Papers by R. Cortez

  1. Impulse-based Particle Methods for Fluid Flow.
    (Ph.D. Thesis, 1995). LBL Report No. 37206

  2. An Impulse-based Approximation of Fluid Motion Due to Boundary Forces.
    J. Comput. Phys., v. 123, (1996), pp. 341-353.

  3. Impulse Variables, Vortex Dipoles and Applications.
    in ESAIM Proceedings from the second International Workshop on Vortex Flows, Montreal, Canada, 1996.

  4. Convergence of High-order Deterministic Particle Methods for the Convection-diffusion Equation
    Comm. Pure Appl. Math., 50 (1997), pp. 1235-1260.

  5. The Dynamics of an Elastic Membrane Using the Impulse Method (with D. Varela)
    J. Comput. Phys., 138 (1997), pp. 224-247.

  6. On the Accuracy of Impulse Methods for Fluid Flow.
    SIAM J. Sci. Comput., 19, No. 4 (1998), pp. 1290-1302.

  7. A Vortex/impulse Method for Immersed Boundary Motion in High Reynolds Number Flows
    J. Comput. Phys., 160, (2000), pp. 385-400.

  8. The Blob Projection Method for Immersed Boundary Problems (with M. Minion).
    J. Comput. Phys., 161 (2000), pp. 428-453.

  9. A Numerical Method For Simulating Fast-Swimming 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. 65-70.

  10. Accurate Projection Methods for the Incompressible Navier-Stokes Equations (with D. Brown and M. Minion).
    J. Comput. Phys., 168 (2001), pp. 464-499.

  11. The Method of Regularized Stokeslets.
    SIAM J. Sci. Comput., 23, No. 4 (2001), pp. 1204-1225.

  12. 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. 10227-10243.

  13. 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. 10243-10253.

  14. 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.

  15. 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. 642-665.

  16. La Dinámica de Fluidos y su Rol en el Estudio de Fenómenos Biológicos.
    Ciencia Al Día Internacional (on-line journal), Volume 5, Number 2, 2004.

  17. 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 38-45.

  18. 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.

  19. Parametric Resonance in Immersed Boundaries.
    (with C.S. Peskin, J. Stockie and D. Varela), SIAM J. Appl. Math, Vol. 65(2), 2004, pp.494-520.

  20. A Study of Bacterial Flagellar Bundling.
    (with H. Flores, E. Lobaton, S. Mendez-Diez and S. Tlupova), Bull. Math. Biol., Vol. 67, 2005, pp.137-168.

  21. Modeling physiological resistance in bacterial biofilms.
    (with N. Cogan and L. Fauci), Bull. Math. Biol., Vol. 67, 2005, pp.831-853.

  22. Interaction between anthropod filiform hairs in a fluid environment.
    (with B. Cummins, T. Gedeon, and I. Klapper), J. Theoretical Biol., Vol. 247, 2007, pp.266-280.

  23. Fluid dynamics of self-propelled micro-organisms, from individuals to concentrated populations.
    (with L. Cisneros, C. Dombrowski, R. Goldstein, and J. Kessler), Experiments in Fluids, Vol. 43, 2007, pp.737-753.

  24. The Method of Images for Regularized Stokeslets, (with J. Ainley, S. Durkin, R. Embid and P. Boindala). J. Comput. Phys., Vol.227, 2008, pp. 4600-4616.

  25. Unexpected bipolar flagellar Arrangements and Long-range 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.

  26. Boundary Integral Solutions of Coupled Stokes and Darcy Flows, (with S. Tlupova). J. Comput. Phys., Vol. 228, 2009, pp. 158-179.

  27. R. Cortez, B. Cummins, K. Leiderman, D. Varela (2010).
    Computation of Three-Dimensional Brinkman Flows Using Regularized Methods, J. Comput. Phys., 229(20), pp. 7609-7624.

  28. V. Aranda, R. Cortez, L. J. Fauci (2011).
    Stokesian peristaltic pumping in a three-dimensional tube with a phase-shifted asymmetry, Physics of Fluids, 23, pp. 081901.

  29. J. C. Chrispell, R. Cortez, D. B. Khismatullin, L. J. Fauci (2011).
    Shape oscillations of a droplet in an Oldroyd-B fluid, Physica D, 240(20), pp. 1593-1601.

  30. 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. 574-586.

  31. R. Cortez, M. J. Nicholas, (2012).
    Slender body theory for Stokes flows with regularized forces, CAMCoS, 7(1), pp. 33-62.

  32. B. Cummins, R. Cortez, I. M. Foppa, J. Walbeck, J. M. Hyman. (2012).
    A spatial model of mosquito host-seeking behavior, PLoS Computational Bology, 8(5) e1002500.

  33. 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, 169-187.

  34. 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, 169-187.

  35. Hamlington, K., Kwan, Y.Y., Fujioka, H., Cortez, R., Gaver, D. P. (2013).
    Evaluation of Grid-Based and Grid-Free Methods to Model Microchannel Transport-Reaction. SIAM Journal of Scientific Computing, 35(4), B846-B867.

  36. Hoffmann, F., Cortez, R. (2014).
    A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D. J. Comput. Phys., 258, 1-13.

  37. Simons, J., Olson, S., Cortez, R., Fauci, J. (2014).
    The Dynamics of Sperm Detachment from Epithelium in a Coupled Fluid-biochemical Model of Hyperactivated Motility. J. Theor. Bio., 354, 81-94.

  38. Cortez, R., Nguyen, H.-N. (2014).
    Reduction of the Regularization Error of the Method of Regularized Stokeslets for a Rigid Object Immersed in a Three-Dimensional Stokes Flow. Communications in Computational Physics, 15(1), 126-152.

  39. Nguyen, H., Cortez, R., Fauci, L. (2014).
    Computing Flows Around Microorganisms: Slender-body Theory and Beyond. Amer. Math Monthly, 121810-823.

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

  41. Cortez, R., Varela, D. (2015).
    A General System of Images for Regularized Stokeslets and Other Elements Near a Plane Wall. J. Comput. Phys., 285, 41-54.

  42. Aranda, V., Cortez, R., Fauci, L. (2015)
    A Model of Stokesian Peristalsis and Vesicle Transport in a Three-dimensional Closed Cavity. J. Biomechanics, 48(9), 1631-1638.

  43. Simons, J., Fauci, L., Cortez, R. (2015)
    Three-dimensional Model of the Interaction of Driven Elastic Filaments in a Stokes Flow With Applications to Sperm Motility. J. Biomechanics, 48(9), 1639-1651.

Mathematics Education publications

  1. Cortez, R., Davenport, D., Medina, H., Narayan, D. (2007)
    Diversity Issues in Undergraduate Research. In Promoting Undergraduate Research in Mathematics - Joseph Gallian (Ed.). pp. 237-250. AMS.

  2. 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. 348-55), Mathematics Teaching in the Middle School (MTMS), 19(6), 324-26.

  3. Anhalt, C.O., Cortez, R. (2015)
    Mathematical Modeling: a Structured Process. Mathematics Teacher, 108(6), 446-452.

  4. 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), 342-349.

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

  6. 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 6-8, Anthony Fernandes, Sandra Crespo, and Marta Civil (Eds.), National Council of Teachers of Mathematics (NCTM).

  7. Anhalt, C.O., Staats, S., Cortez, R., Civil, M.
    Mathematical Modeling and Culturally Relevant Pedagogy , to appear.

Papers submitted and in preparation

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

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

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