Tuesday, September 17, 4pm-5:15pm
Rolla Building G5

Samuel Walsh
Associate Professor
Mathematics Department
University of Missouri

Title: Water waves with smooth exponentially localized vorticity

Abstract: In this talk, we discuss recent success in establishing the existence of solutions to the water wave problem with exponentially decaying vorticity. These are two-dimensional stationary waves in a finite-depth body of water beneath vacuum. An external gravitational force acts in the bulk, and the effects of surface tension are felt on the air-sea interface. Our approach involves modeling the corresponding stream function as a spike solution to a singularly perturbed elliptic PDE. This is joint work with Mats Ehrnström (NTNU) and Chongchun Zeng (Georgia Tech). 

Host: Murphy

Friday, October 11, 4pm-5:15pm
Rolla Building G5

Jiangguo Liu
Professor
Department of Mathematics
Colorado State University

Title: Weak Galerkin Finite Element Methods for Partial Differential Equations

Abstract:  In this talk, we discuss the novel weak Galerkin (WG) finite element methods for several different types of partial differential equations (PDEs).  The WG methodology provides reconstructed weak gradient or divergence or curl at the discrete level through integration by parts. Then these reconstructed discrete gradient or divergence or curl can be used to approximate the classical counterparts in the variational forms for the elliptic, elasticity, and Stokes equations.  WG allows use of polytopal meshes.  Combined with time-marching schemes, WG finite element methods can be developed for time-dependent PDEs.  We shall discuss efficient implementation strategies for WG in Matlab and C++.  Numerical results of WG for various applications (Darcy flow, Stokes flow, linear elasticity) will be presented. This talk is based on a series of joint work with several collaborators.

Host: He

Friday, October 25, 4pm-5:15pm
Rolla Building G5

Satoshi Masaki
Associate Professor
Department of Systems Innovation
Graduate School of Engineering Science
Osaka University

Title: Scattering for mass-critical Klein-Gordon equation in high dimensions

Abstract: We consider the asymptotic behavior of solutions to the mass-critical Klein-Gordon equation. Because of the nonlinear nature, there are several kinds of possible behavior. In this talk, I consider a sharp criterion for scattering. The two-dimensional case was previously studied by Killip-Stovall-Visan. We extend the result to higher dimensions. One difficulty is the non-polynomial nature of the nonlinearity. This talk is based on joint work with Guo (Monash) and Cheng (Nanjing).

Host: Murphy

Friday, November 8, 4pm-5:15pm
Rolla Building G5

Keith Promislow
Professor and Chair
Department of Mathematics
Michigan State University

 Title: The Packing Dichotomy and Morphological Complexity in Amphiphilic Polymers

Abstract:  Amphiphlilic molecules, also known as surfactants, are composed of two components, one with a strong affinity for a solvent and one with a strong aversion. When blended with solvent they undergo a novel phase separation process that produces morphologies that are of molecular width in one or more directions (thin). A key benchmark problem is to predict the evolution of a codimension one interface that is actively absorbing molecules that are dispersed at low density within the solvent. This leads to a fundamental ``packing dichotomy'' that balances the energetic preference for the dispersed molecules to join a structure against the preference for the structure to remain thin. We model this system with the Functionalized Cahn Hilliard free energy, and analyze its gradient flow, rigorously deriving a curve-lengthening evolution for codimension-one interfaces immersed in a solvent with a weak dispersion of amphiphilic molecules. We supplement the analysis with detailed simulations that show that as the initial density of dispersed molecules is increased the curve lengthening regime gives way to pearling (internal micelle formation) and a bicycle-chain buckling evolution that generates corners, endcaps, and loops. Further increases in initial density lead to curve splitting. We show that the resolution of the packing dichotomy lead to delicate choices that underpin what the experimental literature calls the onset of morphological complexity. 

Host: Han

Friday, November 15, 4pm-5:15pm
Rolla Building G5

Michael Schneier
Math Research Center Postdoctoral Fellow
Department of Mathematics
University of Pittsburgh

Host: Singler

Friday, November 22, 4pm-5:15pm
Rolla Building G5

Qi Wang
Professor
Department of Mathematics
University of South Carolina

Host: Han

Tuesday, December 3, 4pm-5:15pm
Rolla Building G5

Host: Insall

Friday, December 6, 4pm-5:15pm
Rolla Building G5

Jun-Ichi Segata
Professor
Department of Mathematical Sciences
Kyushu University

Host: Murphy