Computers and the Math-pedition!

By Joyce Lin · November 15, 2010 · 
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As we’re packing our last-minute items, we are carefully checking to make sure we have all the software we need on our computers to help model our findings once we start taking measurements in Antarctica. Along with all the experimental data, we will need some powerful numerical analysis and simulations to understand what we have found.

Getting my computer ready for Antarctica!

Our research includes taking measurements of the electrical properties of sea ice in order to better understand the way sea ice grows and melts. In order to model the sea ice, we have to take several different measurements. Among other things, we need to determine sea ice’s resistivity, which is how much a material resists electric current through that material. For example, metals exhibit low resistivity (and thus are very good conductors of electric current), whereas rubber has very high resistivity—which is why electricians wear rubber gloves to protect themselves from electric shocks! A common method of computing the resistivity of a material is by using a device called a four-probe Wenner array (http://en.wikipedia.org/wiki/Electrode_array).

Diagram of a Wenner array, from http://en.wikipedia.org/wiki/Electrode_array

These long, thin probes are inserted into the material along a line at equal distances from each other. Current is injected into the outer two probes and the voltage drop across the inner two probes is used (along with Ohm’s law) to calculate the resistivity.

But what if our material has an odd shape? Will this affect how the current flows through the material, and how will this affect the results?

Our sea ice cores are long, thin cylinders. We can use 3D modeling to see how the current lines would look. First, we build images of the cylinder and the probes by using a software package called COMSOL. The computer breaks the surface into triangular pieces and solves equations on vertices of those triangles.

Computerized mesh for sea ice core and probes

Notice how there are more triangular pieces where the probes are touching the cylinder? That’s because we need more triangular pieces to resolve the areas of greater structural detail.

We ask the computer to inject current into the outer two probes, and then we look at the voltage distribution.

Voltage distribution for a Wenner array

and more importantly, how the current lines appear

Electric current lines for a Wenner array

Notice that the probes and the shape of the sea ice core have a big impact on the shapes of the lines. We’re bringing down a lot of equipment that will exhibit this type of behavior (called fringing effects), but with some good modeling, we’ll be able to understand our results!

About the author

Joyce Lin.

I am a postdoctoral fellow in the Department of Mathematics at the University of Utah.
To see what Joyce has been up to in Antarctica, check out the Photo Blog.
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