Earthquake Machine Lite: Activity 1 of 2

This activity is the first in a two part sequence designed to increase students' understandings about earthquakes. It will address the following questions: What is an earthquake?; What is the role of a model in science?; and How are scientific ideas constantly changing? The activity involves the construction of a model ('The Earthquake Machine') that allows students to explore stick-slip behavior of some faults. Teacher background material, references, standards alignments, and a zipped file containing a slide demonstration of the Earthquake Machine and supporting animations are provided. Educational levels: Middle school, High school

The Broken Ray Transform in nn Dimensions with Flat Reflecting Boundary

We study the broken ray transform on $n$-dimensional Euclidean domains where the reflecting parts of the boundary are flat and establish injectivity and stability under certain conditions. Given a subset $E$ of the boundary $\partial \Omega$ such that $\partial \Omega \setminus E$ is itself flat (contained in a union of hyperplanes), we measure the attenuation of all broken rays starting and ending at $E$ with the standard optical reflection rule applied to $\partial \Omega \setminus E$. By localizing the measurement operator around broken rays which reflect off a fixed sequence of flat hyperplanes, we can apply the analytic microlocal approach of Frigyik, Stefanov, and Uhlmann for the ordinary ray transform by means of a local path unfolding. This generalizes the author's previous result for the square, although we can no longer treat reflections from corner points. Similar to the result for the two dimensional square, we show that the normal operator is a classical pseudo differential operator of order -1 plus a smoothing term with $C_{0}^{\infty}$ Schwartz kernel.Comment: 22 pages, 5 figure

An Inverse Source Problem in Radiative Transfer with Partial Data

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a certain subset of the domain, which we call the visible set. Furthermore, it is shown for an open dense set of $C^{\infty}$ absorption and scattering coefficients that one can recover the part of the wave front set of the source that is supported in the microlocally visible set, modulo a function in the Sobolev space $H^{k}$ for $k$ arbitrarily large. This is an extension to the full data case, which is considered in \cite{inversesource}.Comment: 27 pages, 2 figures, accepted to Inverse Problem

Earthquake Machine Lite: Activity 2 of 2

This activity continues and compliments the previous Earthquake Machine activity by pointing out the advantages and limitations of the Earthquake Machine model, explaining the causes of earthquakes and extending students' understanding about earthquake generation, occurrence, and prediction through the collection and interpretation of data. It addresses the following questions: How frequently do earthquakes occur?; Are all earthquakes large events?; How frequently do large events occur?; Can earthquakes be predicted?; How does the Earthquake Machine model compare to global data?; and How do scientists strive for objectivity in their results? It uses the Earthquake Machine models and slide presentation from the previous activity and includes homework exercises, teacher background materials, standards alignments, and references. Educational levels: Middle school, High school

Analysis and Synthesis of Metadata Goals for Scientific Data

The proliferation of discipline-specific metadata schemes contributes to artificial barriers that can impede interdisciplinary and transdisciplinary research. The authors considered this problem by examining the domains, objectives, and architectures of nine metadata schemes used to document scientific data in the physical, life, and social sciences. They used a mixed-methods content analysis and Greenberg’s (2005) metadata objectives, principles, domains, and architectural layout (MODAL) framework, and derived 22 metadata-related goals from textual content describing each metadata scheme. Relationships are identified between the domains (e.g., scientific discipline and type of data) and the categories of scheme objectives. For each strong correlation (\u3e0.6), a Fisher’s exact test for nonparametric data was used to determine significance (p \u3c .05). Significant relationships were found between the domains and objectives of the schemes. Schemes describing observational data are more likely to have “scheme harmonization” (compatibility and interoperability with related schemes) as an objective; schemes with the objective “abstraction” (a conceptual model exists separate from the technical implementation) also have the objective “sufficiency” (the scheme defines a minimal amount of information to meet the needs of the community); and schemes with the objective “data publication” do not have the objective “element refinement.” The analysis indicates that many metadata-driven goals expressed by communities are independent of scientific discipline or the type of data, although they are constrained by historical community practices and workflows as well as the technological environment at the time of scheme creation. The analysis reveals 11 fundamental metadata goals for metadata documenting scientific data in support of sharing research data across disciplines and domains. The authors report these results and highlight the need for more metadata-related research, particularly in the context of recent funding agency policy changes

Time-Dependent Thermal Imaging of Circular Inclusions

This paper considers the inverse problem of locating one or more circular inclusions in a two-dimensional domain using thermal boundary data, specifically, the input heat flux and measured boundary temperature. The forward problem is governed by the heat equation. We show how the position and size of such defects can be recovered using the boundary data and various approximations of the solution to the forward problem. We also consider the stability of the algorithm involved to recover the defects

Using Leaves as a Model for Teaching Watershed Concepts in Natural Resources Science and Engineering Programs

Core Ideas Watershed is an important concept in science and engineering of natural resources. Introducing watershed concept using a leaf that students see every day is novel. Using leaf analogy, watershed concept can be taught universally. This article examines the effects of using leaves, something most students see every day and have some familiarity with, as an analogy for the concept of watersheds in an undergraduate water resources engineering course. The ultimate goal of the leaf/watershed analogy and associated instruction is to increase students’ understanding of hydrology principles, which in turn may facilitate better watershed management through increased public awareness, increased adoption of appropriate best management practices, and improved policy decisions. The assessment was performed with junior and senior undergraduate students enrolled in a Water Resource Engineering course. The assessment results showed that overall, students benefitted from the leaf analogy as a tool for learning watersheds. However, this effect varied depending on students’ learning style preferences