Luncheon address : the Greenspan era : lessons for the future

Greenspan, Alan ; Monetary policy

Shock-Wave Heating Model for Chondrule Formation: Prevention of Isotopic Fractionation

Chondrules are considered to have much information on dust particles and processes in the solar nebula. It is naturally expected that protoplanetary disks observed in present star forming regions have similar dust particles and processes, so study of chondrule formation may provide us great information on the formation of the planetary systems. Evaporation during chondrule melting may have resulted in depletion of volatile elements in chondrules. However, no evidence for a large degree of heavy-isotope enrichment has been reported in chondrules. In order to meet this observed constraint, the rapid heating rate at temperatures below the silicate solidus is required to suppress the isotopic fractionation. We have developed a new shock-wave heating model taking into account the radiative transfer of the dust thermal continuum emission and the line emission of gas molecules and calculated the thermal history of chondrules. We have found that optically-thin shock waves for the thermal continuum emission from dust particles can meet the rapid heating constraint, because the dust thermal emission does not keep the dust particles high temperature for a long time in the pre-shock region and dust particles are abruptly heated by the gas drag heating in the post-shock region. We have also derived the upper limit of optical depth of the pre-shock region using the radiative diffusion approximation, above which the rapid heating constraint is not satisfied. It is about 1 - 10.Comment: 58 pages, including 5 tables and 15 figures, accepted for publication in The Astrophysical Journa

Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel

The mixed membership stochastic blockmodel is a statistical model for a graph, which extends the stochastic blockmodel by allowing every node to randomly choose a different community each time a decision of whether to form an edge is made. Whereas spectral analysis for the stochastic blockmodel is increasingly well established, theory for the mixed membership case is considerably less developed. Here we show that adjacency spectral embedding into $\mathbb{R}^k$, followed by fitting the minimum volume enclosing convex $k$-polytope to the $k-1$ principal components, leads to a consistent estimate of a $k$-community mixed membership stochastic blockmodel. The key is to identify a direct correspondence between the mixed membership stochastic blockmodel and the random dot product graph, which greatly facilitates theoretical analysis. Specifically, a $2 \rightarrow \infty$ norm and central limit theorem for the random dot product graph are exploited to respectively show consistency and partially correct the bias of the procedure.Comment: 12 pages, 6 figure

Nickel-cadmium cells

A high energy density nickel cadmium cell of aerospace quality was designed. The approach used was to utilize manufacturing techniques which produce highly uniform and controlled starting materials in addition to improvements in the overall design. Parameters controlling the production of plaque and both positive and negative plate were studied. Quantities of these materials were produced and prototype cells were assembled to test the proposed design