Abstract

Two-dimensional boundary layer flows in quiet disturbance environments are known to become unstable to Tollmien–Schlichting waves. The experimental work of Liepmann et al. (J Fluid Mech 118:187–200, 1982), Liepmann and Nosenchuck (J Fluid Mech 118:201–204, 1982) showed how it is possible to control and reduce unstable Tollmien–Schlichting wave amplitudes using unsteady surface heating. We consider the problem of an oncoming planar compressible subsonic boundary layer flow with a three-dimensional vibrator mounted on a flat plate, and with surface heating present. It is shown using asymptotic methods based on triple-deck theory that it is possible to choose an unsteady surface heating distribution to cancel out the response due to the vibrator. An approximation based on the exact formula is used successfully in numerical computations to confirm the findings. The results presented here are a generalisation of the analogous results for the two-dimensional problem in Brennan et al. (J Fluid Mech 909:A16-1, 2020).

Alzheimer's disease, the most common form of dementia, is a systemic neurological disorder associated with the formation of toxic, pathological aggregates of proteins within the brain that lead to severe cognitive decline, and eventually, death. In normal physiological conditions, the brain rids itself of toxic proteins using various clearance mechanisms. The efficacy of brain clearance can be adversely affected by the presence of toxic proteins and is also known to decline with age. Motivated by recent findings, such as the connection between brain cerebrospinal fluid clearance and sleep, we propose a mathematical model coupling the progression of toxic proteins over the brain's structural network and protein clearance. The model is used to study the interplay between clearance in the brain, toxic seeding, brain network connectivity, aging, and progression in neurodegenerative diseases such as Alzheimer's disease. Our findings provide a theoretical framework for the growing body of clinical results showing that clearance plays an important role in the etiology, progression and treatment of Alzheimer's disease.

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We examine and compare a variety of modelling frameworks to analyse and optimise a fleet management schedule. Given a set of tasks, in addition to the skills and availability of collaborators and vehicles we generate work schedules adhering to the priorities of TECMIC including minimising the number of collaborators used, minimising breaks, and minimising collaborator overtime. The objective being to uncover the optimal schedule with respect to their priorities. We evaluate potential schedules using a cost function defined by TECMIC's objectives, and aim to minimise the cost function with a genetic algorithm. In addition, we propose a systematisation of the problem in terms of integer programming.