Constrained dogleg methods for nonlinear systems with simple bounds

We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affine-scaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is named Constrained Dogleg method. It generates only strictly feasible iterates. Global and locally fast convergence is ensured under standard assumptions. The method has been implemented in the Matlab solver CoDoSol that supports several diagonal scalings in both spherical and elliptical trust region frameworks. We give a brief account of CoDoSol and report on the computational experience performed on a number of representative test problem

Computational design and analysis of MOVPE reactors

This paper presents a fundamental numerical analysis of flow and heat transfer in a vertical rotating disk reactor. These reactors are commonly used for growing thin films via chemical vapor deposition. Under certain conditions, rotating disk reactors have been found to exhibit multiple steady states, where desirable and undesirable flow patterns co-exist at the same conditions. The focus of this research is to predict the onset of multiplicity with respect to key system parameters, and thereby give guidance on reactor design and operation. Using bifurcation analysis algorithms we directly track what we believe is a global stability limit (the onset of multiple solutions). Results for a model system with constant physical and transport properties along with the Boussinesq approximation are compared to a model with actual fluid properties for nitrogen gas coupled with the ideal gas law

Vapor-phase synthesis and characterization of ZnSe nanoparticles

Compound semiconductor nanoparticles are an exciting class of materials whose unique optical and electronic properties can be exploited in a variety of applications, including optoelectronics, photovoltaics, and biophotonics. The most common route for synthesizing such nanoparticles has been via liquid-phase chemistry in reverse micelles. This paper discusses a flexible vapor-phase technique for synthesis of crystalline compound semiconductor nanoparticles using gas-phase condensation reactions near the stagnation point of a counterflow jet reactor. ZnSe nanoparticles were formed by reacting vapors of dimethylzinc: triethylamine adduct and hydrogen selenide at 120 Torr and room temperature (28 °C). No attempt was made to passivate the surface of the particles, which were collected as random aggregates on silicon wafers or TEM grids placed downstream of the reaction zone. Particle characterization using TEM, electron diffraction, Raman and EDAX revealed that the aggregates consisted of polycrystalline ZnSe nanoparticles, almost monodisperse in size (with diameters of ~40 nm). The polycrystalline nanoparticles appear to have been formed by coagulation of smaller single-crystalline nanoparticles with characteristic size of 3-5 run

A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory

We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The initial stages can even be computed diagrammatically. The method is formulated within the framework of an exact renormalization group for SU(N) Yang-Mills gauge theory, incorporating an effective cutoff through a manifest spontaneously broken SU(N|N) gauge invariance. We demonstrate the technique with a compact calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing, for the first time at finite N