Past Applied Analysis and Mechanics Seminar

29 November 2004
17:00
Bjorn Sandstede
Abstract
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.
  • Applied Analysis and Mechanics Seminar
8 November 2004
17:00
Andrew Lorent
Abstract
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.
  • Applied Analysis and Mechanics Seminar
1 November 2004
17:00
Mario Nardone
Abstract
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.
  • Applied Analysis and Mechanics Seminar
7 June 2004
17:00
Abstract
The talk will discuss the variationnal problem on finite dimensional normed spaces and Finsler manifolds. We first review different notions of ellipticity (convexity) for parametric integrands (densities) on normed spaces and compare them with different minimality properties of affine subspaces. Special attention will be given to Busemann and Holmes-Thompson k-area. If time permits, we will then present the first variation formula on Finsler manifolds and exhibit a class of minimal submanifolds.
  • Applied Analysis and Mechanics Seminar

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