Hurdles are questions that do not necessarily have correct answers. A successful solution approaches the problem thoughtfully and creatively, using modelling to address the problem. Several assumptions may need to be made over the course of your answer. Each calculation does not need to be executed perfectly for an answer to be chosen. A creative, logical approach, or even a qualitative, well-justified answer can be selected. Below are some examples of hurdles released in previous years.
I was driving from Harford, CT to Danbury, CT on the I 84. The traffic was moving smoothly and safely at the speed limit. The number of automobiles was at the absolute maximum density allowed by the speed limit and safe spacing between vehicles. As I entered Harford, far ahead of me at Waterbury a single driver noticed something across the interstate and slowed by 5 mph for 5 seconds. How long did it take for me to get from Hartford to Danbury How different would the answers be for 1 mph for 1 second or 10 mph for 10 seconds?
Solid glass spheres of various sizes sit on a bed of sand in a large glass box. On this mini-desert, beetles crawl vigorously in search of food. The masses of the glass spheres range from that of individual sand grains to much larger than the beetles.
Every morning beetle food and a small amount of sand are shaken uniformly onto the surface. This continues until the added sand has a height many times that of the largest glass spheres.
Determine the height distribution above the original sand surface for the various size spheres as a function of the time.
Once upon a time, a man named Laffer drew a curve on a paper napkin that influenced the course of national economic policy in the USA in the 1980s. In abbreviated form, the argument behind the roughly bell shaped curve was at zero tax rate the government derived zero tax revenue and at the 100% tax rate (whatever that means), the government also derives zero tax revenue. Thus, except at the peak of the curve, for each derived revenue, there are higher and lower tax rates that will produce the same revenue for the government. Laffer's point was that the government should be able to choose a lower tax rate the produces the same tax revenue.
Create a suitable model for the economy and determine whether Laffer's hypothesis is true or false. Make sure the model is sufficiently complex (i.e. non-linear) that it captures the features required to mimic the US economy.
At the end of World War II there was a popular song that went something like this:
“Mares eat oats,
And does eat oaks,
And little lambs eat ivy”
Taking all this at face value we have a closed ecological system with three herbivores and three species of plants. Since it’s not clear that the proliferation of one species of animal or plant is consistent with the success of the others, one might expect some competition. Starting with reasonably equal amounts of everything, what happens?
A recent USA Today article featured a story about the discovery of a species of spider in Australia that seems to have arrived there by long-distance dispersal. For more details here. The argument made on the basis of DNA forensics is that these spiders are most closely related to those in Africa and that they got to Australia by some form of long-distance dispersal (i.e. by water or air). This is in stark contrast to the more traditional idea of vicariance, which holds that closely related species are present on separate continents because their ancestors were separated by continental breakup. In this hurdle, your task is to consider different means of long-distance dispersal, the physical factors that favor and disfavor such dispersal and how such factors conspire to make for a successful dispersal. Specifically, for the case of the spiders in the original article, propose different scenarios for how this 10,000 km dispersal might have taken place, and come up with a rate constant for such dispersals in number of spider arrivals per million years. You may find some inspiration from a recent Science Magazine report on the new species that arrived on the west coast of the United States as a result of the tragic 2010 Japan earthquake and subsequent tsunami (Science, 357, 1402–1406 (2017).
Squirrels bury, for future use, more acorns than they eventually eat. Such buried acorns have a much higher chance of becoming oak trees than those that just fall on to the ground. Thus, the squirrels' inefficiency leads to more oak trees, hence the likelihood of more squirrels. The co-evolution of squirrels and oak trees is thereby interconnected. What is the optimal percentage inefficiency for the squirrels?
Consider a plane surface that is composed of a rectangular array of atoms onto which a single layer of foreign atoms can be absorbed. Each absorbed atom sits on top of a surface atom. The nature of these absorbed atoms is such that one cannot have more than two in a continuous line (horizontally, vertically and diagonally).
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