Papers by R. Cortez

Impulsebased Particle Methods for Fluid Flow.
(Ph.D. Thesis, 1995). LBL Report No. 37206

An Impulsebased Approximation of Fluid Motion Due to Boundary Forces.
J. Comput. Phys., v. 123, (1996), pp. 341353.

Impulse Variables, Vortex Dipoles and Applications.
in ESAIM Proceedings from the second International Workshop on
Vortex Flows, Montreal, Canada, 1996.
 Convergence of Highorder Deterministic
Particle Methods for the Convectiondiffusion Equation
Comm. Pure Appl. Math., 50 (1997), pp. 12351260.
 The Dynamics of an Elastic Membrane
Using the Impulse Method (with D. Varela)
J. Comput. Phys., 138 (1997), pp. 224247.

On the Accuracy of Impulse Methods for Fluid Flow.
SIAM J. Sci. Comput., 19, No. 4 (1998), pp. 12901302.

A Vortex/impulse Method for Immersed Boundary Motion in
High Reynolds Number Flows
J. Comput. Phys., 160, (2000), pp. 385400.

The Blob Projection Method for Immersed Boundary Problems
(with M. Minion).
J. Comput. Phys., 161 (2000), pp. 428453.

A Numerical Method For Simulating FastSwimming Motions,
In Computational Modeling in Biological Fluid Dynamics
(L. Fauci and S. Gueron, ed.), IMA Volumes in Mathematics and its Applications,
v. 124, (2001), Springer, pp. 6570.

Accurate Projection Methods for the Incompressible NavierStokes Equations
(with D. Brown and M. Minion).
J. Comput. Phys., 168 (2001), pp. 464499.

The Method of Regularized Stokeslets.
SIAM J. Sci. Comput., 23, No. 4 (2001), pp. 12041225.

Dynamics of Complex Interfaces I: Rheology, Diffusion and Morphology.
(with A. El Afif, D. DeKee and D. P. Gaver III),
J. Chem. Phys., 118, no. 22 (2003), pp. 1022710243.

Dynamics of Interfaces II: Diffusion and Morphology.
(with A. El Afif, D. DeKee and D. P. Gaver III),
J. Chem. Phys., 118, no. 22 (2003), pp. 1024310253.

Modeling of Mass Transport into Immiscible Polymeric
Blends
(with A. El Afif, D. DeKee and D. P. Gaver III),
Macromolecules, 36 no. 24 (2003), pp. 9216  9229.

Investigation of bend and shear waves in a geometrically exact
elastic rod model.
(with T. C. Bishop and O. O. Zhmudsky), J. Comput. Phys.,
193, no. 2 (2004), pp. 642665.
 La
Dinámica de Fluidos y su Rol en el Estudio de Fenómenos
Biológicos.
Ciencia Al Día Internacional (online journal), Volume 5, Number 2, 2004.
 Simulation of Swimming Organisms: Coupling Internal Mechanics
with External Fluid Dynamics.
(with Lisa Fauci, Nathaniel Cowen and Robert Dillon),
Computing in Science and Engineering, Vol. 6, No. 3, May/June 2004, pp 3845.
 The Method of Regularized Stokeslets in Three Dimensions:
Analysis, Validation, and Application to Helical Swimming.
(with L. Fauci and A. Medovikov), Phys. Fluids, Vol. 17, 031504, 2005.
 Parametric Resonance in Immersed Boundaries.
(with C.S. Peskin, J. Stockie and D. Varela), SIAM J. Appl. Math,
Vol. 65(2), 2004, pp.494520.

A Study of Bacterial Flagellar Bundling.
(with H. Flores, E. Lobaton, S. MendezDiez and S. Tlupova),
Bull. Math. Biol., Vol. 67, 2005, pp.137168.

Modeling physiological resistance in bacterial biofilms.
(with N. Cogan and L. Fauci), Bull. Math. Biol., Vol. 67, 2005, pp.831853.

Interaction between anthropod filiform hairs
in a fluid environment.
(with B. Cummins, T. Gedeon, and I. Klapper),
J. Theoretical Biol., Vol. 247, 2007, pp.266280.

Fluid dynamics of selfpropelled microorganisms,
from individuals to concentrated populations.
(with L. Cisneros, C. Dombrowski, R. Goldstein, and J. Kessler),
Experiments in Fluids, Vol. 43, 2007, pp.737753.

The Method of Images for Regularized
Stokeslets, (with J. Ainley, S. Durkin, R. Embid and P. Boindala). J. Comput. Phys.,
Vol.227, 2008, pp. 46004616.
 Unexpected bipolar flagellar
Arrangements and Longrange Flows Driven by Bacteria Near Solid Boundaries,
(with L. Cisneros, J. Kessler, R. Ortiz and M. Bees). Phys. Rev. Lett. Vol.101(16),
2008, pp. 168102.
 Boundary Integral Solutions of Coupled Stokes and Darcy Flows,
(with S. Tlupova). J. Comput. Phys., Vol. 228, 2009, pp. 158179.

R. Cortez, B. Cummins, K. Leiderman, D. Varela (2010).
Computation of ThreeDimensional Brinkman Flows
Using Regularized Methods, J. Comput. Phys.,
229(20), pp. 76097624.
 V. Aranda, R. Cortez, L. J. Fauci (2011).
Stokesian peristaltic pumping in a threedimensional tube
with a phaseshifted asymmetry, Physics of Fluids, 23, pp. 081901.
 J. C. Chrispell, R. Cortez, D. B. Khismatullin, L. J. Fauci (2011).
Shape oscillations of a droplet in an OldroydB fluid,
Physica D, 240(20), pp. 15931601.
 H. V. Nguyen, R. Ortiz, R. Cortez, L. J. Fauci, (2011).
The action of waving cylindrical rings
in a viscous fluid, J. Fluid Mech., 671, pp. 574586.
 R. Cortez, M. J. Nicholas, (2012).
Slender body theory for Stokes flows with regularized forces,
CAMCoS, 7(1), pp. 3362.
 B. Cummins, R. Cortez, I. M. Foppa, J. Walbeck, J. M. Hyman. (2012).
A spatial model of mosquito
hostseeking behavior, PLoS Computational Bology, 8(5) e1002500.
 K. Leiderman, E.L. Bouzarth, R. Cortez, A.T. Layton, (2013).
A Regularization Method for
the Numerical Solution of Periodic Stokes Flow, J. Comput. Phys, 238, 169187.

Olson, S. D., Lim, S., Cortez, R. (2013).
Modeling the dynamics of an elastic rod with intrinsic curvature and twist using a
regularized Stokes formulation. J. Comput. Phys., 238, 169187.

Hamlington, K., Kwan, Y.Y., Fujioka, H., Cortez, R., Gaver, D. P. (2013).
Evaluation of GridBased and GridFree Methods to
Model Microchannel TransportReaction. SIAM Journal of Scientific Computing, 35(4), B846B867.

Hoffmann, F., Cortez, R. (2014).
A fast numerical method for computing doublyperiodic regularized Stokes flow in 3D.
J. Comput. Phys., 258, 113.

Simons, J., Olson, S., Cortez, R., Fauci, J. (2014).
The Dynamics of Sperm Detachment from Epithelium in a Coupled
Fluidbiochemical Model of Hyperactivated Motility.
J. Theor. Bio., 354, 8194.

Cortez, R., Nguyen, H.N. (2014).
Reduction of the Regularization Error of the Method of Regularized Stokeslets
for a Rigid Object Immersed in a ThreeDimensional Stokes Flow.
Communications in Computational Physics, 15(1), 126152.

Nguyen, H., Cortez, R., Fauci, L. (2014).
Computing Flows Around Microorganisms: Slenderbody Theory and Beyond.
Amer. Math Monthly, 121810823.

Wrobel, J.K., Cortez, R., Fauci, L. (2014).
Modeling Viscoelastic Networks in Stokes Flow.
Phys. Fluids, 26113102.

Cortez, R., Varela, D. (2015).
A General System of Images for Regularized Stokeslets and
Other Elements Near a Plane Wall.
J. Comput. Phys., 285, 4154.

Aranda, V., Cortez, R., Fauci, L. (2015)
A Model of Stokesian Peristalsis and Vesicle Transport in a Threedimensional Closed Cavity.
J. Biomechanics, 48(9), 16311638.

Simons, J., Fauci, L., Cortez, R. (2015)
Threedimensional Model of the Interaction of Driven Elastic Filaments in a Stokes Flow
With Applications to Sperm Motility.
J. Biomechanics, 48(9), 16391651.
Mathematics Education publications

Cortez, R., Davenport, D., Medina, H., Narayan, D. (2007)
Diversity Issues in Undergraduate Research.
In Promoting Undergraduate Research in Mathematics  Joseph Gallian (Ed.). pp. 237250. AMS.

Cortez, R. Anhalt, C. (2014).
Readers Write – More on modeling eliciting activities:
A correction response to “Model Eliciting Activities: A Home Run” by Marta T. Magiera (February 2013 issue, pp. 34855),
Mathematics Teaching in the Middle School (MTMS), 19(6), 32426.

Anhalt, C.O., Cortez, R. (2015)
Mathematical Modeling: a Structured Process.
Mathematics Teacher, 108(6), 446452.

Felton, M.D., Anhalt, C.O., Cortez, R. (2015)
Going With the Flow: Challenging Students to Make Assumptions.
Mathematics Teaching in the Middle School, 20(6), 342349.

Anhalt, C.O., Cortez, R. (2015)
Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation.
Journal of Mathematics Teacher Education, xxx(x), xxxyyy.

Anhalt, C.O., Cortez, R., Aliceson C. Smith (2017).
Mathematical Modeling: Creating Opportunities for
Participation in Mathematiccs, book chapter in Access and Equity: Promoting High Quality Mathematics in Grades 68, Anthony Fernandes, Sandra Crespo, and Marta Civil (Eds.), National Council of Teachers of Mathematics (NCTM).

Anhalt, C.O., Staats, S., Cortez, R., Civil, M.
Mathematical Modeling and Culturally Relevant Pedagogy , to appear.
Papers submitted and in preparation

Wrobel, J., Cortez, R., Varela, D., Fauci, L.
Regularized Image System for Stokes Flow Outside a Solid Sphere.
submitted July 2015.

Highorder Interpolation Kernels With Explicit Formulas.
(with R. Blake, C. Duncan, R. Miller and L. Pérez). In preparation.
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