2014 AWM at SIAM Abstracts

AWM Workshop Career Panel: Women and Challenges in Mathematics, Science, and Engineering I

Beating the Imposter Syndrome

Authors:Margot Gerritsen, Stanford University, USA, margot.gerritsen@stanford.edu

Abstract. Many competitive and successful students and professionals at times feel like impostors. “I am not as smart as they think I am”, or “One sure day, I will disappoint my advisor” are frequently occurring thoughts. In a study of several hundred graduate students at Stanford, we asked about this Impostor Syndrome. I’d like to share some of the results, as well as my own thoughts on how the often negative and sometimes paralyzing thoughts that surface can be turned around. We all need mentors and to connect with a community in our work, and we need this at every career stage. I will tell some stories of successes and failures with these from my own career. I will draw some key conclusions about what to look for in a mentor. And I will reflect on the related topic of community, where the supports and the engagement are bi-directional and dynamic.

My Intertwined Paths: Career and Family

Authors: Lois Curfman McInnes, Argonne National Laboratory, U.S., curfman@mcs.anl.gov

Abstract. A rich mixture of both career and family characterizes my life during the past twenty years since I earned a PhD in applied mathematics. I’ll discuss my intertwined paths — as a researcher at Argonne National Laboratory and as a parent. I will highlight career paths at national laboratories, with emphasis on the diverse opportunities for impact in interdisciplinary computational science. Also, I will reflect on my ongoing choices for work-life balance, including addressing the ‘two-body’ problem, parenting, and care for aging parents.

From Law of Large Numbers…

Authors: Fengyan Li, Rensselaer Polytechnic Institute, USA, lif@rpi.edu

Abstract. I would like to share some aspects from my own academic experiences, such as holding positive attitudes, planning and making preparation, and the importance of having good mentors.

On the Importance of Good Mentoring and having an Engaging Community

Authors: Mary Silber, Northwestern University, USA, msilber@uchicago.edu

Abstract. We all need mentors and to connect with a community in our work, and we need this at every career stage. I will tell some stories of successes and failures with these from my own career. I will draw some key conclusions about what to look for in a mentor. And I will reflect on the related topic of community, where the supports and the engagement is bi-directional and dynamic.

On the Road Again: My Experience as an Early-career Mathematician

Authors: Anne Shiu, University of Chicago, USA, annejls@math.tamu.edu

Abstract. As a mathematician in the transition between postdoc and tenure-track, I will reflect on my experiences thus far and highlight some of the resources that have supported my career. I will also discuss my experience with the academic job market, the two-body problem, pursuing funding opportunities, and seeking a balance between work and personal/family commitments.

AWM Workshop Career Panel: Women and Challenges in Mathematics, Science, and Engineering II

Two Jobs, Two Children, and Two Cars: What can Possibly go Wrong?

Authors: Barbara Lee Keyfitz, The Ohio State University, USA, bkeyfitz@math.ohio-state.edu

Abstract. Some time in the last millennium — but it seems longer ago than that — my husband and I set out to start a family and find permanent academic jobs, more or less at the same time. Employer-provided daycare, spousal accommodation, and parental leave were yet to be invented. Nonetheless, we benefited from many factors: The novelty of the situation, our willingness to explore different parts of the country and different types of institutions, and our optimism and our determination to do the best we could for our careers and for our family. This talk will summarize our strategies, and will consider what we could have done better.

Perspectives of an Assistant Professor

Authors: Joan Lind, University of Tennessee, USA, jlind@utk.edu

Abstract. I will reflect on my career path, which did not follow the trajectory I expected. Instead of continuing in a career focused solely on teaching, I moved from being an assistant professor at a teaching university to one at a research university. Along with my career path, I will share the advice I received along the way that shaped this journey. In addition, I will reflect on my experiences of being an assistant professor at two different types of institutions.

Changing Directions

Authors: May Boggess, Arizona State University, U.S., May.Boggess@asu.edu

Abstract. We were often told to choose a research area we love. But there are a lot of different kinds of math I love; in fact, any math is fun! In this talk I will share my reflections on how I came to the research area I work in now and factors you can consider when making that difficult choice yourself.

Career Panel Discussion with Speakers from Two Parts of the Minisymposium

MiSun Min, Argonne National Laboratory, U.S., mmin@mcs.anl.gov
Xueying Wang, Washington State University, USA, xueying@math.wsu.edu

Abstract. Abstract not available at time of publication.

AWM – Workshop on Numerical and Theoretical Approaches for Nonlinear Partial Differential Equations: Research Talks by Recent Ph.D.s I

Nonlinear Traveling Waves for a Model of the Madden-Julian Oscillation

Authors: Shengqian Chen, University of Wisconsin, Madison, USA, shengqianchen11@163.com

Abstract. The Madden-Julian oscillation (MJO) is a planetary-scale wave envelope of cloud and storm activities in the tropics. MJO significantly affects other components of the atmosphere-ocean-earth system. Recently, a nonlinear model is presented for capturing MJO’s features. I will present the exact nonlinear traveling wave solutions based on the model’s energy conservation. The solution allows for explicit comparisons between features of linear and nonlinear waves, such as dispersion relations and eligible traveling wave speeds.

Fast Sweeping Methods for Steady State Problems for Hyperbolic Conservation Laws

Authors: Weitao Chen, University of California, Irvine, USA, weitaoc@ucr.edu

Abstract. Fast sweeping methods are efficient interactive numerical schemes originally designed for solving stationary Hamilton-Jacobi equations. Their efficiency relies on Gauss-Seidel type nonlinear iterations, and a finite number of sweeping directions. We generalize it to hyperbolic conservation laws with source terms. The algorithm is obtained through finite difference discretization, with the numerical fluxes evaluated in WENO fashion, coupled with Gauss-Seidel iterations. High order accuracy and the capability of resolving shocks are achieved. In further study, we incorporate multigrid method to improve the efficiency.

Nonlinear Neutral Inclusions: Assemblages of Spheres and Ellipsoids

Authors: Silvia Jimenez Bolanos, Colgate University, USA, sjimenez@colgate.edu

Abstract. If a neutral inclusion is inserted in a matrix containing a uniform applied electric field, it does not disturb the field outside the inclusion. The well known Hashin coated sphere is an example of a neutral coated inclusion. In this talk, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated spheres and ellipsoids.

Energy-Conserving Discontinuous Galerkin Methods for the Vlasov-Ampere System

Authors: Xinghui Zhong, Michigan State University, USA, zhongxh@math.msu.edu

Abstract. In this talk, we propose energy-conserving numerical schemes for the Vlasov-Ampere (VA) systems. The VA system is a model used to describe the evolution of probability density function of charged particles under self consistent electric filed in plasmas. It conserves many physical quantities, including the total energy which is comprised of the kinetic and electric energy. Unlike the total particle number conservation, the total energy conservation is challenging to achieve. For simulations in longer time ranges, negligence of this fact could cause unphysical results, such as plasma self heating or cooling. In our work, we develop the first Eulerian solvers that can preserve fully discrete total energy conservation. The main components of our solvers include explicit or implicit energy-conserving temporal discretizations, an energy-conserving operator splitting for the VA equation and discontinuous Galerkin finite element methods for the spatial discretizations. We validate our schemes by rigorous derivations and benchmark numerical examples such as Landau damping, two-stream instability and bump-on-tail instability.

AWM – Workshop on Numerical and Theoretical Approaches for Nonlinear Partial Differential Equations: Research Talks by Recent Ph.D.s II

Numerical Optimization Method for Simulation Based Optimal Design Problems

Authors: Carmen Caiseda, Inter American University of Puerto Rico, Puerto Rico, ccaiseda@bayamon.inter.edu

Abstract. The numerical optimization of simulation based problem is an interdisciplinary area of study that includes the optimization with PDE constraints area in applied mathematics. The Finite Element Method to find the numerical solution of a PDE subject to third-type boundary conditions as the ones that model electromagnetic phenomena, adjoint and direct differentiation gradients, and proper orthogonal decomposition are some of some of the topics of interest that continue to develop optimal design of devices.

A Characterization of the Reflected Quasipotential

Authors: Kasie Farlow, United States Military Academy, USA, kasie.farlow@usma.edu

Abstract. Our purpose here is to characterize the reflected quasipotential in terms of a first-order Hamilton-Jacobi equation. Because it is continuous but not differentiable in general the characterization will be in terms of viscosity solutions. Using conventional dynamic programming ideas, along with a complementarity problem formulation of the effect of the Skorokhod map on absolutely continuous paths, we will derive necessary conditions in the form of viscosity-sense boundary conditions.

Analysis of Finite Difference Schemes for Diffusion in Spheres with Variable Diffusivity

Authors: Ashlee N. Ford Versypt, Massachusetts Institute of Technology, USA, ashleefv@okstate.edu

Abstract. Three finite difference schemes are compared for discretizing the spatial derivatives of the diffusion equation in spherical coordinates for the general case of variable diffusivity, D. Five diffusivity cases are considered: 1) constant D, 2) time-dependent D, 3) spatially-dependent D, 4) concentration-dependent D, and 5) implicitly time-dependent and spatially-dependent D. The results point to one of the schemes as the preferred finite difference method for numerically solving the diffusion equation in spheres with variable diffusivity.

Analysis of Si Models with Multiple Interacting Populations Using Subpopulations with Forcing Terms

Authors: Evelyn Thomas, Bennett College For Women, USA, evelyn.k.thomas@gmail.com

Abstract. As a system of differential equations describing an epidemiological system becomes large with multiple connections between subpopulations, the expressions for reproductive numbers and endemic equilibria become algebraically complicated, which makes drawing conclusions based on biological parameters difficult. We present a new method which deconstructs the larger system into smaller subsystems, captures the bridges between the smaller systems as external forces, and bounds the reproductive numbers of the full system in terms of reproductive numbers of the smaller systems, which are algebraically tractable. This method also allows us to analyze the size of the endemic equilibria.

AWM Poster Presentations

Fast Iterative Methods for The Variable Diffusion Coefficient Equation in a Unit Disk

Authors: Aditi Ghosh, Texas A&M University, USA, amathematics@gmail.com

Abstract. Variable coefficient diffusion equation has widespread applications in many areas of Engineering and Industrial research like the flow in porous media and Tomography. We present here fast, iterative methods to solve this equation with applications to the Ginzburg Landau equation. Our technique is based on solution of Poisson and Helmholtz equation in a unit disc using fast FFT and recursive relations. The performance of this fast method is illustrated with some numerical examples.

The Asymptotic Analysis of a Thixotropic Yield Stress Fluid in Squeeze Flow

Authors: Holly Grant, Virginia Tech, USA, hollyt@vt.edu

Abstract. The partially extending strand convection model, combined with a Newtonian solvent, is investigated for a viscoelastic fluid in biaxial extensional (squeeze) flow. For a prescribed tensile stress, the asymptotic analysis, while not simple, is an essential tool for the physical interpretation of the distinct stages in evolution. The overall picture that emerges captures a number of features that are associated with thixotropic yield stress fluids, such as delayed yielding and hysteresis for up-and-down stress ramping.

Traveling Fronts to the Combustion and the Generalized Fisher-Kpp Models

Authors: Tingting Huan, University of Connecticut, USA, tingting.huan@uconn.edu

Abstract. We show the nonexistence of traveling fronts in the combustion model with fractional Laplacian (−Δ)s
when s∈(0, 1/2]. Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the usual Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling fronts for different ranges of the fractional power s for the generalized Fisher-KPP type model.

Sexual Cannibalism As An Optimal Strategy in Fishing Spiders

Authors: Sara Reynolds, University of Nebraska, Lincoln, USA, s-sreynol5@math.unl.edu

Abstract. We consider a model, based on the aggressive spillover hypothesis, where we link a female’s propensity to cannibalize a mate to her aggression towards prey. Higher levels of aggression lead to higher food consumption and lower mating rates, a trade-off in fitness. We find an optimal aggression level and analyze its effects on the frequency and type of sexual cannibalism. We then compare our results to existing models of sexual cannibalism.

A Local Grid Mesh Reinement for a Nonlocal Model of Mechanics

Authors: Feifei Xu, Florida State University, USA, winterflyfei@gmail.com

Abstract. Nonlocal problems are based on integro-diferential equations, which do not involve spatial derivatives. This makes it possible to deal with discontinuous solutions. We are most interested in the numerical results for piecewise solutions with a jump discontinuity. A local grid reinement method is then investigated for two-dimensional nonlocal model, which would be suitable for the curve discontinuous path. With the reine meshes, optimal convergence behaviors are achieved.

Three Model Problems for 1-D Particle Motion with the History Force in Viscous Fluids

Authors: Shujing Xu, Claremont Graduate University, USA, flora.xushujing@gmail.com

Abstract. We consider various model problems that describe rectilinear particle motion in a viscous fluid under the influence of the history force. These problems include sedimentation, impulsive motion, and oscillatory sliding motion. The equations of motion are integro-differential equations with a weakly singular kernel. We provide analytical solutions using Laplace transforms and discuss the mathematical relation between the sedimentation and impulsive start problems. We also compare several numerical schemes and benchmark them against the analytical results.