Glass Capillary X-ray Waveguides Scott M. LaBrake December, \thisyear Dedication: To my wife Sandra and my daughter Alexandra. Acknowledgments: First and foremost I would like to thank my beautiful wife Sandra for all of her love and support over the last eight years. I could not have completed this without you. There are not enough words to express how I feel about you. You are my best friend ...

We show there exists a continuous compactly supported function ' de ned on the reals satsifying '(x) = c0'(2x) + c1'(2x 1) + c2'(2x 2) if and only if c1 = 1, c0 + c2 = 1, and jc0j; jc2j < 1. The functions ' are examples of scaling functions from the theory of wavelets. x

The Scott rank of a countable structure is a measure, coming from the proof of Scott’s isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of Lω1ω) is the set of Scott ranks of countable models of that theory. In ZFC + PD we give a descriptive-set-theoretic classification of the sets of ordinals which are the Scott spectrum of a ...

In this paper, the definition of meet-continuity on $L$-directedcomplete posets (for short, $L$-dcpos) is introduced. As ageneralization of meet-continuity on crisp dcpos, meet-continuity on$L$-dcpos, based on the generalized Scott topology, ischaracterized. In particular, it is shown that every continuous$L$-dcpo is meet-continuous and $L$-continuous retracts ofmeet-continuous $L$-dcpos are al...

Some 40 years ago, Dana Scott proved that every countable Scott set is the standard system of a model of PA. Two decades later, Knight and Nadel extended his result to Scott sets of size ω1. Here, I show that assuming the Proper Forcing Axiom (PFA), every proper Scott set is the standard system of a model of PA. I define that a Scott set X is proper if it is arithmetically closed and the quotie...

This paper considers the implications of James Scott’s Seeing Like a State (1998) and The Art of Not Being Governed (2009) for state-building efforts in Afghanistan and the Democratic Republic of the Congo (DRC). In Seeing Like a State, Scott warns of the problems associated with top-down planning efforts to improve the human condition. In The Art of Not Being Governed, Scott discusses the ‘art...

in this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the gray-scott model, in which spot patterns have been observed. we focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. a complete bifurcation study of these solutions is presented. the main mathematic...

My research combines analysis, computation, and modeling to understand problems stemming from general pattern forming systems. My thesis work applied dynamical systems techniques to understand localized structures in reaction-diffusion systems. Most of these patterns can be understood as stationary or traveling wave solutions to partial differential equations (PDEs). More recently I have focuse...