# Weekly Colloquium

The Department hosts a weekly colloquium on Fridays at 2pm, usually in Southern Hall, room 303. If you would like to present, please contact Dr. Huiqing Zhu with a title and abstract. Please see our tips on abstracts below. You can also find links to previous years' titles and abstracts below.

 Date Presenter, Affiliation Title, Abstract 24 Apr 2015 Dr. Gopinath Subramanian Multiscale modeling of rubbery elastomersDamage accumulation in rubbery elastomers is a long-timescale problem of interest to many engineering applications. This talk will present a method for computing reaction rates on a Generalized Force-Modified Potential Energy Surface, how these rates relate to damage accumulation, and some (very) preliminary results on the Accelerated Molecular Dynamics of rubbery elastomers. 17 Apr 2015 Dr. Noah Rhee A numerical method for calculating minimum distance to near Earth objectsCalculating minimum distance between two celestial bodies orbiting the same star is a difficult task even when computational methods are employed. In this talk we address this problem for the case involving Earth and a coplanar comet, and we offer a detailed discussion of a novel tandem application of two well-known rootfinding methods to solve it. 10 Apr 2015 Jiu Ding, USM From Google Matrix to the Spectral Analysis of  Perturbed MatricesWe describe the concept of the PageRank introduced by the co-founders Brin and Page of the Google company. Then we study the spectrum of the Google Matrix, the world's largest matrix. Finally we give a spectral analysis for rank-$$1$$ and more general rank-$$k$$ perturbed matrices. 27 Mar 2015 James Lambers, USM A Crash Course on Matrices, Moments and QuadratureThe aim of this talk is to give an overview of the beautiful mathematical relationships between matrices, moments, orthogonal polynomials, quadrature rules and Krylov subspace methods. The underlying goal is efficient numerical methods for estimating $$I[f]={\mathbf u}^T f(A){\mathbf v}$$, where $${\mathbf u}$$ and $${\mathbf v}$$ are vectors, $$A$$ is a symmetric nonsingular matrix, and $$f$$ is a smooth function. An obvious application is the computation of some elements of the matrix $$f(A)$$, not all. Quadratic forms can yield error estimates in methods for solving systems of linear equations, computing parameters in least squares or total least squares problems, in Tikhonov regularization, and in spectral methods for the numerical solution of PDE. The main idea is to write $$I[f]$$ as a Riemann-Stieltjes integral, then apply Gaussian quadrature rules. The nodes and weights are given by the eigenvalues and eigenvectors of tridiagonal matrices whose nonzero coefficients describe the three-term recurrences satisfied by the associated orthogonal polynomials, which can be generated elegantly via the Lanczos algorithm. We will see that it can be very fruitful to mix techniques coming from different areas. The resulting algorithms can also be of interest to scientists and engineers who are solving problems in which computation of bilinear forms arises naturally. 20 Mar 2015 Wonryull Koh, USM Accelerated algorithms for discrete stochastic simulation of reaction--diffusion systemsStochastic simulation of a reaction-diffusion system enables computational investigation of the system’s spatiotemporal activity and stochastic variations within. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system’s state over time, it can be too slow for many practical applications. We present algorithms for accelerated stochastic simulation of biochemical reaction-diffusion systems. We present numerical results that illustrate the improvement in simulation speed achieved by our algorithms. We discuss strategies to facilitate adjusting the balance between the degree of exactness in simulation and the simulation speed. 13 Feb 2015 D. L. Young, Taiwan University The Localized Method of Approximated Particular Solutions for Solving Incompressible Navier-Stokes EquationsThis talk will focus on demonstrating that the Localized Method of Approximated Particular Solutions (LMAPS) is a stable, accurate tool for simulating multidimensional, incompressible viscous flow fields governed by the Navier-Stokes equations. The LMAPS is tested by non-uniform point distribution, extremely narrow rectangular domain, internal flow, velocity or pressure driven flow and high velocity or pressure gradient, etc. All results are similar with results of FEM or other existing literature, and it is concluded that the LMAPS has high potential to be applied to more complicated engineering applications. A further attempt to solve three-dimensional Navier-Stokes equations will be addressed and discussed. 30 Jan 2015 Bernd Schroeder, USM How not to prove a certain inequality from applied mathematics.This talk will present an inequality that arose in a colleague's analysis of the behavior of micro-air vehicles. We will discuss how a theorist who had stopped doing analysis a decade ago can become involved in such activities. We will specifically focus on some approaches that turned out to not work, because these indicate the challenges that lie ahead for attempts to generalize the inequality or to simplify that presenter's (rather tedious) proof. 23 Jan 2015 Drew Lewis, University of Alabama in Tuscaloosa When is a polynomial a coordinate?For a ring $$R$$, a polynomial $$f \in R[x_1,\ldots,x_n]$$ is called a coordinate if there exist $$n-1$$ other polynomials $$g_2,\ldots,g_n$$ such that $$R[f,g_2,\ldots,g_n]=R[x_1,\ldots,x_n]$$ (so $$(f,g_2,\ldots,g_n)$$ forms a system of coordinates for the polynomial ring in the usual sense). A natural question to ask is: given a polynomial, how can one tell if it is a coordinate or not?  We will discuss several candidate criteria such as pseudo-coordinates, stable coordinates, and hyperplanes, with an emphasis on some concrete examples.

## Tips on abstracts

Dear speaker: We like to maintain a list of titles, topics, and abstracts, so that we (and you) have a record of who has visited and talked about which topic.

• The topic should be short, similar to the headlines in the AMS subject classifications.
• Please aim for no more than 100 words in your abstract. We're not fanatically rigorous about this, but an abstract should summarize the essence of a presentation, not give every detail. It’s a sales pitch, not a business plan. Keeping the abstract at 100 words also is a good preparatory step for a concise and informative talk that communicates the salient points of your work.
• You may notice that we are MathJax-enabled, so feel free to use $$\mathrm{\LaTeX}$$ markup in your abstract when appropriate.