Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Algebraic geometry (1)
- Amphibolite (1)
- Bedrock (1)
- Bezouts theorem (1)
- Budyko-Widiasih Model (1)
-
- Climate (1)
- Combinatorics (1)
- Doppler-free saturated fluorescence spectroscopy (1)
- Dynamical systems (1)
- Erosion rates (1)
- Fast-slow systems (1)
- Fluorescence spectroscopy (1)
- Frequency comb (1)
- Garnet hornblendite (1)
- Generalized Ramsey numbers (1)
- Geometric singular perturbation theory (1)
- Graph theory (1)
- High precision measurement (1)
- Hysteresis (1)
- Ice-albedo feedback (1)
- Integer programming (1)
- Intersection number (1)
- Jormungand state (1)
- Landslides (1)
- Legendre polynomials (1)
- Linear programming (1)
- Linear relaxation (1)
- Lithium D1 D2 (1)
- Lithium spectroscopy (1)
- Mathematical climatology (1)
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Intersection Number Of Plane Curves, Margaret E. Nichols
Intersection Number Of Plane Curves, Margaret E. Nichols
Honors Papers
In algebraic geometry, seemingly geometric problems can be solved using algebraic techniques. Some of the most basic geometric objects we can study are polynomial curves in the plane. In this paper we focus on the intersections of two curves. We address both the number of times two curves intersect at a given point, counting multiplicity (whatever that means), and the total number of intersections of the curves, again counting multiplicity. The former is known as the intersection number of the curves at the point. This concept, although geometrically motivated, can be described in algebraic terms; it is this relationship which …
A Swarm Of Salesmen: Algorithmic Approaches To Multiagent Modeling, Alexandre Amlie-Wolf
A Swarm Of Salesmen: Algorithmic Approaches To Multiagent Modeling, Alexandre Amlie-Wolf
Honors Papers
This honors thesis describes the algorithmic abstraction of a problem modeling a swarm of Mars rovers, where many "agents" must together achieve a goal. The algorithmic formulation of this problem is based on the traveling salesman problem (TSP), and so in this thesis I offer a review of the mathematical technique of linear programming in the context of its application to the TSP, an overview of some variations of the TSP and algorithms for approximating and solving them, and formulations without solutions of two novel TSP variations which are useful for modeling the original problem.
The Jormungand Climate Model, Christopher V. Rackauckas
The Jormungand Climate Model, Christopher V. Rackauckas
Honors Papers
The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the …
Doppler-Free Saturated Fluorescence Spectroscopy Of Lithium Using A Stabilized Frequency Comb, Michael E. Rowan
Doppler-Free Saturated Fluorescence Spectroscopy Of Lithium Using A Stabilized Frequency Comb, Michael E. Rowan
Honors Papers
The lineshapes of the D1 (22S1/2 → 22P1/2 ) and D2 (22S3/2 → 22P1/2) transitions in lithium were measured using a diode laser that was frequency-stabilized to a Ti:Sapphire 1 GHz optical frequency comb. The excitation was achieved by retroreflecting the diode laser, in effect producing the Doppler-free profiles for the center frequencies of transitions. The observed spectra were compared to density matrix calculations to gain insight into systematic effects including the dependence of Doppler-free profiles on power and polarization angle of the diode. For certain transitions, the method of saturated fluorescence spectroscopy inevitably leads to the presence of extra …
Two-Coloring Cycles In Complete Graphs, Claire Djang
Two-Coloring Cycles In Complete Graphs, Claire Djang
Honors Papers
Inspired by an investigation of Ramsey theory, this paper aims to clarify in further detail a number of results regarding the existence of monochromatic cycles in complete graphs whose edges are colored red or blue. The second half focuses on a proof given by Gyula Károlyi and Vera Rosta for the solution of all R(Cn,Ck).
Controlling Factors On Bedrock River Sinuosity In The Eastern Tibetan Plateau, Lydia Curliss
Controlling Factors On Bedrock River Sinuosity In The Eastern Tibetan Plateau, Lydia Curliss
Honors Papers
Average sinuosity of bedrock rivers across the eastern Tibetan Plateau (including the Yangtze, Mekong, Salween, Irrawaddy, and Tsang Po) ranges from 1.20-1.41. From 25°-30°N, sinuosity marginally increases east to west; over the entire distance of each river, sinuosity increases north to south. Increases in sinuosity parallel a regional tectonic gradient in an area with a marginal climate gradient. Several past studies correlate sinuous bedrock rivers in mountainous regions with gradients in climate, arguing that landslides are the main mechanism by which bedrock rivers increase sinuosity. Other studies find correlations between tectonics and increasing landslide frequency. To investigate the role of …
Thermobarometric Modeling Of The Catalina Amphibolite Unit: Implications For Tectonic And Metasomatic Models, Henry W. Towbin
Thermobarometric Modeling Of The Catalina Amphibolite Unit: Implications For Tectonic And Metasomatic Models, Henry W. Towbin
Honors Papers
On Santa Catalina Island, Ca high-grade amphibolite units overlie progressively lower- grade blueschist units in an inverted stack structure. This juxtaposition of high grade and low-grade metamorphic units has long been the subject of much debate as to the tectonic origins of the formation and how it relates to California's tectonic evolution. Previous petrography and thermobaromety of blocks in the amphibolite unit estimate pressures and temperatures of ~8-11 kbar and ~640-750 °C (Platt, 1975; Sorensen and Barton 1987). These estimates were calculated before many of the computational advances in modern thermobarometry. Using Equilibrium Assemblage Diagrams (EAD) calculated with Theriak Domino, …