# Fall 2014 Applied Mathematics Colloquium

Colloquia are held in Phillips 332, Fridays at 4:00 PM unless otherwise noted. Tea is served at 3:30 PM in Phillips 330.

- Sep 05, Panos Kevrekidis, U. Massachusetts, Amherst, hosted by Jeremy Marzuola
- Sep 12, Qi Wang, U. of South Carolina, hosted by Greg Forest
- Sep 19, Colm Caulfeld, U. of Cambridge, hosted by Rich McLaughlin and Roberto Camassa
- Sep 26, Traian Iliescu, Virginia Tech, hosted by Sorin Mitran
- Oct 03, Wei Cai, UNC Charlotte, hosted by Greg Forest
*Two Mathematical Methods for Scientific Computations*In this talk, we will discuss two new mathematical methods with direct applications in scientific computations. First, we will present an image charge method for Poisson and Poisson-Boltzmann equations in a dielectric sphere and its application in molecular dynamics simulations of biomolecules. Secondly, we will present a local boundary element method (BEM) for Laplace equations by using Feyman-Kac formula and applications for communication-free domain decomposition BEM.

- Oct 10, Ruxandra Dima, U. Cincinnati, hosted by Sorin Mitran
*Large-scale Modeling of the Nanomechanics of Biomolecular Shells*

Large-size biomolecular systems that assemble, disassemble, and self-repair by controlled inputs play fundamental roles in biology. Microtubules are important in cytoskeletal support and cell motility. Physical properties of capsids of plant and animal viruses are important factors in capsid self-assembly, survival of viruses in the extracellular environment, and their cell infectivity. We focus on deciphering the microscopic origin of the physico-chemical properties of such biological assemblies and the molecular mechanisms of their response to controlled mechanical inputs. Because assemblies have modular architecture and strong inter- and intra-molecular coupling that modulate their properties, any approach has to model them on multiple spatial scales. We developed a multi-scale approach, combining coarse- graining1,2,3 with atomic details3,4, implemented on Graphics Processing Units (GPUs) for computational acceleration, to map out the mechanical properties of large size biological systems on experimental timescales. I will present our results for the micromechanics of microtubules4,5,6, related to the mechanism of microtubule disassembly, and our findings regarding the link between discrete microscopic transitions and the continuous mechanical response of the Cowpea Chlorotic Mottle Virus capsid at the macroscopic level7, in direct correspondence with AFM indentation experiments.

- Oct 24, Rick Durrett, Duke U., hosted by Sorin Mitran
*Exact Solution for a Metapopulation Version of Schelling’s Mode*l

In 1971, Schelling introduced a model in which families move if they have too many neighbors of the opposite type. In this paper we will consider a metapopulation version of the model in which a city is divided into $N$ neighborhoods each of which has $L$ houses. There are $\rho NL$ red families and $\rho NL$ blue families for some $\rho < 1/2$. Families are happy if there are $\le \rho_c L $ families of the opposite type in their neighborhood, and unhappy otherwise. Each family moves to each vacant house at rates that depend on their happiness at their current location and that of their destination. Our main result is that if neighborhoods are large then there are critical values $\rho_b<\rho_d<\rho_c$, so that for $\rho<\rho_b$ the two types are distributed randomly in equilibrium. When $\rho>\rho_b$ a new segregated equilibrium appears; for $\rho_b < \rho <\rho_d$ there is bistability, but when $\rho$ increases past $\rho_d$ the random state is no longer stable. When $\rho_c$ is small enough, the random state will again be the stationary distribution when $\rho$ is close to 1/2. If so, this is preceded by a region of bistability.

- Oct 31, Steve Soper, UNC, hosted by Peter Mucha
- Nov 07, James Sneyd, U. of Auckland, hosted by Greg Forest
- Nov 14, Mason Porter, U. of Oxford, hosted by Peter Mucha
- Nov 21, Timothy Elston, UNC, hosted by Greg Forest
- Dec 05, Dan Hu, NYU and Shanghai Jiaotong U., hosted by Jingfang Huang