Phase-Field Free Energy and Boundary Force for Molecular Solvation Abstract: We discuss a phase-filed variational model for the solvation of charged molecules with implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The last part

Title: Immersed Finite Element Methods for Interface Problems Basic idea, Development, Analysis, and Applications Abstract: Simulating a multi-scale/multi-physics phenomenon often involves a domain consisting of different materials. This often leads to the so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if the mesh is aligned with interfaces; otherwise the

Title: Effective models of flow in highly heterogeneous fractured/vuggy porous media   Abstract:  The presence of vugs and fractures in porous media can significantly affect pressure and flow behavior of a fluid. In this talk, I will present the effective models of flow in a porous medium including multi-scale fractures and  several vuggs of various

Title: Semidefinite relaxation of the clustering problem and first-order methods for their solution Abstract: I will discuss a novel relaxation approach for the graph clustering problem. Although intractable in worst-case, much recent research has established that clusters can be recovered if the underlying network or data is well-behaved. In particular, I will provide conditions on

Title: New augmented Lagrangian method for a curvature dependent segmentation model Abstract: Augmented Lagrangian methods (ALMs) have proved to be successful for the minimization of curvature dependent functionals in image processing. However, those ALM based algorithms often suffer from choosing appropriate penalty parameters in the numerical implementation. In this talk, we will discuss our recent

Title: Time reversal acoustic communication in the ocean Abstract: The global marine ecosystem is undergoing significant changes due to human activities and natural processes. These changes call for enhanced capabilities to sample and communicate in the oceans. With this background, underwater acoustic communication has attracted much attention across multiple disciplines, as this key subsea technology

Title: A Priori and a posteriori error estimate for weak Galerkin finite element method on polygonal meshes Abstract:  Polygonal mesh has advantages including lower DOFs requirement for the same level of accuracy and more flexibility in generating mesh, and better mesh quality over standard discretization with quad mesh or triangular mesh. Also the hanging nodes

Title: Determining Optimal Police Patrol Areas…and More: a Research Program in Quantitative Human Geography Abstract:  My research program is rooted in the Quantitative Revolution in Geography that began in the 1950s, and that has culminated in the broad acceptance and use of Geographic Information Systems. More specifically, my research lies in the use of quantitative methods