Recursive Stochastic Effects in Valley Hybrid Inflation

Hybrid Inflation is a two-field model where inflation ends by a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in Ref. [1], these effects are consistently computed. Through an analysis of back-reaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that quasi-stationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. It is found that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, it is found that stochastic effects worsen the blue tilt of the curvature perturbations by an order one factor when compared with the usual slow-roll contribution.Comment: 26 pages, 6 figure

Young's integral inequality with upper and lower bounds

Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this new presentation. The corresponding results for difference equations are given, and several examples are included. We extend these results to piecewise-monotone functions as well.Comment: 8 page

High-voltage dc power processing thermal control and packaging techniques

The power processor operates in several modes, delivering up to 100 amperes of regulated electrical power, operating at input voltages to 375 volts with outputs controlled by an integral microprocessor. Several alternative packaging concepts are discussed and evaluated. High-voltage design applications, power stage interconnection and EMI considerations are also discussed. Preliminary thermal analyses were performed and the results presented for each conceptual approach with parametric study results given for the selected concept