Colloquium index

Vigre seminars

Undergrad seminar

Clifford lectures

"Title"

Abstract:

"Title"

Abstract:

Speaker, Institution

"Title"

Abstract:

Angela Gallegos, Occidental College

"Mechanical and Geometrical Aspects of Uterine Contractions"

Abstract:
Uterine contractions play a critical role in labor and parturition and are an important factor in female reproductive health. However, how uterine contractions are regulated and controlled is not well understood. I analyze how structural components such as muscle layer arrangement and muscle wall geometry affect uterine contractions, utilizing a theoretical framework that makes the force-balance assumption of quasi-static equilibrium. Linear elasticity equations of passive deformation are also considered in order to investigate both non-pregnant and pregnant cases. Numerical analysis indicates that the existent muscle layer is necessary to achieve wall movement in the non-pregnant uterus with realistic forces as well as to minimize movement outside of the uterus organ. Model results indicate that a cylinder is a reasonable approximation to the uterus in the non-pregnant state. Other simulations indicate that the ellipsoid is likely a better approximation than the sphere to the term pregnant uterus and that the process of cervical dilation during labor is mechanically self reinforcing. I discuss biological implications of these results and propose future extensions to the work presented.

Location: Gibson 308

Charles Doering, University of Michigan

"Theoretical, Analytical and Computational Studies of Convection and Turbulence in a Fluid Saturated Porous Layer"

Abstract:
Thermal convection is the buoyancy driven flow resulting when a fluid is heated from below and cooled from above.  Convection in porous media is relevant to a variety of phenomena ranging from geothermal energy transport to fiberglass insulation.  In this presentation we provide some general background as well as describing some current theoretical and computational research where the Darcy-Boussinesq equations are used to study convection and heat transport over a broad range of heating levels as measured by the nondimensional Rayleigh number.  High resolution direct numerical simulations are performed to explore the modes of convection and measure the heat transport as quantified by the Nusselt number, the enhancement factor of total heat flux over pure conduction alone. Rigorous upper estimates on the high Rayleigh number heat transport have been derived and at high Rayleigh numbers they are of the scaling form predicted by Howard's classical marginally stable boundary layer argument. The bounds are compared directly to the results of the simulations as well as to real laboratory experiments.  This is joint work with (former) students Jesse Otero and Lubomira A. Dontcheva, and (former) postdocs Hans Johnston, Rodney A. Worthing, Alexander Kurganov and Guergana Petrova.  It is the content of a paper published in Journal of Fluid Mechanics.

Speaker, Institution

"Title"

Abstract:

Jennifer K. Ryan, Virginia Tech

"Local post-processing for the discontinuous Galerkin method and applications"

Abstract:
In this presentation an overview of post-processing for discontinuous Galerkin methods will be given. This accuracy enhancement technique has been shown to improve discontinuous Galerkin approximations from order k+1 to order 2k+1 for linear hyperbolic equations, where k is the highest polynomial used in the approximation. This talk will focus on extensions of this technique to include nonuniform meshes, post-processing near a discontinuity or boundary, and post-processing for derivatives. The specific technique that we will examine was introduced by Cockburn, Luskin, Shu, and Süli. Using a negative norm estimate along with previous results of Bramble and Schatz as well as Mock and Lax, Cockburn et al. are able to show that the order of accuracy of the approximation can almost be doubled. Additionally, a uniform mesh assumption allows for simple implementation via small matrix-vector multiplications making the application of this post-processor attractive. A discussion of implementation issues surrounding previously used assumptions of the post-processor as well as extension to a variety of problems will be given. Further, applications in aero-acoustics as well as visualization of streamlines will be explored.

David Cox, Amherst University

"Why Eisenstein proved the Eisenstein Critereon and why Schoenemann discovered it first."