Continuous transformation groups and series solution of initial value problems

This paper details an efficient method of deriving séries solutions of initial value problems traditionally encountered in non-linear mechanics. The developed technique, based on the theory of continuous transformation groups, can be used to solve autonomous as well as non-autonomous systems of ordinary differential equations. Solutions to selected problems are presented for illustration. In addition, the notion of invariants of a transformation group provides information on the nature of trajectories of an initial value problem.     

Experimental investigation of a 140-GHz coaxial gyrotron oscillator

We report experimental results on a megawatt power level, 140-GHz coaxial gyrotron oscillator. The gyrotron has an inverted magnetron injection gun (IMIG) designed for operation at up to 95 kV and 88 A. The IMIG has an inner grounded anode which extends from the center of the gun down through the entire length of the tube including the cavity and collector. The IMIG was tested at up to 105 kV and 93 A in 3 μs pulses, achieving an electron beam power of 10 MW. The output power from the coaxial gyrotron cavity was transported to an internal mode converter and a single mirror that coupled the power out transversely from the tube axis. A maximum output power of up to 1 MW was obtained in the TE_27,11 mode at 142 GHz at an efficiency of 16%, about one half of the design efficiency. The reduced efficiency was attributed to nonuniformity of the cathode emission and the sensitivity to the relative alignment of the electron gun, coaxial insert, and cavity. The cathode emission over the azimuthal angle was measured for two cathodes and was shown to be nonuniform due to both temperature and emitter work function nonuniformity. The gyrotron was also tested in two alternate configurations: 1) with the internal mode converter removed (axial output), and 2) with both the internal converter and the coaxial insert removed (empty cavity). In operation in the empty cavity configuration, which is equivalent to a conventional gyrotron oscillator, output power of up to 0.9 MW was observed     

Free boundary viscous flows at micro and mesolevel during liquid composites moulding process

Numerical simulation aspects, related to low Reynolds number free boundary viscous flows at micro and mesolevel during the resin impregnation stage of the liquid composite moulding process (LCM), are presented in this article. A free boundary program (FBP), developed by the authors, is used to track the movement of the resin front accurately by accounting for the surface tension effects at the boundary. Issues related to the global and local mass conservation (GMC and LMC) are identified and discussed. Unsuitable conditions for LMC and consequently GMC are uncovered at low capillary numbers, and hence a strategy for the numerical simulation of such flows is suggested. FBP encompasses a set of subroutines that are linked to modules in ANSYS. FBP can capture the void formation dynamics based on the analysis developed. We present resin impregnation dynamics in two dimensions. Extension to three dimensions is a subject for further research. Several examples are shown and efficiency of different stabilization techniques are compared. Copyright © 2004 John Wiley & Sons, Ltd.     

Iminoethers—III : Tetracyclic quinazolones derived from cyclodipeptide mono iminoethers

Iminoethers derived from a series of prolyl diketopiperazines have been reacted with anthranilic acid to produce tetracyclic quinazolones. It has been shown that the two diastereomeric iminoethers derived from cyclo (l-Pro-l-Val) and cyclo (l-Pro-d-Val) lead to enantiomeric products with the two hydrogens at the asymmetric C atoms oriented trans to each other.     

Methanol diffusion rates through the anode diffusion layer in direct methanol fuel cells from limiting current measurements

Metal foams may be used in direct methanol fuel cells to feed reactants to the catalyst layer and to collect current from the resulting electrochemical reaction. Although the mass transfer from the metal foam to the underlying gas diffusion layer (GDL) is diffusion-dominated, it is found that at a fixed methanol concentration, the limiting current density increases with increasing methanol flow rates. This unexpected result is attributed to the more efficient removal of product CO₂ from the GDL. A methodology is developed to estimate the effective diffusion coefficient of methanol in the anode diffusion layer from limiting current density measurements, and to extract the fraction of GDL volume occupied by CO₂.     

Investigation of fiber motion near solid boundaries in simple shear flow

In this paper, fiber motion near a planar wall was investigated using a planar shear flow apparatus. Fibers were placed (one at a time) perpendicular to the flow direction at various locations throughout the flow field. The location and orientation of each fiber versus time was measured, using an image processing system, until the fiber aligned with the flow direction. When the centroid of the fiber was located at distances greater than a fiber length from the wall, Jeffery's equations governing particle motion were verified. For distances less than a fiber length and greater than a fiber diameter from the wall, the fiber experienced an increased rate of rotation. In this regime, the motion of the fiber could be described by Jeffery's equations if an increased effective shear rate was used. The effective shear rate was found to increase logarithmically with decreasing separation distance. The wall effect was higher for longer aspect ratio fibers and was also a function of orientation; fibers oriented perpendicular to the wall rotated faster than those oriented parallel to the wall at the same separation distance. Once the fiber aligned with the flow direction, it ceased to rotate within the field of view. In this orientation, the wall had a stabilizing effect on the fiber. In efforts to relate the increase in shear rate to the aspect ratio of the fiber and the separation distance between the fiber and a solid wall, a translation model based on the work of De Mestre and Russel was explored. This model allows one to quantify the increase in shear rate experienced by the fiber due to the presence of a wall or obstruction in the flow field. However, the model has its limitations and care should be taken when applying this model outside its realm of validity. When compared to experimental data, the translation model provides a very good estimate of the increased shear rate experienced by the fiber when it is located less than 2/3 of a fiber length from a planar wall. Received: 20 April 2000 Accepted: 28 September 2000     

Spontaneous radial capillary impregnation across a bank of aligned micro-cylinders. Part II: Experimental investigations

This paper presents an experimental approach to study the capillary impregnation of a liquid across an array of parallel micro-cylinders. The technique presented successfully validates the theoretical findings of part I, and provides a methodology to calculate the fill time and the overall capillary impregnation dynamics for any arbitrary cylindrical sample made of aligned micro-cylinders, by taking into account the role of the trapped gas, which opposes and slows down the inward capillary flow.