Adjoint algorithms for the Navier-Stokes equations in the low Mach number limit

This paper describes a derivation of the adjoint low Mach number equations and their implementation and validation within a global mode solver. The advantage of using the low Mach number equations and their adjoints is that they are appropriate for flows with variable density, such as flames, but do not require resolution of acoustic waves. Two versions of the adjoint are implemented and assessed: a discrete-adjoint and a continuous-adjoint. The most unstable global mode calculated with the discrete-adjoint has exactly the same eigenvalue as the corresponding direct global mode but contains numerical artifacts near the inlet. The most unstable global mode calculated with the continuous-adjoint has no numerical artifacts but a slightly different eigenvalue. The eigenvalues converge, however, as the timestep reduces. Apart from the numerical artifacts, the mode shapes are very similar, which supports the expectation that they are otherwise equivalent. The continuous-adjoint requires less resolution and usually converges more quickly than the discrete-adjoint but is more challenging to implement. Finally, the direct and adjoint global modes are combined in order to calculate the wavemaker region of a low density jet. © 2011 Elsevier Inc.

Information theory, inference, and learning algorithms

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

SuperJunction IGBTS: An evolutionary step of silicon power devices with high impact potential

15 years ago the vertical SuperJunction (SJ) concept conceived for SJ power MOSFETs was the last, major breakthrough in the field of silicon power devices. Today, the SuperJunction MOSFET technologies have reached a mature stage characterized by gradual performance improvements. SuperJunction Insulated Gate Bipolar Transistors (SJ IGBTs) could interrupt this stagnation holding promise to revitalize voltage classes from 600 up to 1200 V. Such SJ IGBTs surpass by a very significant margin their SJ MOSFET counterparts both in terms of power handling capability, on-state and turn-off losses, all at the same time. On the higher end of the voltage class, SJ IGBTs would top the performance of 1.2 kV IGBTs by a similar margin. © 2012 IEEE.