SELECTED 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), 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. 74 (2009),  807-826.

            (with Ellen R. Peterson, Thomas P. Witelski, and Rachel Levy)  Stability of traveling waves in thin liquid films driven

            by gravity and surfactant. Hyperbolic Problems (HYP2008), editors E. Tadmor, J.-G. Liu, A. Tzavaras,  pages 855-868. AMS 2009.

            (with C.M. DafermosFinite time emergence of a shock wave for scalar conservation laws. J. Hype. Diff. Eqns.,
            7 (2010), 107-116.  (PDF)

            (with N. Giffen) Shock formation and breaking in particle size-segregation. Discrete and Continuous Dynamical Systems, 27 (2010), 693-715.
             (PDF)


            (with L.B.H. May and K.E. Daniels) Scalar conservation laws with nonconstant coefficients with

            application to particle size segregation in granular flow. J. Nonlinear Science, 20 (6) (2010) 689-707, DOI: 10.1007/s00332-010-9069-7 (PDF)

            (with L.B.H. May, L. Golick, K. Phillips and K.E. Daniels) Shear
driven size segregation of granular materials:
            modeling and experiment. Physical Review E, 81(1) (2010), 051301.

            (with L.B.H. May, N. Giffen and K.E. Daniels) The Gray-Thornton model of granular segregation. Proc. Joint IUTAM-ISIMM
             Symposium on Mathematical Modeling and Physical Instances of Granular Flows. Eds. J.D. Goddard, J.T. Jenkins, P. Giovine.
             American Inst. Physics, 2010, 371-378. (PDF)

           
            (with E.R. Peterson) Radial spreading of surfactant on a thin liquid film.
Appl. Math. Res. Express (2010) doi: 10.1093/amrx/abq015

            (with K. Spayd) The Buckley-Leverett equation with dynamic capillary pressure. SIAM J. Appl. Math., 71 (2011), pp. 1088-1108

            (with K. Spayd and Zhengzheng Hu) Stability of plane waves in two phase porous media flow. Applicable Analysis 91 (2012) , 295-308.


            (with E.R. Peterson) Simulation of surfactant spreading on a thin liquid film. Appl. Math. Comp. 218 (2012) 5157-5167.

            Two Fluid Flow in Porous Media.  Proceedings of the Fourteenth International Conference on Hyperbolic Problems, HYP2012, Padua, Italy. 
            AIMS Applied Mathematics,  vol. 8 (2014), 221--232.

            Smooth Periodic Solutions of a 2x2 System of Nonlinear Hyperbolic Conservation Laws.  Appl. Math. Res. Express (2013) doi: 10.1093/amrx/abt006

           (with K. Spayd and E.R. Swanson) Traveling Waves for Conservation Laws with Cubic Nonlinearity and BBM Type Dispersion.
Journal of Differential
            Equations,  259 (7) 2015, 3216-3232.

           (with E.R. Swanson, S. Strickland and K. Daniels) Surfactant Spreading on a Thin Liquid Film: Reconciling Models and Experiments.
            Journal of Engineering Mechanics (Online). 2014, 1-17. 
URL http://arxiv.org/abs/1306.4881.

          (with M. Strait, R. Levy, L. Cueto-Felgueroso and R. Juanes) Two fluid flow in a capillary tube.  
9th Annual UNCG Regional
           Mathematics and Statistics Conference (eds. Rychtar, Chhetri, Gupta and Shivaji.) Springer Proc. Math. Stat. 109 (2015), 149-161.
 
          (with J. Bostwick and K. E. Daniels)
Elastocapillary deformations on partially-wetting substrates: rival contact-line models.  Soft Matter 10  (2014)       
           7361-7369
           
           (with Stephen Strickland and Karen E. Daniels) Spatiotemporal measurement of surfactant distribution on gravity-capillary waves.
J. Fluid Mech. 777
            (2015) 523-543.  DOI: http://dx.doi.org/10.1017/jfm.2015.352

            (with Gennady A. El and Mark A. Hoefer)   Dispersive and diffusive-dispersive shock waves for non-convex conservation laws. Submitted.
            http://arxiv.org/abs/1501.01681