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.

A simple combinatorial method aiding research on single-walled carbon nanotube growth on substrates

Establishing fabrication methods of carbon nanotubes (CNTs) is essential to realize many applications expected for CNTs. Catalytic growth of CNTs on substrates by chemical vapor deposition (CVD) is promising for direct fabrication of CNT devices, and catalyst nanoparticles play a crucial role in such growth. We have developed a simple method called "combinatorial masked deposition (CMD)", in which catalyst particles of a given series of sizes and compositions are formed on a single substrate by annealing gradient catalyst layers formed by sputtering through a mask. CMD enables preparation of hundreds of catalysts on a wafer, growth of single-walled CNTs (SWCNTs), and evaluation of SWCNT diameter distributions by automated Raman mapping in a single day. CMD helps determinations of the CVD and catalyst windows realizing millimeter-tall SWCNT forest growth in 10 min, and of growth curves for a series of catalysts in a single measurement when combined with realtime monitoring. A catalyst library prepared using CMD yields various CNTs, ranging from individuals, networks, spikes, and to forests of both SWCNTs and multi-walled CNTs, and thus can be used to efficiently evaluate self-organized CNT field emitters, for example. The CMD method is simple yet effective for research of CNT growth methods. © 2010 The Japan Society of Applied Physics.

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.