# 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), 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 ofnchildren 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) Preprint only.

(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. Dafermos) Finite 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. (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 HYP2012, AIMS Appl. Math. 8 (2013), 212-232.

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

(with J. Bostwick and K. E. Daniels) Elastocapillary deformations on partially-wetting substrates: rival contact-line models. Soft Matter 10 (2014), 7361-7369 .

(with K. Spayd and E.R. Swanson) Traveling Waves for Conservation Laws with Cubic Nonlinearity and BBM Type Dispersion. J. Differential Eqns. 259 (2015), 3216-3232. URL http://arxiv.org/abs/1410.5121

(with E.R. Swanson, S. Strickland and K. Daniels) Surfactant Spreading on a Thin Liquid Film: Reconciling Models and Experiments. J. Engineering Math. 94 (2015) pp 63-79. 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 S. L. Strickland, and K. E. Daniels) Spatiotemporal measurement of surfactant distribution on gravity-capillary waves. J. Fluid Mech. 777 (2015) 523-543. URL http://arxiv.org/abs/1502.03467

(with Gennady A. El and Mark A. Hoefer) Expansion shock waves in regularized shallow water theory. Proc. A Roy. Soc. London. 472 (2016) DOI: 10.1098/rspa.2016.0141.

(with Gennady A. El and Mark A. Hoefer) Dispersive and diffusive-dispersive shock waves for non-convex conservation laws. SIAM Review 59(1) (2017), 1-59. URL http://arxiv.org/abs/1501.01681

(with J. B. Bostwick and J.A. Dijksman) Wetting dynamics of a collapsing fluid hole. Phys. Rev. Fluids. 2 (2017), 1-14. URL http://arxiv.org/abs/1512.07826

(with Gennady A. El and Mark A. Hoefer) Stationary Expansion Shocks for a Regularized Boussinesq System. Studies Appl. Math. 139(4) (2017) 1-22. DOI: 10.1111/sapm.12191. URL http://arxiv.org/abs/1601.01071

(with T. Barker, D.G. Schaeffer and J.M.N.T. Gray) Well-posed continuum equations for granular flow with compressibility and mu(I) rheology. Proc. Royal Society, London. 473 (2017). DOI: 10.1098/rspa.2016.0846 URL http://arxiv.org/abs/1610.05135

(with Aaron Bardall and Karen E. Daniels) Deformation of an Elastic Substrate Due to a Resting Sessile Droplet. European J. Applied Mathematics. 29 (2018), 281-300. https://doi.org/10.1017/S0956792517000134 URL http://arxiv.org/abs/1607.01637

(with Elisabeth M. Brown) A Scalar Conservation Law for Plume Migration in Carbon Sequestration. SIAM J. Applied Math. Vol. 78, No. 3 (2018), 1823-1841. ArXiv:1702.06079

(with Zhu Tang, Theodore A. Brzinski and Karen Daniels) Nonlocal rheology of dense granular flow in annular shear experiments. Soft Matter, 14 (2018), 3040 – 3048. DOI: 10.1039/c8sm00047f

(with Gennady A. El, Thibault Congy and Mark A. Hoefer) Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Studies in Applied Mathematics. DOI: 10.1111/sapm.12247. (2019) arXiv: http://arxiv.org/abs/1808.07969

(with David G. Schaeffer, Thomas Barker, Pierre Gremaud, D. Tsuji and J.M.N.T. Gray) Well-posed equations for compressible granular flow in the inertial regime. J. Fluid Mech. (2019), vol. 874, pp. 926–951.

(with Shih-Yuan Chen, Aaron Bardall, and Karen E. Daniels) Distinguishing deformation mechanisms in elastocapillary experiments. Soft Matter, **15 **(2019), 9426 – 943. arXiv: http://arxiv.org/abs/1908.11855.

(with Aaron Bardall, Shih-Yuan Chen, and Karen E. Daniels) Gradient Induced Droplet Motion Over Soft Solids. Submitted (2019) arXiv:1908.09413.