Applied Analysis and Mechanics Seminar
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Mon, 25/04/2005 17:00 |
Christof Melcher (Humboldt University, Berlin) |
Applied Analysis and Mechanics Seminar  |
L1 |
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Wed, 27/04/2005 17:00 |
Nirmalendu Chaudhuri (Australian National University) |
Applied Analysis and Mechanics Seminar |
L1 |
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Mon, 02/05/2005 17:00 |
Matania Ben-Artzi (Hebrew University) |
Applied Analysis and Mechanics Seminar |
L1 |
| An important class of nonlinear parabolic equations is the class of quasi-linear equations, i.e., equations with a leading second-order (in space) linear part (e.g., the Laplacian) and a nonlinear part which depends on the first-order spatial derivatives of the unknown function. This class contains the Navier-Stokes system of fluid dynamics, as well as "viscous" versions (or "regularized") of the Hamilton-Jacobi equation, nonlinear hyperbolic conservation laws and more. The talk will present various recent results concerning existence/uniqueness (and nonexistence/nonuniqueness) of global solutions. In addition, a new class of "Bernstein-type" estimates of derivatives will be presented. These estimates are independent of the viscosity parameter and thus lead to results concerning the "zero-viscosity" limit. | |||
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Mon, 09/05/2005 17:00 |
Kewei Zhang (Sussex) |
Applied Analysis and Mechanics Seminar |
L1 |
| We use the partial differential inclusion method to establish existence of infinitely many weak solutions to the one-dimensional version of the Perona-Malek anisotropic diffusion model in the theory of image processing. We consider the homogeneous Neumann problem as the model requires. . | |||
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Mon, 30/05/2005 17:00 |
Richard D James (Minnesota) |
Applied Analysis and Mechanics Seminar |
L1 |
| Bacteriophage T4 is a virus that attacks bacteria by a unique mechanism. It lands on the surface of the bacterium and attaches its baseplate to the cell wall. Aided by Brownian motion and chemical bonding, its tail fibres stick to the cell wall, producing a large moment on the baseplate. This triggers an amazing phase transformation in the tail sheath, of martensitic type, that causes it to shorten and fatten. The transformation strain is about 50%. With a thrusting and twisting motion, this transformation drives the stiff inner tail core through the cell wall of the bacterium. The DNA of the virus then enters the cell through the hollow tail core, leading to the invasion of the host. This is a natural machine. As we ponder the possibility of making man-made machines that can have intimate interactions with natural ones, on the scale of biochemical processes, it is an interesting prototype. We present a mathematical theory of the martensitic transformation that occurs in T4 tail sheath. Following a suggestion of Pauling, we propose a theory of an active protein sheet with certain local interactions between molecules. The free energy is found to have a double-well structure. Using the explicit geometry of T4 tail sheath we introduce constraints to simplify the theory. Configurations corresponding to the two phases are found and an approximate formula for the force generated by contraction is given. The predicted behaviour of the sheet is completely unlike macroscopic sheets. To understand the position of this bioactuator relative to nonbiological actuators, the forces and energies are compared with those generated by inorganic actuators, including nonbiological martensitic transformations. Joint work with Wayne Falk, WF [-at-] ddt [dot] biochem [dot] umn [dot] edu Wayne Falk and R. D. James, An elasticity theory for self-assembled protein lattices with application to the martensitic transformation in Bacteriophage T4 tail sheath, preprint. K. Bhattacharya and R. D. James, The material is the machine, Science 307 (2005), pp. 53-54. | |||
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Mon, 06/06/2005 17:00 |
Georg Dolzmann (College Park, Maryland) |
Applied Analysis and Mechanics Seminar |
L1 |
| We derive a two-dimensional compressible elasticity model for thin elastic sheets as a Gamma-limit of a fully three-dimensional incompressible theory. The energy density of the reduced problem is obtained in two steps: first one optimizes locally over out-of-plane deformations, then one passes to the quasiconvex envelope of the resulting energy density. This work extends the results by LeDret and Raoult on smooth and finite-valued energies to the case incompressible materials. The main difficulty in this extension is the construction of a recovery sequence which satisfies the nonlinear constraint of incompressibility pointwise everywhere. This is joint work with Sergio Conti. | |||
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Mon, 13/06/2005 17:00 |
Petr Plechac (University of Warwick) |
Applied Analysis and Mechanics Seminar |
L1 |
