March 9, 9:30 am
in room MTH 3206, University of Maryland,
College Park
Hamiltonian Systems, Symmetry and Computational Models of DNA
Supercoiling
Prof. J. Maddocks
Department of Mathematics and
Institute for Physical Science and Technology
University of Maryland
College Park
jhm@Glue.umd.edu
There are a number of recent articles that adopt a simple elastic rod as a
rudimentary model for the supercoiling of DNA or other long chain molecules.
The typical reference cited for the elasticity theory is Love's 1927 treatise.
However the theories of both the statics and dynamics of rods is an active and
contemporary research area within the field of mechanics with many
comparatively recent advances.
In this lecture I will describe a formulation of the equilibrium conditions
for rods in terms of a boundary value problem for a seven degree of freedom
Hamiltonian system. In addition to being an effective description of the
``classic" case, the model encompasses non-uniform and non-isotropic rods that
are curved in their natural state. The Hamiltonian formulation provides a
natural setting for efficient numerical solution using collocation and
parameter continuation. The only numerical difficulty is associated with
nonisolation of solutions due to the presence of continuous symmetries.
The lecture will include the demonstration of an interactive package for the
visualization of bifurcation diagrams and associated solutions in nonlinear
two-point boundary value problems.
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