Applied Analysis and Mechanics Seminar
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Mon, 11/10/2004 17:00 |
Peter Lax (Courant Institute) |
Applied Analysis and Mechanics Seminar  |
L1 |
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Mon, 18/10/2004 17:00 |
Toby O'Neil (Open University) |
Applied Analysis and Mechanics Seminar |
L1 |
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Mon, 25/10/2004 17:00 |
Ali Taheri (Oxford) |
Applied Analysis and Mechanics Seminar |
L1 |
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Mon, 01/11/2004 17:00 |
Mario Nardone (Oxford) |
Applied Analysis and Mechanics Seminar |
L1 |
| While the classification of crystals made up by just one atom per cell is well-known and understood (Bravais lattices), that for more complex structures is not. We present a geometric way classifying these crystals and an arithmetic one, the latter introduced in solid mechanics only recently. The two approaches are then compared. Our main result states that they are actually equivalent; this way a geometric interpretation of the arithmetic criterion in given. These results are useful for the kinematic description of solid-solid phase transitions. Finally we will reformulate the arithmetic point of view in terms of group cohomology, giving an intrinsic view and showing interesting features. | |||
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Mon, 08/11/2004 17:00 |
Andrew Lorent (Oxford) |
Applied Analysis and Mechanics Seminar |
L1 |
| Marstrand's Theorem is a one of the classic results of Geometric Measure Theory, amongst other things it says that fractal measures do not have density. All methods of proof have used symmetry properties of Euclidean space in an essential way. We will present an elementary history of the subject and state a version of Marstrand's theorem which holds for spaces whose unit ball is a polytope. | |||
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Mon, 15/11/2004 17:00 |
Jan Kolar (Prague) |
Applied Analysis and Mechanics Seminar |
L1 |
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Mon, 29/11/2004 17:00 |
Bjorn Sandstede (Surrey) |
Applied Analysis and Mechanics Seminar |
L1 |
| Coherent structures, or defects, are interfaces between wave trains with possibly different wavenumbers: they are time-periodic in an appropriate coordinate frame and connect two, possibly different, spatially-periodic travelling waves. We propose a classification of defects into four different classes which have all been observed experimentally. The characteristic distinguishing these classes is the sign of the group velocities of the wave trains to either side of the defect, measured relative to the speed of the defect. Using a spatial-dynamics description in which defects correspond to homoclinic and heteroclinic orbits, we then relate robustness properties of defects to their spectral stability properties. If time permits, we will also discuss how defects interact with each other. | |||
