BU/Brown PDE Seminar

Each month, a joint PDE seminar between the Departments of Mathematics at Boston University and Brown University and the Division of Applied Mathematics at Brown University will be held. The schedule and location for these events can be found below. To view abstracts, move your mouse over a title. Please visit the BU/Brown PDE Seminar archive page for past events in this seminar series.

Spring 2010

Wednesday, 3 February 2010, 3:30-5:30pm in Room 110 (182 George Street) at Brown

Speakers	Titles
Bob Rink (Vrije Universiteit Amsterdam)	Integrable continuum approximations for the Fermi-Pasta-Ulam lattice: a mechanism for metastability The Fermi-Pasta-Ulam experiment is famous for the unexpected recurrent behavior of long waves. Attempts to explain this observation usually involve an approximation by a KdV equation and a non-rigorous KAM argument. A rigorous justification of the KdV approximation for finite times was given only recently, independently by Bambusi-Ponno and Wayne-Schneider. In this talk I will show how to derive the KdV equation as a resonant normal form, and I will present an improvement to this first approximation. This is a step towards the justification of the so-called metastability scenario.
Marta Lewicka (University of Minnesota)	Scaling laws and reduced theories of the prestrained elastic filmsThis talk will concern the analysis and the rigorous derivation of plate and shell models for thin films exhibiting residual stress at free equilibria. Examples of such structures include growing tissues (e.g. leaves). There, it is conjectured that the cell division results in the formation of non-Euclidean 'target metrics', leading to complicated morphogenesis of the tissue which tries to adapt itself to its internally imposed metric. A possible analysis of these phenomena uses the variational point of view. It departs from the model of 3d non-Euclidean elastic energy, which measures the pointwise deviation of the given deformation from orientation preserving realizations of the target metric. For metrics with non-zero Riemann curvature, the infimum of this energy is strictly positive at free equilibria, that is in the absence of boundary conditions or body forces. In this setting, we analyze the scaling of the energy minimizers in terms of the reference plate's thickness and rigorously derive the corresponding limiting theories, as the vanishing thickness Γ-limits. The theories are differentiated by the embeddability properties of the target metrics - in the same spirit as different scalings of external forces lead to a hierarchy of nonlinear elastic plate theories as recently displayed by Friesecke, James and Müller. Some new relationships with non-smooth isometric embeddings of 2d metrics (on the mid-plate) into R³ are also exhibited.

Speakers

Titles

Bob Rink (Vrije Universiteit Amsterdam)

Integrable continuum approximations for the Fermi-Pasta-Ulam lattice: a mechanism for metastability The Fermi-Pasta-Ulam experiment is famous for the unexpected recurrent behavior of long waves. Attempts to explain this observation usually involve an approximation by a KdV equation and a non-rigorous KAM argument. A rigorous justification of the KdV approximation for finite times was given only recently, independently by Bambusi-Ponno and Wayne-Schneider. In this talk I will show how to derive the KdV equation as a resonant normal form, and I will present an improvement to this first approximation. This is a step towards the justification of the so-called metastability scenario.

Marta Lewicka (University of Minnesota)

Scaling laws and reduced theories of the prestrained elastic filmsThis talk will concern the analysis and the rigorous derivation of plate and shell models for thin films exhibiting residual stress at free equilibria. Examples of such structures include growing tissues (e.g. leaves). There, it is conjectured that the cell division results in the formation of non-Euclidean 'target metrics', leading to complicated morphogenesis of the tissue which tries to adapt itself to its internally imposed metric. A possible analysis of these phenomena uses the variational point of view. It departs from the model of 3d non-Euclidean elastic energy, which measures the pointwise deviation of the given deformation from orientation preserving realizations of the target metric. For metrics with non-zero Riemann curvature, the infimum of this energy is strictly positive at free equilibria, that is in the absence of boundary conditions or body forces. In this setting, we analyze the scaling of the energy minimizers in terms of the reference plate's thickness and rigorously derive the corresponding limiting theories, as the vanishing thickness Γ-limits. The theories are differentiated by the embeddability properties of the target metrics - in the same spirit as different scalings of external forces lead to a hierarchy of nonlinear elastic plate theories as recently displayed by Friesecke, James and Müller. Some new relationships with non-smooth isometric embeddings of 2d metrics (on the mid-plate) into R³ are also exhibited.

Wednesday, 24 February 2010, 3:30-5:30pm in Room MCS 137 (111 Cummington Street) at Boston University

Speakers Titles

Gigliola Staffilani (MIT) TBAABSTRACT

Tobias Schneider (Harvard University) TBAABSTRACT
Wednesday, 17 March 2010, 3:30-5:30pm in Room 110 (182 George Street) at Brown:

Speakers Titles

Arnd Scheel (University of Minnesota) TBA
Wednesday, 28 April 2010, 3:30-5:30pm in Room MCS 137 (111 Cummington Street) at Boston University

Speakers	Titles
Gigliola Staffilani (MIT)	TBAABSTRACT
Tobias Schneider (Harvard University)	TBAABSTRACT