CMU Applied Mathematics Seminar

Fall 2018

Organizers



If you would like to give a talk, please email any one of us.

Meeting Times

Fridays, 2:00pm – 3:00pm, in Pearce 223. 

Past seminars: Fall 2015, Spring 2015, Fall 2014, Spring 2016, Fall 2017, Spring 2018

Schedule

Date

Speaker

Title

10/12/18

TBA

TBA

10/19/18

Yip, Nung Kwan (Purdue University)

Dynamics of a second order gradient model for phase transitions

01/25/19

TBA

TBA

02/01/19

TBA

TBA

02/08/19

TBA

TBA

02/15/19

TBA

TBA

03/01/19

(4pm - 5pm)

Shixu Meng (University of Michigan)

Qualitative approaches to inverse scattering and wave motion in complex media

03/15/19

TBA

TBA

03/22/19

TBA

TBA

03/29/19

TBA

TBA

04/12/19

TBA

TBA

04/19/19

(1:30pm - 2:30pm)

Lewei Zhao (Wayne State Univ.)

Finite Element Method for Laplace Equation in Two-dimensional Domains with a Singular Fracture




09/27/19

Shan, Chunhua (Univ of Toledo)

TBA



Speaker: Yip, Nung Kwan
Title: Dynamics of a second order gradient model for phase transitions
Abstract: We prove in a radially symmetric geometry, the convergence in the sharp interfacial limit, to motion by mean curvature of a second order gradient model for phase transition. This is in spirit similar to the classical Allen-Cahn theory of phase boundary motion. However the corresponding dynamical equation is fourth order thus creating some challenging difficulties for its analysis. A characterization and stability analysis of the optimal profile are performed which are in turn used in the proof of convergence of an asymptotic expansion. (This is joint work with Drew Swartz.)

Speaker: Shixu Meng
Title :Qualitative approaches to inverse scattering and wave motion in complex media
Abstract: The mathematical theory of wave scattering describes the interaction of waves (e.g., sound or electromagnetic) with natural or manufactured perturbations of the medium through which they propagate. The goal of inverse wave scattering (or in short imaging) is to estimate the medium from observations of the wave field. It has applications in a broad spectrum of scientific and engineering disciplines, including seismic imaging, radar, astronomy, medical diagnosis, and non-destructive material testing. Qualitative approaches to inverse scattering problems have been the focus of much activity in the mathematics community. Examples are the linear sampling method, the factorization method, use of transmission eigenvalues, Stekloff eigenvalues and so on. Reverse time migration methods and the closely related matched field or matched filtering array data processing techniques are related to such qualitative approaches. In this talk I shall first present qualitative imaging methods in an acoustic waveguide with sound hard walls. The waveguide terminates at one end and contains an unknown obstacle of compact support or has deformed walls, to be determined from data gathered by an array of sensors that probe the obstacle with waves and measure the scattered response. To further shed light on qualitative approaches to imaging in complex media, I shall present higher-order wave homogenization in periodic media, where such media have been used with success to manipulate waves toward achieving super-focusing, sub-wavelength imaging, cloaking, and topological insulation.

Speaker: Lewei Zhao
Title: Finite Element Method for Laplace Equation in Two-dimensional Domains with a Singular Fracture
Abstract: We study the Laplace equation in 2D with a line Dirac Delta function on the right hand side. We establish the regularity of this problem described by weighted Sobolev space near the endpoint of the singular line. Our numerical method relies on element not across the singular line and graded mesh controlled by a grading parameter. Numerical examples are shown to verify the optimal convergence rate.

Speaker: TBA
Title:
Abstract: