Differential Equations and Applications Seminar
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Thu, 29/04/2010 16:30 |
Alain Goriely (University of Oxford) |
Differential Equations and Applications Seminar  |
DH 1st floor SR |
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Thu, 06/05/2010 16:30 |
Arezki Boudaoud (Department of Biology Ecole Normale Supérieure de Lyon) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| How does form emerge from cellular processes? Using cell-based mechanical models of growth, we investigated the geometry of leaf vasculature and the cellular arrangements at the shoot apex. These models incorporate turgor pressure, wall mechanical properties and cell division. In connection with experimental data, they allowed us to, on the one hand, account for characteristic geometrical property of vein junctions, and, on the other hand, speculate that growth is locally regulated. | |||
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Thu, 13/05/2010 16:30 |
Thomas Erneux (Universite Libre de Bruxelles) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| In the first part of my presentation, I plan to review several applications modelled by delay differential equations (DDEs) starting from familiar examples such as traffic flow problems to physiology and industrial problems. Although delay differential equations have the reputation to be difficult mathematical problems, there is a renewed interest for both old and new problems modelled by DDEs. In the second part of my talk, I’ll emphasize the need of developing asymptotic tools for DDEs in order to guide our numerical simulations and help our physical understanding. I illustrate these ideas by considering the response of optical optoelectronic oscillators that have been studied both experimentally and numerically. | |||
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Thu, 20/05/2010 16:30 |
Gero Miesenboeck (Oxford) |
Differential Equations and Applications Seminar |
L2 |
| An emerging set of methods enables an experimental dialogue with biological systems composed of many interacting cell types—in particular, with neural circuits in the brain. These methods are sometimes called “optogenetic” because they employ light-responsive proteins (“opto-“) encoded in DNA (“-genetic”). Optogenetic devices can be introduced into tissues or whole organisms by genetic manipulation and be expressed in anatomically or functionally defined groups of cells. Two kinds of devices perform complementary functions: light-driven actuators control electrochemical signals; light-emitting sensors report them. Actuators pose questions by delivering targeted perturbations; sensors (and other measurements) signal answers. These catechisms are beginning to yield previously unattainable insight into the organization of neural circuits, the regulation of their collective dynamics, and the causal relationships between cellular activity patterns and behavior. | |||
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Thu, 27/05/2010 16:30 |
Kody Law (University of Warwick) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, as a result of the effective potential created by a stable vortex in the other component. The resulting vortex-bright solitary waves, which naturally generalize the recently experimentally observed dark-bright solitons, are examined both in the homogeneous medium and in the presence of parabolic and periodic external confinement and are found to be very robust. | |||
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Thu, 03/06/2010 16:30 |
Alexander Movchan (University of Liverpool) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Bloch Floquet waves are considered in structured media. Such waves are dispersive and the dispersion diagrams contain stop bands. For an example of a harmonic lattice, we discuss dynamic band gap Green’s functions characterised by exponential localisation. This is followed by simple models of exponentially localised defect modes. Asymptotic models involving uniform asymptotic approximations of physical fields in structured media are compared with homogenisation approximations. | |||
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Thu, 10/06/2010 16:30 |
Chris Howls (University of Southampton) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
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Thu, 17/06/2010 16:30 |
Leonid Bunimovich (Georgia Tech USA) |
Differential Equations and Applications Seminar |
OCCAM Common Room (RI2.28) |
| The question in the title seems to be neglected in the studies of open dynamical systems. It occurred though that the features of dynamics may play a role comparable to the one played by the size of a hole. For instance, the escape through the smaller hole could be faster than through the larger one. These studies revealed as well a new role of the periodic orbits in the dynamics which could be exactly quantified in some cases. Moreover, this new approach allows to characterize the elements of networks by their dynamical properties (rather than by static ones like centrality, betweenness, etc.) | |||
