Brenton leMesurier

Associate Professor of Mathematics

Room 200, Randolph Scott Small Building
Department of Mathematics
College of Charleston
Charleston, SC 29424

Phone (843) 953-5917, messages -5730, FAX -1410.

Last revised January 10, 2012.

Disclaimer Don't trust anything you read on the internet, including this --- Douglas Adams.

This site is being replaced by https://blogs.cofc.edu/lemesurierb/, so it exists mainly to hold some stuff that I have not moved yet.

For students enrolled in my courses, the main web destination is OAKS, at https://lms.cofc.edu/

Recently Taught Courses

Math 120 (Introductory Calculus), Fall 2011
Math 245 (Numerical Methods and Mathematical Computing), Fall 2011
Math 246 (Mathematical Computing and Programming Laboratory), Fall 2011
Calculus III (Math 221), Spring 2011
Calculus II (Math 220), Fall 2010
Numerical Analysis (Math 445) and Numerical Analysis 1 (Math 545), Spring 2009

Curriculum Vitae

If you are curious about my professional activities and education, read my Curriculum Vitae, last updated in June 2011.

Mathematical Interests

My main research area is self-focusing of nonlinear waves, particularly as it occurs in plasma physics laser propagation and vibrations in long biological molecules: proteins and DNA. Much if this work involves numerical methods for approximation solution of these and other nonlinear evolution equations. Recently I have added consideration of random effects to the mathematical models, leading to Stochastic Differential Equations.

Some Recent Talks, Publications, and Preprints

Lately I have been working on numerical methods for Hamiltonian systems of differential equations that exactly respect multiple conservation laws for the equations (energy, momentum, angular momentum, etc.) and applications to some models of energy transfer along protein molecules. My most recent paper on this, Studying Davydov's ODE model of wave motion in alpha-helix protein using exactly energy-momentum conserving discretizations for hamiltonian systems, appeared in Mathematics and Computers in Simulation, online in December 2010. You can access the preprint version, and if you have appropriate access, the final published version.
Modeling thermal effects on nonlinear wave motion in biopolymers by a discrete nonlinear Schrödinger equation with damping and stochastic driving, slides for a talk at the SIAM Conference on Nonlinear Waves and Coherent Structures, September 9-12, 2006.
The paper Wave energy self-trapping by self-focusing in large molecular structures: a damped stochastic discrete nonlinear Schrödinger equation model on joint work with CofC undergraduate Barron Whitehead, appeared in Physica D: Nonlinear Phenomena volume 225, 1 January 2007, pages 1-12. It is also published online at DOI online. This link should work from on-campus at the CofC, or anywhere else with a suitable online subscription. Otherwise, a preprint version from January 2006 is available online, but the final version is substantially revised, particularly by the use of improved numerical methods, which are described in the more recent talk above.
The paper Beam stabilization in the 2D nonlinear Schrödinger equation with attractive potential by beam splitting and radiation appeared in Physical Review E volume 70, 046614, 28 October 2004. There is a preprint available.
The paper Regularization and control of self-focusing in the 2D cubic Schrödinger equation by attractive linear potentials appeared in Physica D: Nonlinear Phenomena volume 184, 1 October 2003, pages 226-236. This was a special issue on Complexity and Nonlinearity in Physical Systems to Honor Alan Newell. Yes, there is a preprint available.