The First Three Rungs of the Cosmological Distance Ladder

It is straightforward to determine the size of the Earth and the distance to the Moon without making use of a telescope. The methods have been known since the 3rd century BC. However, few amateur or professional astronomers have worked this out from data they themselves have taken. Here we use a gnomon to determine the latitude and longitude of South Bend, Indiana, and College Station, Texas, and determine a value of the radius of the Earth of 6290 km, only 1.4 percent smaller than the true value. We use the method of Aristarchus and the size of the Earth's shadow during the lunar eclipse of 2011 June 15 to derive an estimate of the distance to the Moon (62.3 R_Earth), some 3.3 percent greater than the true mean value. We use measurements of the angular motion of the Moon against the background stars over the course of two nights, using a simple cross staff device, to estimate the Moon's distance at perigee and apogee. Finally, we use simultaneous CCD observations of asteroid 1996 HW1 obtained with small telescopes in Socorro, New Mexico, and Ojai, California, to derive a value of the Astronomical Unit of (1.59 +/- 0.19) X 10^8 km, about 6 percent too large. The data and methods presented here can easily become part of a beginning astronomy lab class.Comment: 34 pages, 11 figures, accepted for publication in American Journal of Physic

The computational hardness of pricing compound securities

It is generally assumed that you can make a financial asset out of any underlying event or combination thereof, and then sell a security. We want to show that while this is theoretically true from the financial engineering perspective, compound securities might be intractable to price. Even given no information asymmetries, or adversarial sellers, it might be impossible or very computationally intensive to put a value on these, and the associated computational complexity might afford an advantage to the party with more compute power. We have proved a PSPACE complexity bound on pricing unbounded compound options without assuming information asymmetries, and have also obtained exponentially increasing lower bounds on the number of queries required to price k-layered securities

Parametric dependence studies on cracking of clay

We have studied the shrinkage-crack patterns formed in the process of drying of clay/water slurries employing simple laboratory experiments. Both isotropic and directional drying was studied. The objective has been to examine the correlation between the solvent, materials parameters and the crack patterns. Attempt is made to fit the observations to specific models. The dynamics of the pattern formation process and the geometric properties of the crack patterns are found to be in conformity with the hydrodynamic model by Lee and Routh [W.P. Lee, A.F. Routh, Langmuir 20 (2004) 9887]