Computation

At the heart of Computational Physics lies numerical simulation. Most real-world physics problems cannot be solved analytically due to the inherent complexities of the system; fortunately, much can be learned through computer modeling and analysis. Research in this area deals with constructing these models and simulating physical interactions.

Meteorology

We have involved students in several meteorological projects at St. Thomas. These include investigations into the Lorenz and the Rayleigh-Bénard models of the atmosphere. These models are broad simplifications of the full Navier-Stokes equations that describe the atmosphere, yet hopefully retain some of its characteristic behaviors. Hence by studying these models we hope to glean, in a manageable way, an intuition about how the atmosphere works. As a complement, we also have investigated a more complete version of the atmospheric equations using the Advanced Regional Prediction System (ARPS), a very involved computer program developed at the University of Oklahoma. Using this simulation, we are able to take real-time atmospheric data (called a "sounding") and predict whether or not a storm will develop. Comparing our results to ground truth (i.e. does a storm actually occur?) allows us to better understand the degree to which the atmosphere is well characterized by the simulation as well as the sensitivity to its input values (i.e. the sounding).

For variety (and fun), we also constructed a tornado vortex chamber (TVC) - a non-computational project - in order to visually represent tornadoes.

Our work in this area led to the following journal article:
Knox, J.A., and Ohmann, P.R. (2006). Iterative solutions of the gradient wind equation. Computers and Geosciences 32, 656-662.

Soil Science

Acid rain is an environmental problem that has garnered international attention for the past 30 years.  One problem it causes is depletion of calcium in forest systems, leading to a decrease in soil pH levels. This has resulted in great losses of vegetation in some areas. However, not all regions have been strongly affected by calcium depletion; some have appeared to find alternative sources of calcium to counter these losses. One hypothesis is that calcium may be replenished through diffusion from underground sources. Our research shows a consistency between the concentration of calcium in the soil at Walker Branch Watershed (WBW) in Tennessee and the replenishment of lost calcium via diffusion from the underlying bedrock. We constructed a computational model of calcium diffusion to model the WBW system; results include an estimate of the upward calcium transport of 6.5 kg/ha/yr at the soil surface through diffusion from bedrock 20 meters underneath. This may be sufficient to make up for the calcium leached away by acid rain.

Our research work was published in the following article:
Grigal, D.F., and Ohmann, P.R. (2005). Calcium and Forest Systems: Diffusion from Deep Sources. Soil Science 170 (2), 129-136.

Other

In the spirit of scientific inquiry, we explore other topics of interest as opportunities arise. For example, this has included modeling equilibrium charge distributions on conductors, which we have turned into a computational project in Phys 341: Electricity and Magnetism. We also play a supportive role in other departmental investigations, turning our collaboration into a particularly rich experience for our students.