The Social Consciousness of Mark Twain

A thesis presented to the faculty of the School of Social Sciences at Morehead State University in partial fulfillment of the requirements for the Degree of Master of Arts in History by Rose W. Caudill on December 4, 1975

Simulating gravitational motion, gas dynamics, and structure in the cosmos

We provide introductory explanations and illustrations of the $N$-body hydrodynamics code Charm N-body GrAvity solver (ChaNGa). ChaNGa simulates the gravitational motion and gas dynamics of matter in space, with the goal of modeling galactic and/or cosmological structure and evolution. We discuss the algorithm for leapfrog integration and smoothed particle hydrodynamics and computer science concepts used by the program, including the binary data structure for the particle positions. Our presentation borrows from the doctoral dissertation of J.\ G.\ Stadel. Problems are provided in order to use ChaNGa to learn or solidify some cosmological concepts.Comment: Accepted by the American Journal of Physics. Two important supplementary documents are include

Isospectral Sets for Fourth-Order Ordinary Differential Operators

Let L(p)u = D4u - (p1u’)’ + p2u be a fourth-order differential operator acting on L2[0; 1] with p ≡ (p1; p2) belonging to L2ℝ[0, 1] x L2ℝ[0, 1] and boundary conditions u(0) = u\u27\u27(0) = u(1) = u\u27\u27(1) = 0. We study the isospectral set of L(p) when L(p) has simple spectrum. In particular we show that for such p, the isospectral manifold is a real-analytic submanifold of L2ℝ[0, 1] x L2ℝ[0, 1] which has infinite dimension and codimension. A crucial step in the proof is to show that the gradients of the eigenvalues of L(p) with respect to p are linearly independent: we study them as solutions of a non-self-ajdoint fifth-order system, the Borg system, among whose eigenvectors are the gradients