Compatibility Studies of Various Refractory Materials in Contact with Molten Silicon

The production of low cost, efficient solar cells for terrestrial electric power generation involves the manipulation of molten silicon with a present need for noncontaminating, high temperature refractories to be used as containment vessels, ribbon-production dies, and dip-coated substrates. Studies were conducted on the wetting behavior and chemical/physical interactions between molten silicon and various refractory materials

Weakly nonlinear stability analysis of MHD channel flow using an efficient numerical approach

We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Using a non-standard numerical approach, we compute the linear growth rate correction and the first Landau coefficient, which in a sufficiently strong magnetic field vary with the Hartmann number as $\mu_{1}\sim(0.814-\mathrm{i}19.8)\times10^{-3}\textit{Ha}$ and $\mu_{2}\sim(2.73-\mathrm{i}1.50)\times10^{-5}\textit{Ha}^{-4}$. These coefficients describe a subcritical transverse velocity perturbation with the equilibrium amplitude $|A|^{2}=\Re[\mu_{1}]/\Re[\mu_{2}](\textit{Re}_{c}-\textit{Re})\sim29.8\textit{Ha}^{5}(\textit{Re}_{c}-\textit{Re})$ which exists at Reynolds numbers below the linear stability threshold $\textit{Re}_{c}\sim 4.83\times10^{4}\textit{Ha}.$ We find that the flow remains subcritically unstable regardless of the magnetic field strength. Our method for computing Landau coefficients differs from the standard one by the application of the solvability condition to the discretized rather than continuous problem. This allows us to bypass both the solution of the adjoint problem and the subsequent evaluation of the integrals defining the inner products, which results in a significant simplification of the method.Comment: 16 pages, 10 figures, revised version (to appear in Phys Fluids

Asymptotic Implied Volatility at the Second Order with Application to the SABR Model

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.Comment: 27 pages; v2: typos fixed and a few notation changes; v3: published version, typos fixed and comments added. in Large Deviations and Asymptotic Methods in Finance, Springer (2015) 37-6

Gender and Crime: Offense Patterns and Criminal Court Sanctions

The relation between gender and criminality is strong, and is likely to remain so. Women have traditionally been much less likely than men to commit violent crimes, and that pattern persists today. Rates of female involvement in some forms of property crime-notably petty theft and fraud-appear to be increasing. However, while the relative increase in women\u27s property crime involvement is significant, female participation even in these crimes remains far less than that of men. The relation of gender to case processing decisions in the criminal justice system varies from stage to stage. Although the pertinent literature is plagued by methodological and interpretive problems, several tentative conclusions can be offered. Women are more likely than men, other things equal, to be released on recognizance; however, when bail is set, the amount of bail does not appear to be affected by the defendant\u27s gender. There is no clear evidence that the defendant\u27s gender systematically affects prosecution, plea negotiation, or conviction decisions. In sentencing, however, women appear to receive systematic leniency except when they are convicted of high-severity offenses

Gender and Crime: Offense Patterns and Criminal Court Sanctions

The relation between gender and criminality is strong, and is likely to remain so. Women have traditionally been much less likely than men to commit violent crimes, and that pattern persists today. Rates of female involvement in some forms of property crime-notably petty theft and fraud-appear to be increasing. However, while the relative increase in women\u27s property crime involvement is significant, female participation even in these crimes remains far less than that of men. The relation of gender to case processing decisions in the criminal justice system varies from stage to stage. Although the pertinent literature is plagued by methodological and interpretive problems, several tentative conclusions can be offered. Women are more likely than men, other things equal, to be released on recognizance; however, when bail is set, the amount of bail does not appear to be affected by the defendant\u27s gender. There is no clear evidence that the defendant\u27s gender systematically affects prosecution, plea negotiation, or conviction decisions. In sentencing, however, women appear to receive systematic leniency except when they are convicted of high-severity offenses

The Sentencing of White-Collar Criminals in Federal Courts: A Socio-Legal Exploration of Disparity

This Article addresses that question by examining judicial sentencing philosophy as applied to white-collar criminality and reporting data that illuminate the operation of that philosophy. Part I of the Article argues that the traditional purposes and limits of criminal sentencing may plausibly justify either disparate or comparable sentences in cases of white-collar and common criminality. Part II describes the obstacles to an accurate empirical inquiry into how judges resolve these uncertainties in the theory of punishment. Part III presents a study designed to overcome as many of these obstacles as possible. What is most dramatic is that the resulting data do not appear to support the oft-presumed hypothesis that judges impose lighter sentences on high-status individuals convicted of white-collar crimes than they impose on lower-status individuals convicted of common crimes.4 The data, however, suggest that a significantly increased emphasis on the prosecution of white-collar crimes may encourage sentencing disparities in favor of those convicted as a result. These findings form the Article\u27s conclusion and a foundation for further research