Impedance of a sphere oscillating in an elastic medium with and without slip

The dynamic impedance of a sphere oscillating in an elastic medium is considered. Oestreicher's formula for the impedance of a sphere bonded to the surrounding medium can be expressed simply in terms of three lumped impedances associated with the displaced mass and the longitudinal and transverse waves. If the surface of the sphere slips while the normal velocity remains continuous, the impedance formula is modified by adjusting the definition of the transverse impedance to include the interfacial impedance.Comment: 10 pages, 2 figure

Studies of protein designability using reduced models

One the most important problems in computational structural biology is protein designability, that is, why protein sequences are not random strings of amino acids but instead show regular patterns that encode protein structures. Many previous studies that have attempted to solve the problem have relied upon reduced models of proteins. In particular, the 2D square and the 3D cubic lattices together with reduced amino acid alphabets have been examined extensively and have lead to interesting results that shed some light on evolutionary relationship among proteins. Here, additionally to the 2D square lattice, we study the 2D triangular and 3D face centered cubic (fcc) lattices, we perform designability studies using different shapes embedded in the 2D square lattice, and we use machine learning algorithms to classify binary sequences folding to highly- or poorly-designable conformations.;In the first part of the thesis we extend the transfer matrix method to the 2D triangular lattice. The transfer matrix method is a highly efficient method of enumerating all conformations within a compact lattice area that has earlier been developed for the 2D square and 3D cubic lattices. In addition we also enumerated all compact conformations within simple geometries on the 2D triangular and 3D face centered cubic (fcc) lattices using a standard backtracking algorithm.;In the second part of the thesis we described protein designability studies on various shapes in the 2D square lattice using a reduced hydrophobic-polar (HP) amino acid alphabet. We used a simple energy function that counted the number of H-H, H-P and P-P interactions within a restricted set of protein shapes that have the same number of residues and non-bonded contacts. We found a difference in the designabilities of different protein shapes.;Finally, in the third part of the thesis we used standard machine learning algorithms to classify two classes of protein sequences. We first performed a designability study for two shapes, using a binary HP alphabet, on the 2D triangular lattice and separated highly- and poorly-designable conformations. Highly-designable conformations had many sequences folding to them with the lowest energy and poorly-designable conformations had few or no sequences folding to them. Sequences were classified as highly- or poorly-designable depending on whether they folded to highly- or poorly-designable structures. Using several machine learning algorithms such as Decision Tree, Naive Bayes, and Support Vector Machine, we were able to classify highly- and poorly-designable sequences with high accuracy