Junior Applied Mathematics Seminar
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Fri, 23/10/2009 16:30 |
Yichao Zhu (University of Oxford) |
Junior Applied Mathematics Seminar  |
DH 1st floor SR |
| 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. | |||
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Fri, 06/11/2009 16:30 |
Kit Yates (University of Oxford) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
| 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. | |||
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Fri, 20/11/2009 16:30 |
Jason Zhong (University of Oxford) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
| 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. | |||
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Fri, 04/12/2009 16:30 |
Ornella Cominetti (University of Oxford) |
Junior Applied Mathematics Seminar |
DH 3rd floor SR |
| Soft (fuzzy) clustering techniques are often used in the study of high-dimensional datasets, such as microarray and other high-throughput bioinformatics data. The most widely used method is Fuzzy C-means algorithm (FCM), but it can present difficulties when dealing with nonlinear clusters. In this talk, we will overview and compare different clustering methods. We will introduce DifFUZZY, a novel spectral fuzzy clustering algorithm applicable to a larger class of clustering problems than FCM. This method is better at handling datasets that are curved, elongated or those which contain clusters of different dispersion. We will present examples of datasets (synthetic and real) for which this method outperforms other frequently used algorithms | |||
