Research and Theses

In addition to in-class projects, Math Modeling graduate students at Humboldt State must complete a thesis project as part of their degree. Projects tend to be practical and directly applicable to a specific scientific question. This gives students a broader context for the math they are studying and a deeper understanding of the application problem their model can help solve.

Thesis projects allow students to work with other departments on problems to solve. Each student’s thesis committee must have an outside member, whether from another discipline or from outside the university. And Math Modeling students take courses with those from other programs within environmental systems, expanding the scope of problems their work can help solve. This interdisciplinary focus is a unique attribute of HSU’s program.

Thesis projects in Math Modeling have consistently been honored with top awards. For his thesis involving a model for landmine removal, Paul Burgess and his thesis advisor Ken Owens received the 2004 Intel Environment award, which came with a $50,000 prize. Three Math Modeling theses in recent years have also won the McConkey Outstanding Thesis Award, which recognizes distinguished scholarly achievement at the master’s level. Nominations are accepted from all disciplines, so Math Modeling projects stand out for their high level of accomplishment.

Another area of research examines the use of individual-based models (IBMs) for applied and theoretical ecology, led by mathematics Prof. Steve Railsback. He collaborates with ecologists, biologists, environmental engineers, and software professionals on research goals including:

  • Developing a conceptual basis for individual-based ecology
  • Applying fish IBMs to river management questions such as: How do changes in flow and temperature affect fish populations? What effects do loss of pools, increased turbidity, competition, predation, and habitat connectivity have on population dynamics?
  • Using IBMs to test and develop ecological theory
  • Developing software and software engineering approaches for IBMs.
  • Integrating IBMs in ecological and modeling courses at HSU and other institutions.

Thesis projects in Mathematical Modeling

Recent theses in Math Modeling have examined a wide diversity of topics. They range from measuring how plants sense gravity to working with foresters on understanding how fires spread. Such research and critical thinking prepares students for the real problem-solving challenges they will face in their career. The following thesis projects are not the only theses completed in recent years but they are representative of research within our program.

Energy and Sustainability Research

Darrell Ross, "A Distributed Renewable Energy System Meeting 100% of Electricity Demand in Humboldt County: A Feasibility Study." The study compared energy demand in Humboldt County with the availability of wind, wave, solar and biomass energy. It found that enough renewable energy is available to supply Humboldt County but not in a timely fashion. Without suitable energy storage capability, the county would have to import power in times of shortages and sell power in times of excess.

Steven Walker, "Using Transfer Functions to Explain Turbidity in Humboldt Bay, California." This thesis used statistical analyses to determine the degree to which water quality in streams that feed into Humboldt Bay influence the bay's water quality.

Daniel Kanewske, "A Mathematical Model for the Onset of Water Flooding in the Cathode of a Proton Exchange Membrane Fuel Cell." Here a PDE model of water diffusion was developed to predict the onset of water flooding in fuel cell membranes. This project won the Patricia O. McConkey Award for Outstanding Thesis.

Climate Change Research

Thé Thé Kyaw, "Modeling the Effect of Marine Snow Fragmentation by Euphausia Pacifica on Carbon Flux." Carbon is naturally sequestered in the deep ocean when carbon-containing particles called marine snow settle out of the upper layer of the ocean. Small crustaceans called krill have been shown to fragment these particles. This thesis developed a mathematical model to quantify the effect of marine snow fragmentation by krill on the rate of carbon storage. It found that the effect can be substantial in some cases.

Daniele Rosa, "Implementing a Dynamic Allocation Scheme for the Lund- Potsdam-Jena Dynamic Global Vegetation Model." This thesis implemented a new scheme to model how plants respond to elevated CO2 and incorporated the scheme into a global vegetation computer model. This is an important part of understanding how our planet will respond to high levels of CO2.

Conservation Biology

Benjamin Holt, "Stochastic spatial model for the consumption of organic forest soils in a smoldering ground fire." A spatial model for the consumption of organic forest soil (duff) by smoldering combustion is developed. Smoldering ground fires have an enormous impact upon the ecology and management practice of forest lands throughout the temperate zone. This project won the Patricia O. McConkey Award for Outstanding Thesis.

Emily Hobelmann, "Plant Invasion Models—Road Effects." This project involved creating a model to determine conditions in which a road could facilitate the invasion of non-native plants into areas that would otherwise resist invasion.

Chris Panza, "A Model to Assess the Use of Nest Exclosures for Local Population Recovery of the Western Snowy Plover (Charadrius Alexandrinus Nivosus)." While nest exclosures protect nests from predation, they may sometimes lead to increased predation of the adult parents. This thesis developed a mathematical model to assess these two factors in local populations of the endangered Western Snowy Plover.

Intersection of the environment, society, and technology

Paul Burgess, "A Statistical Model of the Area Cleared by a Landmine Removal Vehicle Using Real-Time Kinematic Differential GPS and Inertial Sensing Technologies." The project included developing software to guide landmine-clearing robots and to map the ground cleared of landmines. The main mathematical result was using conditioning to compute the probable location of the landmine-clearing device. This project won the Patricia O. McConkey Award for Outstanding Thesis and the 2004 Intel Environment Award, which came with a $50,000 prize.

Stephanie Souza, "Using the Hough Transform to Detect Fish in Freshwater Creek." A Hough transform is capable of detecting lines in noisy images. We used this technique to detect fish outlines in underwater video. We hope to use this technique to some day automate the estimation of salmon and steelhead populations.

Ari Kornfeld, "Measuring and Modeling the Gravitropic Response of Oat Shoots (Avena Sativa)." This thesis investigated the biochemical mechanisms behind plants' ability to sense a gravitational field and orient themselves in it. The project combined experimental data collection and modeling of the bending angles of oat shoots. The data analysis relied on automation and sophisticated image-processing techniques.

View a complete list of all theses.