Oscillations and stability of rotating superfluids

It is predicted that neutron stars contain a liquid interior of superfluid neutrons and superconducting protons.  The effect of these superfluid components on the various oscillation modes and stability of a rotating neutron star is investigated. We model our superfluid using a simple non-relativistic, two-fluid model, where one fluid consists of the superfluid neutrons and the second fluid contains all the remaining constituents (protons, electrons).  The two fluids are coupled through the equation of state, in particular by entrainment, and are free to rotate at different rotation rates around the same axis.  The initial approach involves Eulerian perturbation theory and subsequently a Lagrangian perturbation framework is developed.  The advantage of the Lagrangian framework is that we can construct a canonical energy for the system allowing us to develop stability criteria fro superfluid stars analogous to the single fluid results by Friedman and Shutz [39].  At present our stability analysis neglects the entrainment effect, and its inclusion is the focus of future work.  However, we do include entrainment in our normal mode investigations.  We consider a self-gravitating, Newtonian, superfluid cylinder.  Numerically, we investigate the normal mode solutions and investigate their dependence on the relative rotation rate and on entrainment.  We observe avoided crossings of modes and the onset of a two-stream instability at a critical relative background rotation rate. Our investigations are complicated by the presence of various singularities. As a result there exists situations for which we are unable to obtain a numerical solution.  To check our numerics we limit our investigations to situations where these numerical problems are not encountered.  We discover this corresponds to negative values of the entrainment function, α.  Although it is predicted that in the neutrons star core the entrainment will be positive, negative entrainment is not physically unrealistic.  In fact it has been shown [28] that it is what is predicted for neutron star crusts.</p

Epithalamion

56 p. Prepared from Alexander Grosart's The Complete Works in Prose and Verse of Edmund Spenser [1882] by R.S. Bear at the University of Oregon. The text is in the public domain. This edition is dedicated to Pattiebuff Bear

Fowre hymnes

38 p. Prepared from The Complete Works in Verse and Prose of Edmund Spenser [Grosart, London, 1882] by R.S. Bear at the University of Oregon. The text is in the public domain

Colin Clovts come home againe

25 p. Based upon that found in The Complete Works in Verse and Prose of Edmund Spenser [Grosart, London, 1882] by R.S. Bear at the University of Oregon. Paragraphing in the original was by indentation; here it is indicated by the skipped line. The text is in the public domain

Processes and rates of shoreline bluff recession at Lake Sharpe, South Dakota

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references.Lake Sharpe is the center of three reservoirs formed by dams built by the U.S. Army Corps of Engineers on the Missouri River in South Dakota in the early 1960's. The design service life of the reservoir is 400 to 700 years based on the expected rate of erosion of the shoreline to the boundary of the Federally purchased land. In only thirty years however, this buffer zone has already been eroded and the shoreline continues to retreat into private land in some locations. Processes of shoreline erosion at Lake Sharpe were observed in the field and correlated to bank geology. Active processes of erosion observed included: slump, block slide, debris flow, toppling, slaking, and gullying. Each process was unique to the physical properties of the bank material. Long term rates of erosion were measured at twenty stations from historical profile surveys conducted by the U.S. Army Corps of Engineers. Total shoreline retreat at each station was found to be not related to bank material or retreat process Total shoreline losses varied from 28 ft to 622 ft since the filling of the reservoir. This yields an average rate of retreat of 1 to 22 ft/yr. Predominant wind fetch and bank height are not related to total shoreline loss. Graphs of average amount of retreat over time at each site show that the trend of retreat rate does vary with geology and retreat process. Most sites had a generally constant retreat rate after an initial high rate except the gravel sites where retreat is decreasing in rate. The factor causing the extreme erosion is the ease of erosion of the bank materials and their tendency to stay in suspension until they reach deep water. Because the fine grained bank materials are carried away in suspension rather than be deposited to form a protective beach, the toe of the bluff is continuously subjected to wave action and retreat continues. Only at the shorelines where the there is a significant sand or gravel layer does a protective beach develop to slow the retreat rate