Junior Applied Mathematics Seminar
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Tue, 18/10/2011 13:15 |
Amy Smith (Oxford Centre for Collaborative Applied Mathematics) |
Junior Applied Mathematics Seminar  |
DH 1st floor SR |
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Motivated by the study of micro-vascular disease, we have been investigating the relationship between the structure of capillary networks and the resulting blood perfusion through the muscular walls of the heart. In order to derive equations describing effective fluid transport, we employ an averaging technique called homogenisation, based on a separation of length scales. We find that the tissue-scale flow is governed by Darcy's Law, whose coefficients we are able to explicitly calculate by averaging the solution of the microscopic capillary-scale equations. By sampling from available data acquired via high-resolution imaging of the coronary capillaries, we automatically construct physiologically-realistic vessel networks on which we then numerically solve our capillary-scale equations. By validating against the explicit solution of Poiseuille flow in a discrete network of vessels, we show that our homogenisation method is indeed able to efficiently capture the averaged flow properties. |
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Tue, 01/11/2011 13:15 |
Laura Gallimore (Oxford Centre for Collaborative Applied Mathematics) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
| Cell motility is a crucial part of many biological processes including wound healing, immunity and embryonic development. The interplay between mechanical forces and biochemical control mechanisms make understanding cell motility a rich and exciting challenge for mathematical modelling. We consider the two-phase, poroviscous, reactive flow framework used in the literature to describe crawling cells and present a stripped down version. Linear stability analysis and numerical simulations provide insight into the onset of polarization of a stationary cell and reveal qualitatively distinct families of travelling wave solutions. The numerical solutions also capture the experimentally observed behaviour that cells crawl fastest when the surface they crawl over is neither too sticky nor too slippy. | |||
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Fri, 18/11/2011 15:30 |
Mohit Dalwadi (Oxford Centre for Industrial and Applied Mathematics) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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A common way to replace body tissue is via donors, but as the world population is ageing at an unprecedented rate there will be an even smaller supply to demand ratio for replacement parts than currently exists. Tissue engineering is a process in which damaged body tissue is repaired or replaced via the engineering of artificial tissues. We consider one type of this; a two-phase flow through a rotating high-aspect ratio vessel (HARV) bioreactor that contains a porous tissue construct. We extend the work of Cummings and Waters [2007], who considered a solid tissue construct, by considering flow through the porous construct described by a rotating form of Darcy's equations. By simplifying the equations and changing to bipolar variables, we can produce analytic results for the fluid flow through the system for a given construct trajectory. It is possible to calculate the trajectory numerically and couple this with the fluid flow to produce a full description of the flow behaviour. Finally, coupling with the numerical result for the tissue trajectory, we can also analytically calculate the particle paths for the flow which will lead to being able to calculate the spatial and temporal nutrient density. |
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Tue, 29/11/2011 13:15 |
Gemma Fay (Oxford Centre for Industrial and Applied Mathematics) |
Junior Applied Mathematics Seminar |
DH 3rd floor SR |
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Turbidity currents are fast-moving streams of sediment in the ocean |
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