This Week in Mathematics

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Entries for this week: 9
Monday January 26, 2015

Biomathematics Journals
Channel Density Distributions Explain Spiking Variability in the Globus Pallidus: A Combined Physiology and Computer Simulation Database Approach
    - Joel Tabak,
Time: 6:30 Room: Dirac Library

Special Mathematics Colloquium [url]
Blended Atomistic-to-Continuum Hybrid Methods for Modeling Crystalline Materials
    - Xingjie Helen Li, Brown University
Time: 3:35 pm Room: 101 LOV
More Information

Tuesday January 27, 2015

Applied PDE Seminar [url]
Two benchmarks of simulating stochastic dynamics with challenges of long-time simulation and non-globally Lipschitz continuous coefficients
    - Helen Li, Brown University
Time: 3:30-4:20 Room: LOV107
Abstract/Desc: In this talk, I will discuss simulations of two benchmarks arising from shock clustering and invariant random matrix ensembles, respectively. I will first illustrate the computation of coarsely self-similar flow turbulence which can be modeled by Smoluchowski 's dynamics with additive kernel K(x,y)=x+y. Long time numerical integration approach fails for getting the self-similar solutions due to the accumulated errors. In contrast, dynamic renormalization and fixed point algorithms are applied to the results of shortly evolved dynamics, and successfully overcome these difficulties. These methods not only capture the asymptotic behavior of the exact self-similar solutions, but also approximate the first moments with errors in satisfaction. Secondly, I will focus on computing stochastic differential equations with non-globally Lipschitz continuous coefficients: the Dyson Brownian Motion (DBM). The Dyson Brownian Motion describes the stochastic evolution of N points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler scheme to numerically solve the Dyson Brownian motion and sample the equilibrium measure for non-quadratic potentials. The scheme is observed to be stable for time steps of O(1/N^2) and to relax exponentially fast to the equilibrium measure with a rate constant of O(1) independent of N. This allows us to use the Dyson Brownian motion to sample NXN Hermitian matrices from the invariant ensembles.

Wednesday January 28, 2015

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Faculty Meeting
Faculty Meeting
Time: 3:35 Room: 101 LOV

Brain Mapping Seminar [url]
Processing MRI Data
    - Monica Hurdal, Mathematics, FSU
Time: 10:00am Room: LOV 002A

Biomathematics Seminar [url]
Models of (i) Facial Landmarks and (ii) Immune System Dynamics
    - Jeremy Anthony and Zachary Monaco, Mathematics, FSU
Time: 3:35pm Room: LOV 107
Abstract/Desc: Modeling papers on (i) facial landmarks and (ii) immune system dynamics will be discussed.

Friday January 30, 2015

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

Mathematics Colloquium [url]
A Highly Accurate and Highly Efficient Computational Framework for Geophysical and Biological Multiphase Flows
    - Qinghai Zhang, University of Utah
Time: 3:35 pm Room: 101 LOV
More Information

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