## Primary tabs

## Analysis and its Applications Seminar

#### On the first critical field of a Ginzburg-Landau type problem for anisotropic superconductors

### Abstract

Superconductivity is an important phenomenon in condensed matter physics. There have been significant efforts devoted to understanding this phenomenon, and different physical models have been proposed to describe and predict behaviors of superconductors. The celebrated Ginzburg-Landau model has been well accepted as a macroscopic model for isotropic superconductors. However, for a large class of high temperature superconductors, a common feature is the discrete layered structure which makes these materials highly anisotropic and thus cannot be described appropriately by the Ginzburg-Landau model (a continuous model). In this talk, we will discuss the Lawrence-Doniach model which is a modification of the Ginzburg-Landau model to account for the discrete layered structure. One of the central questions in the mathematical study of such problems is to understand the defect structure in the material subject to magnetic fields of different strengths. We will present some recent results on the first critical field corresponding to a phase transition in the material from the superconducting state to the mixed state (coexistence of superconducting and normal states). This is a delicate physical regime which requires comprehensive machineries in the analysis.## Quantitative Biology Colloquium

#### An Overview of Pathogenicity Prediction Methods

### Abstract

Proving a causal link between a gene variant and disease is time consuming and expensive. By utilizing models which try to predict which mutations will be harmful, we can help improve quality of research as well as patient care. These models use a variety of methods and data to determine whether given genetic mutations are likely to be associated with disease. We'll be reviewing several current methods for pathogenicity prediction, and discussing the importance of these methods for clinical studies and understanding the genetics of disease.## Brown Bag Seminar

#### SIAM Lunch with a Computational Scientist from Lawrence Berkeley National Lab -- Matthew Zahr

### Abstract

Matthew Zahr is a recent PhD graduate obtaining his degree in Computational and Mathematical Engineering from Stanford in 2016. He is now the Luis W. Alvarez Postdoctoral Fellow in the Mathematics Group of the Computational Research Division at the Lawrence Berkeley National Laboratory (LBNL). Having received the Department of Energy (DoE) Computational Science Graduate Fellowship, he did at least two summer internships as a graduate student in DoE labs, including at LBNL and Sandia National Lab. And, he works on computational, data science, and uncertainty problems which is a hot research area. Come enjoy informal discussions with him over lunch and get advice about internship/postdoc opportunities, mathematical careers at the DoE, etc.## Applied Math Colloquium

#### Integrated computational physics and numerical optimization

### Abstract

Optimization problems governed by partial differential equations are ubiquitous in modern science, engineering, and mathematics. They play a central role in optimal design and control of multiphysics systems, data assimilation, and inverse problems. However, as the complexity of the underlying PDE increases, efficient and robust methods to accurately compute the objective function and its gradient becomes paramount. To this end, I will present a globally high-order discretization of PDEs and their quantities of interest and the corresponding fully discrete adjoint method for use in a gradient-based PDE-constrained optimization setting. The framework is applied to solve a slew of optimization problems including the design of energetically optimal flapping motions, the design of energy harvesting mechanisms, and data assimilation to dramatically enhance the resolution of magnetic resonance images. In addition, I will demonstrate that the role of optimization in computational physics extends well beyond these traditional design and control problems. I will introduce a new method for the discovery and high-order accurate resolution of shock waves in compressible flows using PDE-constrained optimization techniques. The key feature of this method is an optimization formulation that aims to align discontinuous features of the solution basis with the discontinuities in the solution. The method is demonstrated on a number of one- and two-dimensional transonic and supersonic flow problems. In all cases, the framework tracks the discontinuity closely with curved mesh elements and provides accurate solutions on extremely coarse meshes.