interpolative method which is proposed to be effective for sparse case bases. The method applies equally to nominal, continuous and mixed domains, and does not depend upon an embedding n-dimensional space. In continuous Euclidean problem domains, the method is shown to be a generalisation of the Shepard's Interpolation method. We term the retrieval algorithm the Generalised Shepard Nearest Neighbour (GSNN) method. A novel aspect of GSNN is that it provides a general method for interpolation over nominal solution domains. The performance of the retrieval method is examined with reference to the Iris classification problem,and to a simulated sparse nominal value test problem. The introducion of a solution-space metric is shown to out-perform conventional nearest neighbours methods on sparse case bases.

Case base reduction using solution-space metrics

In this paper we propose a case base reduction technique which uses a metric defined on the solution space. The technique utilises the Generalised Shepard Nearest Neighbour (GSNN) algorithm to estimate nominal or real valued solutions in case bases with solution space metrics. An overview of GSNN and a generalised reduction technique, which subsumes some existing decremental methods, such as the Shrink algorithm, are presented. The reduction technique is given for case bases in terms of a measure of the importance of each case to the predictive power of the case base. A trial test is performed on two case bases of different kinds, with several metrics proposed in the solution space. The tests show that GSNN can out-perform standard nearest neighbour methods on this set. Further test results show that a caseremoval order proposed based on a GSNN error function can produce a sparse case base with good predictive power.