%% Papers Published
@article{fds166446,
Author = {E.L. Bouzarth and D. Richeson},
Title = {Topological Helicity for Framed Links},
Journal = {Journal of Knot Theory and its Ramifications},
Volume = {13},
Number = {8},
Pages = {1007-1019},
Year = {2004},
url = {http://dx.doi.org/10.1142/S0218216504003664},
Abstract = {We introduce topological helicity, an invariant for oriented
framed links. Topological helicity provides an elementary
means of computing helicity for a magnetic flux rope by
measuring its knotting, linking, and twisting. We present an
equivalence relation, reconnection-equivalence, for framed
links and prove that topological helicity is a complete
invariant for the resulting equivalence classes. We conclude
by showing that one can use magnetic reconnection to
transform one collection of linked flux ropes into another
collection if and only if they have the same
helicity.},
Doi = {10.1142/S0218216504003664},
Key = {fds166446}
}
@article{fds166444,
Author = {E.L. Bouzarth and H. Pfister},
Title = {Helicity conservation under Reidemeister
Moves},
Journal = {American Journal of Physics},
Volume = {74},
Number = {2},
Pages = {141-144},
Year = {2006},
Month = {February},
url = {http://dx.doi.org/10.1119/1.2142691},
Abstract = {We discuss a connection between two fields that appear to
have little in common: plasma physics and mathematical knot
theory. Plasma physicists are interested in studying
helicity conservation in magnetic flux ropes and knot
theorists commonly consider “Reidemeister moves,”
transformations that preserve a property called
“knottedness.” To study the tangling, twisting, and
untwisting of magnetic flux ropes, it is helpful to know
which topological transformations conserve helicity.
Although the second and third types of Reidemeister moves
applied to a magnetic flux rope clearly conserve the
helicity of the flux rope, the first type of Reidemeister
move appears to be in conflict with helicity conservation.We
show that all three Reidemeister moves conserve helicity in
magnetic flux ropes.},
Doi = {10.1119/1.2142691},
Key = {fds166444}
}
@article{fds166441,
Author = {E.L. Bouzarth and A. Brooks and R. Camassa and H. Jing and T.J.
Leiterman, R.M. McLaughlin and R. Superfine and J. Toledo and L.
Vicci.},
Title = {Epicyclic orbits in a viscous fluid about a precessing rod:
Theory and experiments at the micro and macro
scales},
Journal = {Physical Review E},
Volume = {76},
Pages = {016313},
Year = {2007},
url = {http://dx.doi.org/10.1103/PhysRevE.76.016313},
Abstract = {We present experimental observations and quantified
theoretical predictions of the nanoscale hydrodynamics
induced by nanorod precession emulating primary cilia motion
in developing embryos. We observe phenomena including micron
size particles which exhibit epicyclic orbits with coherent
fluctuations distinguishable from comparable amplitude
thermal noise. Quantifying the mixing and transport physics
of such motions on small scales is critical to understanding
fundamental biological processes such as extracellular
redistribution of nutrients. We present experiments designed
to quantify the trajectories of these particles, which are
seen to consist of slow orbits about the rod, with secondary
epicycles quasicommensurate with the precession rate. A
first-principles theory is developed to predict trajectories
in such time-varying flows. The theory is further tested
using a dynamically similar macroscale experiment to remove
thermal noise effects. The excellent agreement between our
theory and experiments confirms that the continuum
hypothesis applies all the way to the scales of such
submicron biological motions.},
Doi = {10.1103/PhysRevE.76.016313},
Key = {fds166441}
}
@article{fds172887,
Author = {E.L. Bouzarth and M.L. Minion},
Title = {A multirate time integrator for regularized
Stokeslets},
Journal = {Journal of Computational Physics},
Volume = {229},
Number = {11},
Pages = {4208-4224},
Year = {2010},
Month = {June},
url = {http://dx.doi.org/doi:10.1016/j.jcp.2010.02.006},
Abstract = {The method of regularized Stokeslets is a numerical approach
to approximating solutions of fluid–structure interaction
problems in the Stokes regime. Regularized Stokeslets are
fundamental solutions to the Stokes equations with a
regularized point-force term that are used to represent
forces generated by a rigid or elastic object interacting
with the fluid. Due to the linearity of the Stokes
equations, the velocity at any point in the fluid can be
computed by summing the contributions of regularized
Stokeslets, and the time evolution of positions can be
computed using standard methods for ordinary differential
equations. Rigid or elastic objects in the flow are usually
treated as immersed boundaries represented by a collection
of regularized Stokeslets coupled together by virtual
springs which determine the forces exerted by the boundary
in the fluid. For problems with boundaries modeled by
springs with large spring constants, the resulting ordinary
differential equations become stiff, and hence the time step
for explicit time integration methods is severely
constrained. Unfortunately, the use of standard implicit
time integration methods for the method of regularized
Stokeslets requires the solution of dense nonlinear systems
of equations for many relevant problems. Here, an alternate
strategy using an explicit multirate time integration scheme
based on spectral deferred corrections is incorporated that
in many cases can significantly decrease the computational
cost of the method. The multirate methods are higher-order
methods that treat different portions of the ODE explicitly
with different time steps depending on the stiffness of each
component. Numerical examples on two nontrivial
three-dimensional problems demonstrate the increased
efficiency of the multi-explicit approach with no
significant increase in numerical error.},
Doi = {doi:10.1016/j.jcp.2010.02.006},
Key = {fds172887}
}
%% Papers Submitted
@article{fds181414,
Author = {E.L. Bouzarth and A.T. Layton and Y.-N. Young},
Title = {Modeling a Semi-Flexible Filament in Cellular Stokes Flow
Using Regularized Stokeslets},
Year = {2010},
Key = {fds181414}
}
@article{fds181416,
Author = {E.L. Bouzarth and M.L. Minion},
Title = {Modeling Non-Slender Bodies with the Method of Regularized
Stokeslets},
Year = {2010},
Key = {fds181416}
}
@article{fds181417,
Author = {E.L. Bouzarth and M.L. Minion},
Title = {Modeling Slender Bodies with the Method of Regularized
Stokeslets},
Year = {2010},
Key = {fds181417}
}
%% Other
@misc{fds166442,
Author = {E.L. Bouzarth},
Title = {Regularized Singularities and Spectral Deferred Correction
Methods: A Mathematical Study of Numerically Modeling Stokes
Fluid Flow},
Year = {2008},
url = {http://search.lib.unc.edu/search?R=UNCb5803305},
Key = {fds166442}
}
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Mathematics Department