Publications and Talks
This is a list of some of my more recent publications and talks. (If you want PDF files for other papers, email me.)
I generally prepare a printable version of the notes for my talks (in latex “article” format, not as a slide-show) with extra background material not actually presented during the talk; hopefully this make these notes more useful to students and to others who are not specialists on the topic.
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 such as mathematical models of energy transfer along protein molecules and pulse propagation across arrays of nonlinear optical waveguides, so most of the stuff here is related to that.
Recent Publications (as of March 2016)
- Continuum approximations for pulses generated by impulsive initial data in binary exciton chain systems. Discrete and Continuous Dynamical Systems B, to appear 2016.
- Energetic pulses in exciton-phonon molecular chains and conservative
numerical methods for quasilinear hamiltonian systems.
Phys. Rev. E 88(3):032707, 2013. - Conservative unconditionally stable discretization methods for
Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules. Physica D 241(1):1–10, January 2012. (Published online 1 Oct 2011.) http://dx.doi.org/10.1016/j.physd.2011.09.012 - Studying Davydov’s ODE model of wave motion in alpha-helix
protein using exactly energy-momentum conserving discretizations for
Hamiltonian systems. Mathematics and Computers in Simulation 82(7):1239-1248, March 2012. (Published online 30 December 2010.) http://dx.doi.org/10.1016/j.matcom.2010.11.017 - Modeling thermal effects on nonlinear wave motion in biopolymers by a
stochastic discrete nonlinear {Schrödinger equation with phase damping. Discrete and Continuous Dynamic Systems Series S, 1(2):317-327, June 2008. - (With CofC undergraduate Barron Whitehead) Wave energy self-trapping by self-focusing in large molecular structures: a damped stochastic discrete nonlinear Schrödinger equation model. Physica D 225(1):1–12, January 2007.
- (With Peter Leth Christiansen, Yuri B. Gaididei, and Jens~Juul Rasmussen) Beam stabilization in the 2D nonlinear Schrödinger equation with attractive potential by beam splitting and radiation. Phys. Rev. E 70, 2004, 046614.
Selected notes from talks
- Modeling The Dynamics of Large Molecules.
Notes for a talk I gave on July 30 to undergraduates in the summer 2012 Multidisciplinary REU Program: Research, Education and Training in Computational Mathematics and Nonlinear Dynamics of Biological, Bio-inspired and Engineering Systems at the Department of Mathematical Sciences of George Mason University. - Stable, Conservative Solution Methods for Large, Stiff Hamiltonian Systems Modeling Coherent Phenomena in Nonlinear Optics and Biophysics.
Extended printable notes for my talk at the June 2012 SIAM Conference on Nonlinear Waves and Coherent Structures, where by “extended”, I mean that these notes contain a lot of background material not actually presented in that 25 minute talk, which hopefully make them more understandable to non-specialists. Even more background is in the lecture notes mentioned next: - Conservative Discretization Methods for Wave Equations, Lattice Equations, and Conservation Laws.
Printable notes for the series of four lectures on that I gave at the summer school on dispersive wave equations at IIMAS, UNAM in Mexico City in June (2012).
This version has had many errors corrected that were discovered during or after the talks, but there are still some minor errors to be corrected (as of June 24). - 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.