On the Robin problem in fractal domains

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution is greater than 0, and some other families of domains were it is equal to 0. We also give a new result on `trap domains', i.e., domains where reflecting Brownian motion takes a long time to reach the center of the domain

The "hot spots" problem in planar domains with one hole

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain

Laboratory Procedure for Measuring the Effectiveness of Dust Control Palliatives

Creation of fugitive dust on unpaved roads results in the loss of up to 25 mm (one inch) of surface aggregate annually (FHWA, 1998). On these roads, shearing forces created by vehicles dislodge the fine aggregate fraction (silt and clay) that binds the coarse aggregate. Turbulent airflow created by vehicles loft these fine particles in plumes of fugitive dust that impact health, safety, and quality of life. The loss of these particles results in raveling of the road surface, culminating in large annual losses of surface aggregate. Chemical dust control (palliatives) is an attractive option. However, there are currently no accepted field or laboratory performance testing procedures for chemical road dust palliatives. The lack of a method to predict palliative performance forces engineers and road managers into a trial-and-error methodology or reliance on personal judgment and supplier claims to determine what will work best on their unpaved road or runway surfaces. The overall objective of this research was to finalize the development of a laboratory test procedure for evaluating different dust control formulations and application rates required to effectively control the airborne suspension of dust particles in the size range (aerodynamic diameter) of 10 μm or less.Pacific Northwest Transportation Consortiu

Sets avoided by Brownian motion

Any fixed cylinder is hit almost surely by a 3-dimensional Brownian motion, but is there a random cylinder that is in the complement? We answer this for cylinders, and then replacing a cylinder with a more general set

Deformation invariance of rational pairs

Rational pairs, recently introduced by Koll\'ar and Kov\'acs, generalize rational singularities to pairs $(X,D)$. Here $X$ is a normal variety and $D$ is a reduced divisor on $X$. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Koll\'ar and Kov\'acs, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In this paper we present several foundational results that are helpful for identifying thrifty resolutions and analyzing their behavior. We also show that general hyperplane sections of rational pairs are again rational. In 1978, Elkik proved that rational singularities are deformation invariant. Our main result is an analogue of this theorem for rational pairs: given a flat family $X\to S$ and a Cartier divisor $D$ on $X$, if the fibers over a smooth point $s\in S$ form a rational pair, then $(X,D)$ is also rational near the fiber $X_s$.Comment: 17 pages. Version 3: added a corollary about proper families over a curve, and a Bertini-type theorem for rational pair

Detecting New Planets in Transiting Systems

I present an initial investigation into a new planet detection technique that uses the transit timing of a known, transiting planet. The transits of a solitary planet orbiting a star occur at equally spaced intervals in time. If a second planet is present, dynamical interactions within the system will cause the time interval between transits to vary. These transit time variations can be used to infer the orbital elements of the unseen, perturbing planet. I show analytic expressions for the amplitude of the transit time variations in several limiting cases. Under certain conditions the transit time variations can be comparable to the period of the transiting planet. I also present the application of this planet detection technique to existing transit observations of the TrES-1 and HD209458 systems. While no convincing evidence for a second planet in either system was found from those data, I constrain the mass that a perturbing planet could have as a function of the semi-major axis ratio of the two planets and the eccentricity of the perturbing planet. Near low-order, mean-motion resonances (within about 1% fractional deviation), I find that a secondary planet must generally have a mass comparable to or less than the mass of the Earth--showing that these data are the first to have sensitivity to sub Earth-mass planets orbiting main sequence stars. These results show that TTV will be an important tool in the detection and characterization of extrasolar planetary systems.Comment: Ph.D. dissertation (2006). 108 page

Super-Brownian motion with reflecting historical paths

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any $\gamma>0$, a "typical" increment of a reflecting historical path over a small time interval $\Delta t$ is not greater than $(\Delta t)^{3/4 - \gamma}$.Comment: 2 figure

A Platform for Proactive, Risk-Based Slope Asset Management, Phase II

INE/AUTC 15.0

A counterexample to the "hot spots" conjecture

We construct a counterexample to the ``hot spots'' conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point of that domain.Comment: 9 pages, published versio

Reframing the Framework: Situated Information Literacy in the Music Classroom

In 2016, the Association of College and Research Libraries (ACRL) released the Framework for Information Literacy for Higher Education (the Framework). The Framework replaces ACRL's Information Literacy Competency Standards for Higher Education, which had been in place since 2000. The departure of the Standards and the subsequent arrival of the Framework represents both a challenge and an opportunity for music librarians. How do we as a profession respond to the Framework, and how can we use it to work most effectively with music students and faculty? In this article, the author connects the ideas underlying the Framework with the concept of situated information literacy, outlining ways in which a situated approach to information literacy instruction enables music librarians to engage with disciplinary faculty, use our subject expertise to its fullest extent, and more readily grapple with changing national standards and guidelines