Past Junior Applied Mathematics Seminar

20 November 2009
16:30
Jason Zhong
Abstract
Hairsine-Rose (HR) model is the only multi sediment size soil erosion model. The HR model is modifed by considering the effects of sediment bedload and bed elevation. A two step composite Liska-Wendroff scheme (LwLf4) which designed for solving the Shallow Water Equations is employed for solving the modifed Hairsine-Rose model. The numerical approximations of LwLf4 are compared with an independent MOL solution to test its validation. They are also compared against a steady state analytical solution and experiment data. Buffer strip is an effective way to reduce sediment transportation for certain region. Modifed HR model is employed for solving a particular buffer strip problem. The numerical approximations of buffer strip are compared with some experiment data which shows good matches.
  • Junior Applied Mathematics Seminar
6 November 2009
16:30
Abstract
Abstract: Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs.
  • Junior Applied Mathematics Seminar
23 October 2009
16:30
Abstract
Dislocation channel-veins and Persist Slip Band (PSB) structures are characteristic configurations in material science. To find out the formation of these structures, the law of motion of a single dislocation should be first examined. Analogous to the local expansion in electromagnetism, the self induced stress is obtained. Then combining the empirical observations, we give a smooth mobility law of a single dislocation. The stability analysis is carried our asymptotically based on the methodology in superconducting vortices. Then numerical results are presented to validate linear stability analysis. Finally, based on the evidence given by the linear stability analysis, numerical experiments on the non-linear evolution are carried out.
  • Junior Applied Mathematics Seminar
8 May 2009
16:30
Thomas Woolley
Abstract
Soliton like structures called “stable droplets” are found to exist within a paradigm reaction<br /> diffusion model which can be used to describe the patterning in a number of fish species. It is<br /> straightforward to analyse this phenomenon in the case when two non-zero stable steady states are<br /> symmetric, however the asymmetric case is more challenging. We use a recently developed<br /> perturbation technique to investigate the weakly asymmetric case.<br />
  • Junior Applied Mathematics Seminar
27 February 2009
16:30
Lennart Hilbert
Abstract
Brownian Molecular Motors are crucial for cell motility, muscle contraction or any other mechanical task carried out by proteins. After a short introduction to protein motors, I will talk about a numerical appraoch I worked on during the last months, which should enable us to deduct properties for a broad range of protein motors. A special focus should lie on the calculation of the eigenvalue spectrum, which gives insight to motors' stability.
  • Junior Applied Mathematics Seminar
30 January 2009
16:30
Athanasios Tsanas
Abstract
The circulatory system is the most important and amongst the most complicated mechanisms in the human body. Consisting of the heart, the arteries and the veins, it is amply aided by a variety of mechanisms aiming to facilitate adequate perfusion of the body tissues at the appropriate pressure. On this talk I am focusing on the development of a computational model which relates patient specific factors (age, gender, whether someone is an athlete/smokes etc) and their effects on different vascular regions which ultimately determine the arterial pressure and the cardiac output.
  • Junior Applied Mathematics Seminar

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