One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve

We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability in this universality class, explicitly calculating amplitudes of the leading order terms.Comment: 24 pages, 5 figure

Lessons from Principals of High-Performing Ethnically Diverse High-Poverty Schools

This study examines practices of principals working in high-performing, high-poverty schools with a high representation of students of color in south central Texas. This study explores how leaders build individual and organizational capacity in high-needs schools. Using a criterion sample, and a conceptual framework focused on leadership for learning, three principals were included in this study. Their schools each had 85% representation of students of color, 85% or more of students qualifying for free/reduced lunch, and at least 85% of students demonstrating mastery on state assessments. Principals demonstrated that while it is paramount to set organizational structures and policies conducive to learning, building a collective effort to adapt such structures and policies is equally important. By building individual and organizational capacity, these principals focused on building a successful learning culture in order to generate high performance in high-poverty schools with a high representation of students of color. The implications and recommendations from this study may appeal to other school leaders who wish to adapt the lessons learned from this research and apply them to their own schools’ unique contexts

Adapting to the digital age: a narrative approach

The article adopts a narrative inquiry approach to foreground informal learning and exposes a collection of stories from tutors about how they adapted comfortably to the digital age. We were concerned that despite substantial evidence that bringing about changes in pedagogic practices can be difficult, there is a gap in convincing approaches to help in this respect. In this context, this project takes a “bottom-up” approach and synthesises several life-stories into a single persuasive narrative to support the process of adapting to digital change. The project foregrounds the small, every-day motivating moments, cultural features and environmental factors in people's diverse lives which may have contributed to their positive dispositions towards change in relation to technology enhanced learning. We expect that such narrative approaches could serve to support colleagues in other institutions to warm up to ever-changing technological advances

Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure

Enhancing microbolometer performance at terahertz frequencies with metamaterial absorbers

For Terahertz (THz) imaging to be useful outside of a laboratory setting, inexpensive yet sensitive detectors such as uncooled microbolometers will be required. Metamaterials can improve THz absorption without significantly increasing the thermal mass or using exotic materials because their absorption is primarily dependent on the geometry of the materials and not their individual optical properties. Finite Element (FE) simulations revealed that an array of squares above a ground plane separated by a dielectric is efficient, yet thin. Metamaterials were fabricated and their absorption characteristics were measured using a Fourier Transform Infrared Spectrometer (FTIR) indicating that the FE simulations are accurate. Metamaterial structures tuned to a quantum cascade laser (QCL) illuminator were incorporated into a bi-material sensor, which was used for detection of THz radiation from the QCL source with good sensitivity. In the case of microbolometers, a bolometric layer needs to be embedded in the metamaterial to form a thin microbridge. Simulations indicated that if the bolometric layer was resistive enough or close enough to the ground plane, then absorption would be largely unaltered. Metamaterials with a conductive Titanium (Ti) layer embedded into the dielectric spacer were fabricated and measured with an FTIR, confirming this behavior.http://archive.org/details/enhancingmicrobo1094537647Civilian, Department of the NavyApproved for public release; distribution is unlimited

The Herbarium And Type Specimens Of Thomas Henry Kearney, Jr. From 1890‐1901

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149754/1/tax02826.pd