RECENT PUBLICATIONS


(with B.L. Hayes) Undercompressive shocks and Riemann problems for scalar conservation laws with
 non-convex fluxes. Proc. A Royal Soc. Edinburgh,       129A (1999), 733-754.

          (with M.R. Schulze) Undercompressive shocks for a system of hyperbolic conservation laws with cubic
 nonlinearity. J. Math. Anal. Appl., 229 (1999), 344-362.

          (with A.L. Bertozzi and A. Munch) Undercompressive shocks in thin film flows. Physica D, 134 (1999),
 431-464.

          (with A.L. Bertozzi and A. M\"unch) Undercompressive shocks in driven thin film flow: computation,
 theory and experiment. Proceedings of the Conference on Trends in Mathematical Physics,
ed. V. Alexiades and G. Siopsis. AMS/IP Studies in Advanced Mathematics, Volume 13 (1999)
pp. 43-68.

          (with P. Gremaud and D.G. Schaeffer) The influence of flow corrective inserts on granular flow
in a conical hopper. International Journal Of Non-linear Mechanics, 35 (2000), 869-882.

         (with A.L. Bertozzi) Existence of undercompressive traveling waves in thin film equations. 
SIAM J. Math. Anal., 32 (2000), 194--213. (PDF)

    (with P. Gremaud and J.V. Matthews) Similarity solutions for granular flows in hoppers.
Proceedings of the SIAM/AMS Conference on Nonlinear PDEs, Dynamics and Continuum Physics,
J. Bona, K. Saxton, R. Saxton, Eds., AMS Contemporary Mathematics Series 255 (2000), 79--95.

         (with R.A. Segal, X. Guan and T.B. Martonen) Mathematical model of airflow in the lungs of
children I: Effects of tumor size and location.  2 (2000), 199--213.

     (with R.A. Segal, X. Guan and T.B. Martonen) Mathematical model of airflow in the lungs of
children II: Effects of ventilatory parameters. J. Theoretical Medicine,   3  (2000), 51--62.

        (with A.L. Bertozzi, A. Munch and K. Zumbrun) Stability of compressive and undercompressive
thin film travelling waves. European J. Applied Math., 12 (2001), 253-291. (PDF).

          (with T.P. Witelski and D.G. Schaeffer) A discrete model for an ill-posed nonlinear parabolic
PDE. Physica D, 160 (2001), 189-221. (PDF).

          (with B.L. Hayes) A nonconvex scalar conservation law with a trilinear flux. Quart. Appl. Math., 59 (2001), 615--635.

         (with R.A. Segal, C.S. Kim and T.B. Martonen) Computer simulations of particle deposition
in the lungs of chronic obstructive pulmonary disease patients. Inhalation Toxicology, 14 (2002),
 705-720.

        (with R. Buckingham and A.L. Bertozzi) Thin film traveling waves and the Navier slip condition.
SIAM J. Applied Math. 63 (2003), 722-744. (PDF).

               (with T.P. Witelski and D.G. Schaeffer) Stability of shear bands in an elastoplastic model for
            granular flow: The role of discreteness. (PDF). Math Models and Methods in Applied Sciences 13
             (2003), 1629-1671.

           (with P.G. LeFloch) Nonclassical Riemann solvers with nucleation.  Proceedings A, Royal Soc. 
           Edinburgh, 134A (2004), 961-984. (PDF)

          (with R. Levy) Comparison of Dynamic Contact Line Models for Driven Thin Liquid Films. 
            Euro. J. Applied Math., 15 (2004), 625-642. (PDF)

          (with R. Levy) Kinetics and nucleation for driven thin film flow.  Physica D, 209 (2005),
            145-163.(PDF)

          (with R. Levy)  The Motion of a Thin Liquid Film Driven by Surfactant and Gravity. 
            SIAM J. Applied Math.,  66 (2006), 1588-1609. (PDF)

                    (with T.P. Witelski and D.G. Schaeffer) Boundary-Value Problems for Hyperbolic Equations
            Related to Steady Granular Flow. Mathematics and Mechanics of Solids, (2007).  (PDF).

          (with J.M.N.T. Gray and A.R. Thornton) Time-dependent solutions for particle-size segregation in
            shallow granular avalanches.  Proc. Roy Soc. 462 (2006), 947--972.  (PDF).

          (with R. E. Wieman) Time-periodic elastoplastic shear-banding related to granular flow. (PDF)
            Submitted to Math. Modeling and Numerical Analysis.                  

           (with R. Levy and T.P. Witelski) Growing Surfactant Waves in Thin Liquid Films Driven by Gravity.
             UCLA-IPAM-NSF Workshop on Thin Films and Fluid Interfaces. AMRX 2006 (2006), 1-21.  (PDF)

            (with R. Levy and T.P. Witelski) The influence of insoluble surfactant on the flow of a thin liquid
            film down an inclined plane.   Euro. J. Appl. Math. 18 (2007), 679-708. (PDF)

            (with JMNT Gray and AR Thornton) Stable solutions of a scalar conservation law for particle-size
             segregation in dense granular avalanches.  Euro. J. Appl. Math. 19 (2008), 1–26.
 
             (with M. McIntyre, E.L. Rowe, J.M.N.T. Gray and A.R. Thornton) Evolution of a Mixing Zone
              in Granular Avalanches. AMRX article abm008 (2008).

            (with R. Levy and P. Taylor) Automated Review of Prerequisite Material for Intermediate-level
             Undergraduate Mathematics, PRIMUS 17 (2007).

             (with P. Gremaud and K. Kleiner) Periodic motion of a mass-spring system. IMA J. Appl. Math. (submitted).