This article addresses a fundamental problem faced by the community employing single-particle ab initio methods: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a new, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new techniques to the derivation and transcription of a few lines of algebra.

How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set.

Experimental data and theoretical predictions of hydrolysis reaction kinetics of model halocarbons and phase equilibria of their associated neutralized salt reaction products are reported for a range of hydrothermal conditions. Specifically, the results of a study of hydrolysis and oxidation of methylene chloride (CH2Cl2) to produce CO2, H2O, and HCl as final mineralized products are presented.

Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allowexactrecovery of the multiresolution representation of a function from its sample values on afiniteset of points in space. We present a detailed study of the application of wavelet concepts to physical problems expressed in such bases.

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms.

Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters. Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds.

Throughout the Plenary and Break-Out Sessions at the Workshop the issue was frequently brought up of linking together computational approaches which traditionally operate on distinct length scales. In response to this interest, an informal discussion was held to examine the prospects for a collaborative initiative on coupling atomistic and continuum methods.

A structure model, based on a rhombohedral random tiling, is proposed for the ‘perfect’ Al-Cu-Fe and Al-Pd-Mn icosahedral phases. Locally, the model has much in common with six-dimensional models, with over 78% of all atoms belonging to an edge-sharing network of Bergman dodecahedra. The size of the tiles in the model is sufficiently small that relatively little atomic motion is required to implement an elementary rearrangement of tiles. Periodic arrangements of the tiles are consistent with known approximant phases. © 1996 Taylor & Francis Group, LLC.

The possibility of π-electron ring currents in C60 has been of interest since the initial identification of the fullerenes and the recent synthesis of these compounds has provided an experimental impetus to magnetic studies. We calculated a vanishingly small π-electron ring-current magnetic susceptibility for C60 and this prediction has recently received experimental verification. We attributed this behavior to a near cancellation of the diamagnetic and Van Vleck paramagnetic terms. The higher fullerenes may become available for study in the near future and recent work by Diedrich et al.