Spencer Hart

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Bio

I'm remembering just now how much I'm not a web designer... My name is Spencer Hart (as you could probably guess). I'm going into my junior year here at BYU. I'm studying Physics and trying to decide whether or not I want to go to med school. I'm the 12th of 13 kids with Gus (Dr. Hart) being the oldest. I am very talkative and outgoing, so you might need to tell me to be quiet every now and then. I just got married at the beginning of May, so that was really exciting. :)


Chaos

For the 2014 Spring Research Conference I presented on some of the chaos exercises we did (largely taken from chapter 3 of Giordano). Here are the slides I used in my presentation. A more formal write-up and code will follow later.

Presentation: Understanding Chaos.odp

Numeric versus Statistical Differentiation Highlights

Here's the executive summary and my preliminary conclusions on statistical vs. numerical differentiation for the binary alloy.

Plots of average data from are from 100 simulations (89 on the 100 by 100). The error bars represent 2 standard deviations from the average.


Course Temperature Grid:

For course temperature grids, lattice size is the primary factor determining whether numerical or statistical differentiation is going to produce better results, though by the time you get up to 10,000 flips per site (fps) on a small grid or 1000 fps on a large grid, either will work fine.

To illustrate the importance of lattice size for a given number of fps, look at the following graphs.


Average specific heat from 100 runs on a 10x10 lattice with error bars (2 standard deviations in width) comparing statistical and numeric differentiation.
Average specific heat from 100 runs on a 50x50 lattice with error bars (2 standard deviations in width) comparing statistical and numeric differentiation.
Average specific heat from 89 runs on a 100x100 lattice with error bars (2 standard deviations in width) comparing statistical and numeric differentiation.