Vibrating quantum billiards on Riemannian manifolds

Quantum billiards provide an excellent forum for the analysis of quantum chaos. Toward this end, we consider quantum billiards with time-varying surfaces, which provide an important example of quantum chaos that does not require the semiclassical ($\hbar \longrightarrow 0$) or high quantum-number limits. We analyze vibrating quantum billiards using the framework of Riemannian geometry. First, we derive a theorem detailing necessary conditions for the existence of chaos in vibrating quantum billiards on Riemannian manifolds. Numerical observations suggest that these conditions are also sufficient. We prove the aforementioned theorem in full generality for one degree-of-freedom boundary vibrations and briefly discuss a generalization to billiards with two or more degrees-of-vibrations. The requisite conditions are direct consequences of the separability of the Helmholtz equation in a given orthogonal coordinate frame, and they arise from orthogonality relations satisfied by solutions of the Helmholtz equation. We then state and prove a second theorem that provides a general form for the coupled ordinary differential equations that describe quantum billiards with one degree-of-vibration boundaries. This set of equations may be used to illustrate KAM theory and also provides a simple example of semiquantum chaos. Moreover, vibrating quantum billiards may be used as models for quantum-well nanostructures, so this study has both theoretical and practical applications.Comment: 23 pages, 6 figures, a few typos corrected. To appear in International Journal of Bifurcation and Chaos (9/01

I\u27ve Got The Blue Ridge Blues : Song

https://digitalcommons.library.umaine.edu/mmb-vp/1714/thumbnail.jp

Equilibrium extraction characteristics of alkyl amines and nuclear fuel metals in nitrate systems: progress report for the period January 1- September 30, 1960 : progress report VII

"November 1, 1960."Includes bibliographical references (pages 20-21)Progress report no. VII; January 1 - September 30, 1960Work performed under subcontract no. 1327 under contract no. W -7405 - Eng - 26 with Union Carbide Nuclear Corporation Oak Ridge, Tennesse

The solvent extraction of nitrosylruthenium by trilaurylamine in nitrate systems : summary report for the period July 1, 1960 to March 31, 1962

"June 1, 1962."Also issued as an Sc. D. thesis, Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1962Summary report; July 1, 1960 to March 31, 1962Work performed under subcontract no. 1327 under contract no. W-7405-Eng-26 with Union Carbide Nuclear Corporation, Oak Ridge, Tennesse

Equilibrium extraction characteristics of alkyl amines and nuclear fuel metals in nitrate systems: progress report for the period July 1 - December 31, 1961 : progress report X

"February 15, 1962."Includes bibliographical references (page 62)Progress report no. 10; July 1 to December 31, 1961Work performed under subcontract no. 1327 under contract no. W -7405 - Eng - 26 with Union Carbide Nuclear Corporation Oak Ridge, Tennesse

Sedimentary aggregates in the Peoria Loess of Nebraska, USA

Loess grain size data used to infer transport direction or wind strength are generally derived from vigorously disaggregated samples. However, these data may not adequately represent the effective particle size distribution during loess transport, if the transported dust contained aggregates of fine-grained material. Thin sections of minimally altered C and BC horizons in the late Pleistocene Peoria Loess of Nebraska, USA, indicate the presence of aggregates with diameters of 30–1000 Am. The larger aggregates (\u3e250 μm) are unlikely to have been transported, and are interpreted as the result of soil faunal activity and other pedogenic processes after deposition. Aggregates smaller than 250 Am could have a similar origin, but laser diffraction particle size analysis suggests that many are sedimentary particles. Comparison of minimally and fully dispersed particle size distributions from each sampling site was used to estimate the modal diameter of aggregates. The aggregate modal diameter becomes finer with decreasing loess thickness, representing increasing distance from the source. A similar trend was observed in the modal diameter of fully dispersed particle size distributions, which represents the mode of sand and silt transported as individual grains. We interpret both trends as the result of sorting during transport, supporting the interpretation that many of the aggregates were transported rather than formed in place. Aggregate content appears to increase with distance from the source, explaining a much more rapid downwind increase in clay content than would be expected if clay were transported as particles smaller than 2 Am diameter. Although the Peoria Loess of Nebraska contains sedimentary aggregates, many of the coarse silt and sand grains in this loess were transported as primary particles, were thoroughly exposed to sunlight and are potentially well suited for luminescence dating

Intensification of North American Megadroughts through Surface and Dust Aerosol Forcing

Tree-ring-based reconstructions of the Palmer drought severity index (PDSI) indicate that, during the Medieval Climate Anomaly (MCA), the central plains of North America experienced recurrent periods of drought spanning decades or longer. These megadroughts had exceptional persistence compared to more recent events, but the causes remain uncertain. The authors conducted a suite of general circulation model experiments to test the impact of sea surface temperature (SST) and land surface forcing on the MCA megadroughts over the central plains. The land surface forcing is represented as a set of dune mobilization boundary conditions, derived from available geomorphological evidence and modeled as increased bare soil area and a dust aerosol source (32deg-44degN, 105deg-95degW). In the experiments, cold tropical Pacific SST forcing suppresses precipitation over the central plains but cannot reproduce the overall drying or persistence seen in the PDSI reconstruction. Droughts in the scenario with dust aerosols, however, are amplified and have significantly longer persistence than in other model experiments, more closely matching the reconstructed PDSI. This additional drying occurs because the dust increases the shortwave planetary albedo, reducing energy inputs to the surface and boundary layer. The energy deficit increases atmospheric stability, inhibiting convection and reducing cloud cover and precipitation over the central plains. Results from this study provide the first model-based evidence that dust aerosol forcing and land surface changes could have contributed to the intensity and persistence of the central plains megadroughts, although uncertainties remain in the formulation of the boundary conditions and the future importance of these feedbacks

Cotton Hollow Harmony / music by Richard A. Writing; words by Chas A. Mason

Cover: drawing of an African American couple gazing into each others eyes; Publisher: Jerome H. Remick and Co. (Detroit)https://egrove.olemiss.edu/sharris_c/1137/thumbnail.jp