Experimental investigations of granular matter flow regimes leading to insight into lahar flow dynamics : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Earth Science at Massey University, Manawatū, New Zealand

The flow of granular material governs numerous natural processes including the aeolian dynamics of sand dune formation, sub-aerial and submarine mass flows, the collective dynamics of ice blocks floating on the ocean, avalanches of debris and snow, as well as volcanic granular-fluid flow processes, such as pyroclastic density currents, volcanogenic debris flows and lahars. Lahars are a particularly important type of granular flow, in regards to its possible effect on human life; they are debris and water-based flows, initiated by volcanic processes. A fascinating aspect about granular matter is the co-existence of behaviour similar to two or all three of the classical states of matter (solid, liquid, gas) and their frequent transitions between these behaviours. Despite the ubiquity of these transitions in nature and industry, the fundamental physics of granular matter remains a mystery, to the extent that a unified theory to describe the motion and behaviour of granular matter is still absent. This study is an attempt to simulate lahars and their erosion/deposition mechanics in the laboratory by making use of a rotating drum. A rotating drum can be treated as an analogue for a lahar because it allows for erosion and deposition to occur as an active region of material flows over a passive, erodible bed. In nature these processes are transitory and highly dynamic, but an experimental analogue allows for the processes to be observed in a steady system. Results include detailed maps of the various regions in a flowing granularmaterial correlated to the speed of rotation of the flows. The changing status of the active and passive regions allows for measurements of the erosion mechanics within the drum. Also, potentially identified are two new phenomena; high speed rotations appear to include features similar to Kelvin-Helmholtz instabilities, and enclosed regions of subrotation, which are referred to as self-enclosed circulation cells (SECCs)

Nonparametric Methods in Astronomy: Think, Regress, Observe -- Pick Any Three

Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for finding the relationship between two variables in astronomy are flawed. In the worst case they can lead without warning to subtly yet catastrophically wrong results, and even in the best case they require more data than necessary. Unfortunately, there is no single best technique for nonparametric regression. Instead, we provide a guide for how astronomers can choose the best method for their specific problem and provide a python library with both wrappers for the most useful existing algorithms and implementations of two new algorithms developed here.Comment: 19 pages, PAS

The set of maps F_{a,b}: x -> x+a+{b/{2 pi}} sin(2 pi x) with any given rotation interval is contractible

Consider the two-parameter family of real analytic maps $F_{a,b}:x \mapsto x+ a+{b\over 2\pi} \sin(2\pi x)$ which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed interval $I$, the set of maps $F_{a,b}$ whose rotation interval is $I$, form a contractible set

Ridge Fusion in Statistical Learning

We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and promote similarity between precision matrix estimates. Block-wise coordinate descent is used for optimization, and validation likelihood is used for tuning parameter selection. Our method is applied in quadratic discriminant analysis and semi-supervised model based clustering.Comment: 24 pages and 9 tables, 3 figure