Rivulet flow round a horizontal cylinder subject to a\ud uniform surface shear stress

The steady flow of a slowly varying rivulet with prescribed flux in the azimuthal direction round a large stationary horizontal cylinder subject to a prescribed uniform azimuthal surface shear stress is investigated. In particular, we focus on the case where the volume flux is downwards but the shear stress is upwards, for which there is always a solution corresponding to a rivulet flowing down at least part of one side of the cylinder. We consider both a rivulet with constant non-zero contact angle but slowly varying width (i.e. de-pinned contact lines) and a rivulet with constant width but slowly varying contact angle (i.e. pinned contact lines), and show that they have qualitatively different behaviour. When shear is present, a rivulet with constant non-zero contact angle can never run all the way from the top to the bottom of the cylinder, and so we consider the scenario in which an infinitely wide two-dimensional film of uniform thickness covers part of the upper half of the cylinder and “breaks” into a single rivulet with constant non-zero contact angle. In contrast, a sufficiently narrow rivulet with constant width can run all the way from the top to the bottom of the cylinder, whereas a wide rivulet can do so only if its contact lines de-pin, and so we consider the scenario in which the contact lines of a wide rivulet de-pin on the lower half of the cylinder

Gravity-driven draining of a thin rivulet with constant width down a slowly varying substrate

The locally unidirectional gravity-driven draining of a thin rivulet with constant width but slowly varying contact angle down a slowly varying substrate is considered. Specifically, the flow of a rivulet in the azimuthal direction from the top to the bottom of a large horizontal cylinder is investigated. In particular, it is shown that, despite behaving the same locally, this flow has qualitatively different global behaviour from that of a rivulet with constant contact angle but slowly varying width. For example, whereas in the case of constant contact angle there is always a rivulet that runs all the way from the top to the bottom of the cylinder, in the case of constant width this is possible only for sufficiently narrow rivulets. Wider rivulets with constant width are possible only between the top of the cylinder and a critical azimuthal angle on the lower half of the cylinder. Assuming that the contact lines de-pin at this critical angle (where the contact angle is zero) the rivulet runs from the critical angle to the bottom of the cylinder with zero contact angle, monotonically decreasing width and monotonically increasing maximum thickness. The total mass of fluid on the cylinder is found to be a monotonically increasing function of the value of the constant width

Detection of a relic X-ray jet in Cygnus A

We present a 200 ks Chandra ACIS-I image of Cygnus A, and discuss a long linear feature seen in its counterlobe. This feature has a non-thermal spectrum and lies on the line connecting the brighter hotspot on the approaching side and the nucleus. We therefore conclude that this feature is (or was) a jet. However, the outer part of this X-ray jet does not trace the current counterjet observed in radio. No X-ray counterpart is observed on the jet side. Using light-travel time effects we conclude that this X-ray 50 kpc linear feature is a relic jet that contains enough low-energy plasma (gamma ~ 10^3) to inverse-Compton scatter cosmic microwave background photons, producing emission in the X-rays.Comment: 4 pages. Proceedings of "High Energy Phenomena in Relativistic Outflows", held in Dublin, Ireland, September 24-28, 200

Decentralized Constraint Satisfaction

We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at distinct network devices that may not be able to communicate but may interfere, we define natural criteria that a CSP solver must possess in order to be practical. We term these algorithms decentralized CSP solvers. The best known CSP solvers were designed for centralized problems and do not meet these criteria. We introduce a stochastic decentralized CSP solver and prove that it will find a solution in almost surely finite time, should one exist, also showing it has many practically desirable properties. We benchmark the algorithm's performance on a well-studied class of CSPs, random k-SAT, illustrating that the time the algorithm takes to find a satisfying assignment is competitive with stochastic centralized solvers on problems with order a thousand variables despite its decentralized nature. We demonstrate the solver's practical utility for the problems that motivated its introduction by using it to find a non-interfering channel allocation for a network formed from data from downtown Manhattan

Coupling CAD and CFD codes within a virtual integration platform

The Virtual Integration Platform (VIP) is an essential component of the VIRTUE project. It provides a system for combining disparate numerical analysis methods into a simulation environment. The platform allows for defining process chains, allocating of which tools to be used, and assigning users to perform the individual tasks. The platform also manages the data that are imported into or generated within a process, so that a version history of input and output can be evaluated. Within the VIP, a re-usable template for a given process chain can be created. A process chain is composed of one or more smaller tasks. For each of these tasks, a selection of available tools can be allocated. The advanced scripting methods in the VIP use wrappers for managing the individual tools. A wrapper allows communication between the platform and the tool, and passes input and output data as necessary, in most cases without modifying the tool in any way. In this way, third-party tools may also be used without the need for access to source code or special modifications. The included case study demonstrates several advantages of using the integration platform. A parametric propeller design process couples CAD and CFD codes to adapt the propeller to given operating constraints. The VIP template helped eliminate common user errors, and captured enough expert knowledge so that the casual user could perform the given tasks with minimal guidance. Areas of improvements to in-house codes and to the overall process were identified while using the integration platform. Additionally, the process chain was designed to facilitate formal optimisation methods

A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations

A thin rivulet or ridge subject to a uniform transverse\ud shear stress at its free surface due to an external airflow

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations

Thioetherification and Etherification Utilizing Trichloroacetimidates Under Thermal Conditions & Progress Towards an Efficient Synthesis of AQX-1125

The synthesis of ethers and thioethers is necessary as the motifs are ubiquitous in natural products, pharmaceuticals, and are quite useful in numerous synthetic applications. While common methodologies prepare simple ether and thioether substrates, the harsh conditions of these techniques make them unsuitable for complex molecules. The requirement for these functional groups to be prepared by facile and efficient means has led to an investigation into O - and S – alkylations occurring solely under thermal conditions utilizing trichloroacetimidates. The alkylation of thiols by the direct displacement of trichloroacetimidates has been accomplished under thermal conditions (heating in refluxing THF). These reactions proceed to the corresponding thioetherification product without the requirement of an added acid, base, or metal catalyst. This facile procedure provides the sulfide in excellent yields with only the formation of the neutral trichloroacetamide as the side product. Formation of the trichloroacetimidate in situ has also been studied, which provides a convenient method for the formation of sulfides from alcohols in a single flask. A similar methodology towards obtaining etherification products has also been investigated. O – Diphenylmethyl and para-methoxybenzyl trichloroacetimidates in refluxing solvent has shown to effectively convert a variety of alcohols to their corresponding ether without disturbing pre-existing functionality. This methodology provides the subsequent etherification products in moderate to excellent yields with only the formation of the neutral trichloroacetamide as the side product. Additionally, the development of a more efficient and concise total synthesis towards the SHIP1 activator AQX-1125 from trans-dehydroandrosterone has been studied. The synthetic approach features an allylic oxidation of the C7 position and ozonolysis to generate key intermediates. Alternative routes have also been proposed and future investigations will aim to complete this project in the future