Melt-preferred orientation, anisotropic permeability, and melt-band formation in a deforming, partially molten aggregate

Shear deformation of partially molten rock in laboratory experiments causes the emergence of melt-enriched sheets (bands in cross-section) that are aligned at about 15-20 degrees to the shear plane. Deformation and deviatoric stress also cause the coherent alignment of pores at the grain scale. This leads to a melt-preferred orientation that may, in turn, give rise to an anisotropic permeability. Here we develop a simple, general model of anisotropic permeability in partially molten rocks. We use linearised analysis and nonlinear numerical solutions to investigate its behaviour under simple-shear deformation. In particular, we consider implications of the model for the emergence and angle of melt-rich bands. Anisotropic permeability affects the angle of bands and, in a certain parameter regime, it can give rise to low angles consistent with experiments. However, the conditions required for this regime have a narrow range and seem unlikely to be entirely met by experiments. Anisotropic permeability may nonetheless affect melt transport and the behaviour of partially molten rocks in Earth's mantle.Comment: 19 pages, 7 figures, accepted for publication in Geophysical Journal International on 3 September 201

Selected Problems on Matroid Minors

This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds\u27s tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte\u27s characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being binary. One very natural such minor-closed class Z consists of those matroids M such that the deletion or the contraction of e is binary for all elements e of M. Chapter 2 is devoted to determining the set of excluded minors for Z. Duality plays a central role in the study of matroids. It is therefore natural to ask the following question: which matroids guarantee that, when present as minors, their duals are present as minors? We answer this question in Chapter 3. We also consider this problem with additional constraints regarding the connectivity and representability of the matroids in question. The main results of Chapter 3 deal with 3-connected matroids

Functional assessment for acute stroke trials: properties, analysis, and application

A measure of treatment effect is needed to assess the utility of any novel intervention in acute stroke. For a potentially disabling condition such as stroke, outcomes of interest should include some measure of functional recovery. There are many functional outcome assessments that can be used after stroke. In this narrative review, we discuss exemplars of assessments that describe impairment, activity, participation, and quality of life. We will consider the psychometric properties of assessment scales in the context of stroke trials, focusing on validity, reliability, responsiveness, and feasibility. We will consider approaches to the analysis of functional outcome measures, including novel statistical approaches. Finally, we will discuss how advances in audiovisual and information technology could further improve outcome assessment in trials

Neighbors of knots in the Gordian graph

We show that every knot is one crossing change away from a knot of arbitrarily high bridge number and arbitrarily high bridge distance.Comment: Accepted by American Mathematical Monthly. New version incorporates referee comment

Sweden\u27s Great Escape: Industrialization and The Changing Productivity Cost of Winter

We combine a paleoclimate reconstruction of the North Atlantic Oscillation (NAO)- a key determinant of Scandinavian winter intensity- with four centuries of historical production data from Sweden, to examine the changing influence of climate variability on production over time. We find the colder, drier winters associated with the negative phase of the NAO led to reduced economic production for much of Swedish history, and that this relationship changed with development: during industrialization, Sweden underwent a transition from ‘level’ effects, where harsh winters lowered average incomes, to ‘growth’ effects, where it reduced growth in improving living standards. Post-industrialization, neither ‘level’ nor ‘growth’ effects remain. We use sectoral production data to show that the growth effects uncovered in the industrialization period are strongest in the sectors of the economy most exposed to the climate and of greatest importance to the industrialization process, namely, transport, manufacturing and construction