Erica McEvoy



Ph.D. Candidate in Applied Mathematics
Department of Mathematics

Mailing
Address:   
Program for Applied Mathematics
University of Arizona
617 N. Santa Rita
Tucson, AZ 85719

 
Phone: (520) 621-2138
E-Mail:
emcevoy (at) math (dot) arizona (dot) edu
Office:  MTL 120M


"The essential fact is that all the pictures which science now draws of nature,
and which alone seem capable of according with observational facts, are mathematical pictures."
-- Sir James Jeans



Research:


I am a member of the Solar and Heliospheric Research Group in the UofA's Lunar and Planetary Laboratory, which is headed by my dissertation advisor Randy Jokipii. In the main part of my doctoral work, I am exploiting results of known theorems in Stochastic Differential Equations to develop a numerical algorithm that accurately models how galactic cosmic rays are diffusively accelerated as they traverse through a shockwave. I've also spent some time studying solutions of the Parker Transport Equation, and have been able to derive a generalized set of stochastic differential equations that solve the P.T.E. in an arbitrary curvilinear coordinate system. My intention is to ultimately unite these projects to gain a clearer understanding of how the geometry of a shockwave affects the acceleration process.

Here's a copy of the paper I wrote for my PhD Oral Comprehensive Exam in December of 2009: paper

Here's an excellent review article for those starting out on numerically solving their own SDEs:
Higham paper

Here's a copy of a review for integrating ODE's in Matlab I wrote for Math 485:
ODE paper

Prior to moving to Arizona, I received my Masters degree in Astronomy/Astrophysics from MIT in 2005, in addition to two bachelor degrees in Physics and Math in 2004. I dabbled in two areas of research while there -- first in the Planetary Astronomy lab with Prof. Jim Elliot (initially as a code monkey for a newly installed CCD camera on the Magellean telescopes, and then as an observational lackey for occultations with Pluto ). Upon realizing that experimental work wasn't my flavor of tea, I moved to doing some really cool high-energy astrophysics research with physics Prof. Paul Joss on long-duration Gamma-Ray Bursts. A link to my Masters thesis is here, as well as further work it spawned with other physics undergrad UROPers.


Recent Talks

Stochastic Processes Approach to Cosmic-Ray Transport

Diffusive Shock Acceleration of Cosmic Rays and their Stochastic Differential Equations

Currently Teaching:

    Fall 2010
        MATH 254: Differential Equations


Curriculum Vitae

S.M. thesis

Funny stuff!