Geothermal studies - Yellowstone National Park /test site 11/, Wyoming

Summary report of diamond drilling in thermal areas of Yellowstone National Park, and method for determining heat flow in thermal area

Prediction of strong shock structure using the bimodal distribution function

A modified Mott-Smith method for predicting the one-dimensional shock wave solution at very high Mach numbers is constructed by developing a system of fluid dynamic equations. The predicted shock solutions in a gas of Maxwell molecules, a hard sphere gas and in argon using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution and other solutions computed from some existing theories for Mach numbers M<50. In the limit of an infinitely large Mach number, the predicted shock profiles are also compared with the DSMC solution. The density, temperature and heat flux profiles calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutionsComment: 22 pages, 9 figures, Accepted for publication in Physical Review

On the 3D steady flow of a second grade fluid past an obstacle

We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in \cite{Koch} and properties of solutions to steady transport equation to get up to arbitrarily small \ep the same decay as the Oseen fundamental solution

Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua

We compare and contrast two types of deformations inspired by mixing applications -- one from the mixing of fluids (stretching and folding), the other from the mixing of granular matter (cutting and shuffling). The connection between mechanics and dynamical systems is discussed in the context of the kinematics of deformation, emphasizing the equivalence between stretches and Lyapunov exponents. The stretching and folding motion exemplified by the baker's map is shown to give rise to a dynamical system with a positive Lyapunov exponent, the hallmark of chaotic mixing. On the other hand, cutting and shuffling does not stretch. When an interval exchange transformation is used as the basis for cutting and shuffling, we establish that all of the map's Lyapunov exponents are zero. Mixing, as quantified by the interfacial area per unit volume, is shown to be exponentially fast when there is stretching and folding, but linear when there is only cutting and shuffling. We also discuss how a simple computational approach can discern stretching in discrete data.Comment: REVTeX 4.1, 9 pages, 3 figures; v2 corrects some misprints. The following article appeared in the American Journal of Physics and may be found at http://ajp.aapt.org/resource/1/ajpias/v79/i4/p359_s1 . Copyright 2011 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the AAP

Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\geq 2$.Comment: 15 pages, 3 figures; v2: addition of two new reference