Efficient pressure-transformer for fluids

Fluid transformer utilizes fluid under pressure at one level to drive series of free pistons in positive displacement pump. Pump in turn delivers hydraulic fluid at different pressure level to a load. Transformer is constructed of corrosion resistant materials and is extremely light and compact in relation to capacity

Two-Dimensional Vortex Sheets for the Nonisentropic Euler Equations: Nonlinear Stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain \emph{a priori} tame estimates on the effective linear problem {in the usual Sobolev spaces} and a suitable Nash--Moser iteration scheme.Comment: to appear in: J. Differential Equations 2018. arXiv admin note: substantial text overlap with arXiv:1707.0267

Charter School Replication: Growing a Quality Charter School Sector

NACSA's Policy Guide series is intended to support state legislatures and charter school advocates in creating policy environments that result in high quality authorizing and high quality schools. This guide outlines key considerations for policymakers committed to supporting the replication of existing successful charter school models

Existence of approximate current-vortex sheets near the onset of instability

The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of the discontinuity near the onset of the instability, Hunter and Thoo have introduced an asymptotic quadratically nonlinear integro-differential equation for the amplitude of small perturbations of the planar discontinuity. The local-in-time existence of smooth solutions to the Cauchy problem for such amplitude equation was already proven, under a suitable stability condition. However, the solution found there has a loss of regularity (of order two) from the initial data. In the present paper, we are able to obtain an existence result of solutions with optimal regularity, in the sense that the regularity of the initial data is preserved in the motion for positive times