Spatial behavior analysis at the global level using fractal geometry.
Previous work has suggested that an estimate of fractal dimension can provide a useful metric for quantifying settlement patterns. This study uses fractal methods to investigate settlement patterns at a global scale showing that the scaling behavior of the pattern of the world's largest cities corresponds to that typically observed for coastlines and rivers. This serves to validate the use of fractal dimension as a scale-independent measure of settlement patterns which can be correlated with other physical features. Such a measure may be a useful validation criterion for models of human settlement and spatial behavior.
We describe linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations which are based on an orbital formulation of the electronic problem. In particular, we discuss some open problems which need to be addressed to improve the performance of these methods, and briefly review some applications to carbon and silicon systems, with a Tight-Binding framework.