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2012-2013 Activity Report

TalkEnergetic Variational Approaches: Some Simple Examples

Date: 04/23/2013

Number of Participants:

Speaker: Chun Liu, Department of Mathematics, PSU

Talk: Tensor Product and its Applications in Physical Algorithms

Date: 04/02/2013

Number of Participants:

Speaker: Yufei Shen, Department of Physics, PSU

Abstract: Quantum theory, in essence, is solving a differential equation called Schrödinger's Equation. For a strongly correlated system, this differential equation is notoriously hard to solve since the eigen-space becomes too big even for supercomputers. One method to solve it numerically is called Time Evolving Block Decimation (TEBD), which use Matrix Product State (MPS) to represent the space of eigenvectors. This method, by embracing quantum entanglement in the approximation, only keeps those eigenstates which are physically significant, thus greatly reduces computational cost. I will also show some results of this method by solving the Bose-Hubbard Hamiltonian.

Talk: Algebraic Multigrid Method and Its Parallelization

Date: 02/12/2013

Number of Participants:

Speaker: Xiaozhe Hu, Department of Mathematics, PSU

Abstract: Developing parallel algorithms for solving large-scale sparse linear systems is an important and challenging task in scientific computing and practical applications. In this talk, I will introduce the unsmoothed aggregation algebraic multigrid method for solving large-scale linear systems. I will give theoretical justifications of its optimality for model problems and its parallelization, especially on GPUs. Two different parallel approaches will be discussed and numerical results will be presented to demonstrate their efficiency.

Activity: SIAM Student Chapter Election

Date: 12/13/2012

Number of Participants:

2011-2012 Activity Report From SIAM Student Chapter at PSU

1. Talk: "The Introduction to Generalized Finite Element Methods".

Date:   11/17/2011

Number of participants: 14

Speaker: Qingqin Qu, Department of Mathematics, PSU

Abstract: The Generalized Finite Element Method is a Galerkin’s method using partition of unity to approximate the solution of a PDE. The GFEM differs from the standard FEM in the construction of the finite dimensional space. Instead of using piecewise polynomials on each element of the triangulation, we define the ﬁnite dimensional subspaceby using partition of unity which combines the local approximationspaces together in order to obtain the global GFEM space. As an extension of the standard FEM, the GFEM is especially convenient for dealing with complicated domains, corner singularities and transmission problems. We get quasi-optimal rates of convergence for the GFEM fortransmission problems and for PDE in polygonal domains.

2. Talk: SIAM Student Chapter Election

Date:   11/29/2011

Number of participants: 13

Speaker: Kun Zhou, Department of Mathematics, PSU

Description: The five students have been nominated to run the president of our chapter. They are Peter Gael, Zhan Huang, Chao Liang, Fei Cao and Ke Han.

3.  Talk: Ginzburg-Landau Model of Superconductivity with Prescribed Topological Degrees Date:   1/26/2012

Number of participants: 20

Speaker: Oleksandr Misiats, Department of Mathematics, PSU

Abstract: Superconductivity is a complete loss of resistivity that occurs in most metals below a certain critical temperature. The key feature of this physical phenomenon is the vortices, or the points where the external magnetic field penetrates the bulk of a superconductor, thus destroying superconductivity. We model the superconducting vortices using the Ginzburg-Landau functional with a specific (degree) boundary condition that creates the same "quantized" vortices as the external magnetic field. We will discuss the issue of well-posedness of such modelling, which reduces to the question of the existence of minimizers for a Ginzburg-Landau functional in certain functional classes. We will also describe the vortex structure of the Ginzburg-Landau minimizers, which may be useful in predicting the locations of the vortices depending on the geometry of a superconductor.

4. Talk: Career Advice from a applied mathematician
Date:   2/2/2012

Number of participants: 16

Speaker: Tim Reluga, Assistant Professor in Department of Mathematics, PSU

Description: Professor Reluga talked about the early-career success that he's enjoying as an interdisciplinary researcher and shared this thoughts on how we graduate students might all be so successful.

5. Talk: A Mathematical Career in Industry
Date:   2/17/2012

Number of participants: 27

Speaker: Jennifer Deang,  Lockheed Martin company

Abstract: In this talk, I will give an overview of my experiences working as a mathematician at Lockheed Martin. Lockheed Martin is a very large technology corporation with major activities in aerospace, energy, information technology, satellites, and simulation. An unbelievable array of problems arise from these activities, and can land on a the desk of the computational scientist, with the plea "Can you help?" The reason it's a problem is nobody has seen something quite like this before. The reason they're coming to you is that your more generalized experience, and ability to construct new algorithms from old ones, you might be able to guide them to an acceptable

solution. I'll try to suggest the range of problems you could find yourself working on if

you choose a research or programming job in an industrial environment such as mine.

Industrial firms hire mathematicians and computational scientists because their training

means they can be given almost any kind of problem, and figure out a reasonable

way to analyze and solve it. The industrial setting includes some features not found in

academia, including time and cost constraints, and work in large projects. Surprisingly,

there can also be room for research projects.

6. Talk: "Homogenization of Thermal-Hydro-Mass Transfer Processes"
Date:   3/27/2012

Number of participants: 15

Speaker Shixin Xu, University of Science and Technology of China

Abstract: In nowadays,  a lot of nuclear power stations have been built, which produce a plenty of nuclear waste.  Most of these waste are buried in deep low-permeability rock area. But since the half-life period of radioactivity of waste is usual very long, we have to consider the possibility of the leakage of waste. We first use the conservation laws to model the thermal-hydro-mass transfer processes. In order to solve this nonlinear coupled system numerically, we should derive the homogenization theory of it.

We first give a priori estimate and then by the method of two-scale convergence for time dependent problem, we get the homogenized

system and corresponding convergence. At last, we also give the 1/2 order error estimate between the solutions  of original problem and

their expansions.

7. Activity: Attending SIAM &MAA Third "Mid-Atlantic Regional Applied Math Student Conference"

Date and location: April 6-7, 2012, on the campus of Shippensburg University.

Number of participants from Penn State: 4

8. Career Exploration Activity: "Their Today, Your Tomorrow"
Date:   5/3/2012

Number of participants: 19

Speaker:  Prapanpong Pongsrilam, Jianyu Chen, Oleksandr Misiats,  Jingyan Zhang,

Jing Li, Tadele Mengesha, Peter gael, Ke Han

Department of Mathematics, PSU

Description: Those who are going to graduate this summer will share their stories of searching for academia or industry jobs, and those who got an internship in summer will share their experiences and provide suggestions. These are all informal talks with sufficient time for Q&A, followed by free discussion during the pizza.

9. Talk: "Some problems in the theory of surface water waves"

Date: 09/11/2012

Number of Participants:

Speaker: Vishal Vasan, Department of Mathematics, PSU

Abstract: I will give a brief introduction to the equations that govern surface gravity waves. These equations are considered a good model for ocean waves, tsunamis and coastal phenomena in certain physical regimes. Next I will present some problems of interest regarding water waves including traditional well-posed problems as well as ill-posed ones. These questions arise from theoretical as well as applied considerations.

10. Talk: "Molecular dynamics models and coarse-grained molecular dynamics models"

Date: 10/03/2012

Number of Participants:

Speaker: Xiantao Li, Department of Mathematics, PSU

Abstract: I will introduce some basic elements in molecular dynamics (MD) models, along with

some ideas to reduce MD models to coarse-grained models with much smaller dimension.

This is particularly useful for the numerical implementation purpose.

11. Talk: Selected topics in transportation network design

Date: 11/08/2012

Number of Participants:

Speaker: Ke Han, Department of Mathematics, PSU

Abstract: Modern transportation networks are coupled to social and to data networks. More specifically, they are viewed as intrinsically multi-agent, dynamic, interdependent, complex and competitive systems involving both physical infrastructure and social interactions facilitated by modern information technology. The design of a transportation network includes not only problems of adding/removing capacity by changing nodes and arc sets, but also the determination of piecewise smooth decision variables like prices, tolls, signals, information accessibility, and other control variables associated with Stackelberg mechanisms and so-called second-best strategies.

In this introductory talk, we will review the game-theoretic aspect of traffic network modeling that dates back to the 1950's (Wardrop's principles), as well as its dynamic extension in the past two decades. We will discuss topics such as the Braess Paradox and the Price of Anarchy, which are of pivotal importance to the design and efficiency of transportation networks. This discussion will be followed by recent advancements in the determination of the aforementioned piecewise smooth decision variables, commonly embedded in a mathematical-program-with-equilibrium-constraints (MPEC) formulation.

### 4th Seminar on Tuesday

Location: Room 114 McAllister

Time: Tuesday, Dec 07, 2010, 05:00pm~05:45pm

Speaker: Zuowei Shen, National University of Singapore

Title:

Abstract:

### 3rd Seminar on Tuesday

Location: Room 106 McAllister

Time: Tuesday, Nov 11, 2010, 05:00pm~05:45pm

Speaker: Peter Gael, Penn State University

Title: Applied Computational Geometry at the Army Research Laboratory (A Research Internship Perspective)

Abstract: In this talk I will discuss my experience working for the US Army Research Laboratory. In addition to some details of my own research while in their employ, I plan to comment generally on areas of Army research and on what it's like to work for the Department of Defense. Regardless of whether you want to be a professor or not, you will find this talk interesting.

### 2nd Seminar on Tuesday

Location: Room 106 McAllister

Time: Tuesday, Sep 21, 2010, 12:10pm~01:25pm

Speaker: Wen Cheng, Penn State University

Title: A novel numerical method for a class of Cauchy problems

Abstract: In this talk we consider the parabolic equations with variable coefficients in $R^n$, and provide a novel approach to compute the solutions numerically. Our method is based on the newly developed Dyson-Taylor Commutator method, which approximates the Green's function for short time analytically. However, the results can be extended to large time as well by a bootstrap scheme. We also prove explicit error estimate in weighted Sobolev spaces, and test our results numerically and compare to other known methods.

### 1st Seminar on Tuesday

Location: Room 106 McAllister

Time: Tuesday, Sep 07, 2010, 12:10pm~01:25pm.

Speaker: Yanxiang Zhao, Penn State University

Title: Adhesion of Two-component Vesicle Membranes

Abstract: We study the adhesion of multi-component vesicle membrane to flat/curved substrates. By introducing a phase field function, we can distinguish the different components of the vesicle membranes, and formulate the total energy in terms of phase field function to describe the equilibrium shapes of the vesicle membranes. By numerically solving the equilibrium equations (Euler-Lagrange equations), we find a number of representative membrane shapes with a variety of parameter values. We discuss the stability of the vesicle membranes enduring the adhesion, and reveal that adhesion can promote the phase separation for the vesicle membranes.

## Seminar Series - Spring 2010

### Seminar on Tuesday

We had the first student seminar of 2010 on

Tuesday, Mar 2nd, 2010, 12:15pm~01:30pm, at Room 114 McAllister

Speaker: Tom Manteuffel, University of Colorado

Title: What is computational mathematics?

Abstract: This talk offers a general retrospection on the development of computational instruments and the numerical algorithms. Our ability to model complex physical systems has benefited more from new mathematical algorithms than from the explosive growth in computer speed. To continue the success, we demand new algorithms that possess both algorithmic and parallel scalability, deal with complex geometry and model complex coupled systems.

### Seminar on Tuesday

We have 2rd student seminar on

Tuesday, Mar 23rd, 2010, 5:00pm~6:10pm, at Room 106 McAllister

Speaker: Tao Wang, Pennsylvania State University

Title: Optimal strategy for wildfire containment

Abstract: This talk introduces a new class of variational problems for differential inclusions, motivated by the control of forest fires. To block the fire, a wall can be constructed progressively in time, at a given speed. In the research, we study the possibility of constructing a wall which completely encircles the fire. Moreover, we derive necessary conditions for an optimal strategy, which minimizes the total area burned by the fire.

### Seminar on Tuesday

We have 3rd student seminar on

Tuesday, Mar 30rd, 2010, 5:00pm~6:00pm, at Room 106 McAllister

Speaker: Yuanyuan Wan, Department of Economics, Pennsylvania State University

Title: Semiparametric estimation of binary decision games of incomplete information with correlated private signals

Abstract:

### Seminar on Tuesday

We have 4th student seminar on

Tuesday, Apr 06, 2010, 5:00pm~6:00pm, at Room 106 McAllister

Speaker: Andong He, Pennsylvania State University

Title: Inertial corrections to the Darcy's law for Hele-shaw flows

Abstract:

### Seminar on Tuesday

We have 5rd student seminar on

Tuesday, Apr 12, 2010, 12:00pm~01:15pm, at Room 106 McAllister

Speaker: Suzanne M. Shontz, Pennsylvania State University (CSE)

Title: Derivative-Free Optimization Algorithms for Mesh Quality Improvement

Abstract: Meshes are generated for use in the numerical solution of partial differential equations (PDEs), which arise in numerous science and engineering applications. It is essential that the meshes be of high quality in that the quality of the mesh affects the PDE solution accuracy as well as the execution time and conditioning of the relevant linear solver. Mesh quality improvement is necessary when the mesh is of less than desirable quality (either from mesh generation or deformation). In the first part of my talk, I will give an introduction to mesh quality improvement. In the second part of my talk, I will describe two derivative-free methods for mesh optimization, namely the pattern search (PS) and multidirectional search (MDS) mesh quality improvement methods, to be used with nondifferential objective functions representing the overall mesh quality. Such objective functions arise when the goal of the mesh optimization problem is to improve the worst quality element in the mesh. I will present numerical results demonstrating the effectiveness of these techniques in improving the worst quality elements of several finite element meshes.

### Seminar on Tuesday

We have 6rd student seminar on

Tuesday, Apr 20, 2010, 12:00pm~01:15pm, at Room 114 McAllister

Speaker: Van Cyr, Vitaliy Gyrya and Manlin Li, Pennsylvania State University

Title: How to find a job?

Abstract: For this seminar we had three speakers. Van gave a comprehensive summary on applying for PostDoc in academic institution, including application materials, important dates for application and useful web resources etc. After Van, Vitaliy outlined his personal experience finding PostDoc in national lab. At last, Manlin delivered a uplifting speech, and shared his own philosophies about hunting job in industry.

### Seminar on Tuesday, November 17th

We will have the 6th student seminar on

Tuesday, Nov 17th, 5:00pm~6:00pm, at 106 McAllister

Speaker: Xiang Xu

Title: Global existence and asymptotic behavior of the Ericksen-Leslie system

Abstract: In this talk we will discuss the classical solutions of a hydrodynamic system modeling the nematic liquid crystal materials. This system is a coupled system of Navier-Stokes equations and kinematic transport equations for the molecular orientations. First using different energetic variational approaches, we can recover the system in different ways and distinguish the conservative and dissipative parts of the induced stress terms. Next based on a modified Galerkin method and the study of higher order energy law, we can prove the existence of global classical solutions in both 2D and 3D cases, with some extra assumptions on those viscosity coefficients. Then by a suitable Lojasiewicz-Simon type inequality, we get the convergence of solutions to a steady state solution as time goes to infinity. Moreover, an estimation of convergence rate is provided. Finally, we reveal the relation between Parodi's condition and certain stability of the system.

### Seminar on Tuesday

We will have the 5th student seminar on

Tuesday, Nov 3rd, 5:00pm~6:00pm, at 106 McAllister

Speaker: Brian Haines

Title: Effective Viscosity and Dynamics of Dilute Bacterial Suspensions: A Three-Dimensional Model

Abstract: We present a Stochastic PDE model for dilute suspensions of bacteria in a three-dimensional Stokesian fluid. This model is used to calculate the statistically-stationary bulk deviatoric stress and effective viscosity of the suspension from the microscopic details of the interaction of an elongated body with the background flow. A bacterium is modeled as a prolate spheroid with self-propulsion provided by a point force, which shows up in the model as an inhomogeneous delta function in the PDE. The bacterium is also subject to a stochastic torque in order to model tumbling (random reorientation). Due to a bacterium's asymmetric shape, interactions with a prescribed generic background flow, such as pure straining or planar shear, cause the bacterium to preferentially align in certain directions. Due to the stochastic torque, the steady-state distribution of orientations is unique for a given background flow. Under this distribution of orientations, self-propulsion produces a
reduction in the effective viscosity. For sufficiently weak background flows, the effect of self-propulsion on the effective viscosity dominates all other contributions, leading to an effective viscosity of the suspension that is lower than the viscosity of the ambient fluid. This is in agreement with recent experiments on suspensions of Bacillus subtilis..