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Why Model The Subsurface?
Access
to fresh water will always be necessary,
and demand for fresh water will continue to increase with population
growth.
Because the overwhelming majority of the earth’s usable
freshwater is stored in the ground, it is becoming increasingly
important to
develop accurate subsurface fluid flow models.

How Do Subsurface Fluids Flow?
The
driving force behind subsurface fluid flow is the hydraulic gradient,
which can be described as the change in the depth of the water
table between two measuring points within a porous medim, divided
by the distance between the two points (a slope!). However
the ability of water to flow through a porous medium is determined by a
material constant called the hydraulic conductivity.
If we fully understood the geologic make-up of the subsurface, and
similarily the distribution of hydraulic conductivity throughout,
subsurface fluid flow modeling would be trivial. The inherent
heterogeneity of the subsurface motivates my research.
If you would like to learn more about my research, please read my research statement and/or contact me.
Undergraduate Research
I
am very interested in teaching,
designing, and encouraging all types of modeling activities for
undergraduates. For example, in my specific research
discipline I have worked with students to
develop basic contaminant flow models. This introductory
research project can serve as a basis for in-depth undergraduate
research that can be further developed by removing
assumptions to create more complicated models, using different
mathematical modeling techniques, and incorporating ideas from other
disciplines such as chemistry and earth science.
Outside
of my applied area, I have also developed a number of modules for Introduction to Applied Mathematics Research, a class that
I created and taught at the University of Iowa. These modules serve as an introduction to
research in a variety of areas and, I believe, a great jumping off point for
undergraduate interdisciplinary research. Current module topics
that I look forward to exploring further include:
- Epidemiology and endemics
- Financial option pricing
- Continuous traffic flow
- Collision modeling using complementarity
- Image compression using wavelets
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