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. , 2007, pp.

Papers submitted and in preparation

1. Modeling physiological resistance in bacterial biofilms.
   (with N. Cogan and L. Fauci), to appear in Bull. Math. Biol.

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

3. Slender Body Theories with Regularized Forces.
   in preparation.