Physical Sciences and Mathematics Commons^™

Betting & Hierarchy In Paleontology, Leonard Finkelman

Faculty Publications

In his Rock, Bone, and Ruin: An Optimist’s Guide to the Historical Sciences, Adrian Currie argues that historical scientists should be optimistic about success in reconstructing the past on the basis of future research. This optimism follows in part from examples of success in paleontology. I argue that paleontologists’ success in these cases is underwritten by the hierarchical nature of biological information: extinct organisms have extant analogues at various levels of taxonomic, ecological, and physiological hierarchies, and paleontologists are adept at exploiting analogies within one informational hierarchy to infer information in another. On this account, fossils serve the role …

Crossed Tracks: Mesolimulus, Archaeopteryx, And The Nature Of Fossils, Leonard Finkelman

Faculty Publications

Organisms leave a variety of traces in the fossil record. Among these traces, vertebrate and invertebrate paleontologists conventionally recognize a distinction between the remains of an organism’s phenotype (body fossils) and the remains of an organism’s life activities (trace fossils). The same convention recognizes body fossils as biological structures and trace fossils as geological objects. This convention explains some curious practices in the classification, as with the distinction between taxa for trace fossils and for tracemakers. I consider the distinction between “parallel taxonomies,” or parataxonomies, which privileges some kinds of fossil taxa as “natural” and others as “artificial.” The motivations …

Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher

Faculty Publications

Current hypotheses regarding the disappearance of Neanderthals (NEA) in Europe fall into two main categories: climate change, and competition. Here we review current research and existing mathematical models that deal with this question, and we propose an approach that incorporates and permits the investigation of the current hypotheses. We have developed a set of differential equations that model population dynamics of anatomically modern humans (AMH) and NEA, their ecological relations to prey species, and their mutual interactions. The model allows investigators to explore each of the two main categories or combinations of both, as well as various forms of competition …

Spectrally Similar Incommensurable 3-Manifolds, David Futer, Christian Millichap

Faculty Publications

Reid has asked whether hyperbolic manifolds with the same geodesic length spectrum must be commensurable. Building toward a negative answer to this question, we construct examples of hyperbolic 3–manifolds that share an arbitrarily large portion of the length spectrum but are not commensurable. More precisely, for every n ≫ 0, we construct a pair of incommensurable hyperbolic 3–manifolds N_n and N^µ_n whose volume is approximately n and whose length spectra agree up to length n.

Both N_n and N^µ_n are built by gluing two standard submanifolds along a complicated pseudo-Anosov map, ensuring that …

Mutations And Short Geodesics In Hyperbolic 3-Manifolds, Christian Millichap

Faculty Publications

In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurability classes by analyzing their cusp shapes.

The knot complements in each class differ by a topological cut-and-paste operation known as mutation. Ruberman has shown that mutations of hyperelliptic surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide geometric and topological conditions under which such mutations also preserve the initial (complex) length spectrum. This work requires us to analyze when least …

Energy And Economy: Recognizing High-Energy Modernity As A Historical Period, Thomas Love, Cindy Isenhour

Faculty Publications

This introduction to Economic Anthropology’s special issue on “Energy and Economy” argues that we might find inspiration for a much more engaged and public anthropology in an unlikely place—19th century evolutionist thought. In addition to studying the particularities of energy transitions, which anthropology does so well, a more engaged anthropology might also broaden its temporal horizons to consider the nature of the future “stage” into which humanity is hurtling in an era of resource depletion and climate change. Net energy (EROEI), or the energy “surplus” on which we build and maintain our complex societal arrangements, is a key tool …

Hidden Symmetries And Commensurability Of 2-Bridge Link Complements, Christian Millichap, William Worden

Faculty Publications

In this paper, we show that any nonarithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of 3-manifolds with nontrivial JSJ-decomposition and rank-two fundamental groups. We also show that the only commensurable hyperbolic 2-bridge link complements are the figure-eight knot complement and the 6²₂ link complement. Our work requires a careful analysis of the tilings of R² that come from lifting the canonical triangulations of …

Factorial Growth Rates For The Number Of Hyperbolic 3-Manifolds Of A Given Volume, Christian Millichap

Faculty Publications

The work of Jørgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that the number of hyperbolic knot complements with a given volume v can grow at least factorially fast with v. A similar statement holds for closed hyperbolic 3-manifolds, obtained via Dehn surgery. Furthermore, we give explicit estimates for lower bounds of N(v) in terms of v for these examples. These results improve upon the work of Hodgson and Masai, which describes examples that grow exponentially fast with v …

The Game Chromatic Number Of Trees And Forests, Charles Dunn, Victor Larsen, Troy Retter, Kira Lindke, Dustin Toci

Faculty Publications

While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then investigate the differences between forests with game chromatic number 3 and 4. In doing so, we present a minimal example of a forest with game chromatic number 4, criteria for determining in polynomial time the game chromatic number of a forest without vertices of degree 3, and an example of a forest with maximum degree …

The Relaxed Edge-Coloring Game And K-Degenerate Graphs, Charles Dunn, David Morawski, Jennifer Firkins Nordstrom

Faculty Publications

The (r, d)-relaxed edge-coloring game is a two-player game using r colors played on the edge set of a graph G. We consider this game on forests and more generally, on k-degenerate graphs. If F is a forest with ∆(F) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆ − j and d ≥ 2j + 2 for 0 ≤ j ≤ ∆ − 1. This both improves and generalizes the result for trees in [10]. More broadly, we generalize the main result in [10] …

Complete Multipartite Graphs And The Relaxed Coloring Game, Charles Dunn

Faculty Publications

Let k be a positive integer, d be a nonnegative integer, and G be a finite graph. Two players, Alice and Bob, play a game on G by coloring the uncolored vertices with colors from a set X of k colors. At all times, the subgraph induced by a color class must have maximum degree at most d. Alice wins the game if all vertices are eventually colored; otherwise, Bob wins. The least k such that Alice has a winning strategy is called the d-relaxed game chromatic number of G, denoted χ _g^d (G). …

Measurement Of Semiconductor Surface Potential Using The Scanning Electron Microscope, Jennifer T. Heath, Chun-Sheng Jiang, Mowafak M. Al-Jassim

Faculty Publications

We calibrate the secondary electron signal from a standard scanning electron microscope to voltage, yielding an image of the surface or near-surface potential. Data on both atomically abrupt heterojunction GaInP/GaAs and diffused homojunction Si solar cell devices clearly show the expected variation in potential with position and applied bias, giving depletion widths and locating metallurgical junctions to an accuracy better than 10 nm. In some images, distortion near the p-n junction is observed, seemingly consistent with the effects of lateral electric fields (patch fields). Reducing the tube bias removes this distortion. This approach results in rapid and straightforward collection of …

Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer

Faculty Publications

We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ^(k)(G). We prove bounds on χ^(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs. We also define the k-clique-relaxed game chromatic number, χ_g^(k)(G), of a graph G. We prove χ_g⁽²⁾(G)≤ 4 for all outerplanar graphs G, and give an example of an outerplanar graph H with χ_g⁽²⁾(H) ≥ 3. Finally, we prove that if H is a member …

Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr

Faculty Publications

Fix nonnegative integers n₁ , . . ., n_d, and let L denote the lattice of points (a₁ , . . ., a_d) ∈ ℤ^d that satisfy 0 ≤ a_i ≤ n_i for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting n_i = n (for all i) in these expressions yields a new …

Scanning Capacitance Spectroscopy On N+-P Asymmetrical Junctions In Multicrystalline Si Solar Cells, Chun-Sheng Jiang, Jennifer T. Heath, Helio R. Moutinho, Mowafak M. Al-Jassim

Faculty Publications

We report on a scanning capacitance spectroscopy (SCS) study on the n⁺-p junction of multicrystalline silicon solar cells. We found that the spectra taken at space intervals of ∼10 nm exhibit characteristic features that depend strongly on the location relative to the junction. The capacitance-voltage spectra exhibit a local minimum capacitance value at the electrical junction, which allows the junction to be identified with ∼10-nm resolution. The spectra also show complicated transitions from the junction to the n-region with two local capacitance minima on the capacitance-voltage curves; similar spectra to that have not been previously reported in …

Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave

Faculty Publications

The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …

The Relaxed Game Chromatic Index Of K-Degenerate Graphs, Charles Dunn

Faculty Publications

The (r, d)-relaxed coloring game is a two-player game played on the vertex set of a graph G. We consider a natural analogue to this game on the edge set of G called the (r, d)-relaxed edge-coloring game. We consider this game on trees and more generally, on k-degenerate graphs. We show that if G is k-degenerate with ∆(G) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆+k−1 and d≥2k² + 4k.

Effect Of Ga Content On Defect States In Cuin1-XGaXSe2 Photovoltaic Devices, Jennifer T. Heath, J. David Cohen, William N. Shafarman, Dongxiang Liao, Angus Rockett

Faculty Publications

Defects in the band gap of CuIn_1-xGa_xSe₂ have been characterized using transient photocapacitance spectroscopy. The measured spectra clearly show response from a band of defects centered around 0.8 eV from the valence band edge as well as an exponential distribution of band tail states. Despite Ga contents ranging from Ga/(In+Ga)=0.0 to 0.8, the defect bandwidth and its position relative to the valence band remain constant. This defect band may act as an important recombination center, contributing to the decrease in device efficiency with increasing Ga content.