Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications of Elizabeth L. Bouzarth    :chronological  alphabetical  combined listing:

%% Papers Published   
   Author = {E.L. Bouzarth and M.L. Minion},
   Title = {A multirate time integrator for regularized
   Journal = {Journal of Computational Physics},
   Volume = {229},
   Number = {11},
   Pages = {4208-4224},
   Year = {2010},
   Month = {June},
   url = {},
   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/},
   Key = {fds172887}

   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.
   Title = {Epicyclic orbits in a viscous fluid about a precessing rod:
             Theory and experiments at the micro and macro
   Journal = {Physical Review E},
   Volume = {76},
   Pages = {016313},
   Year = {2007},
   url = {},
   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}

   Author = {E.L. Bouzarth and H. Pfister},
   Title = {Helicity conservation under Reidemeister
   Journal = {American Journal of Physics},
   Volume = {74},
   Number = {2},
   Pages = {141-144},
   Year = {2006},
   Month = {February},
   url = {},
   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}

   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 = {},
   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
   Doi = {10.1142/S0218216504003664},
   Key = {fds166446}

%% Papers Submitted   
   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}

   Author = {E.L. Bouzarth and M.L. Minion},
   Title = {Modeling Non-Slender Bodies with the Method of Regularized
   Year = {2010},
   Key = {fds181416}

   Author = {E.L. Bouzarth and M.L. Minion},
   Title = {Modeling Slender Bodies with the Method of Regularized
   Year = {2010},
   Key = {fds181417}

%% Other   
   Author = {E.L. Bouzarth},
   Title = {Regularized Singularities and Spectral Deferred Correction
             Methods: A Mathematical Study of Numerically Modeling Stokes
             Fluid Flow},
   Year = {2008},
   url = {},
   Key = {fds166442}
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320