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. page hxp032, 2009.
(with Ellen R. Peterson, Thomas
P. Witelski, and Rachel Levy) Stability of traveling waves in
thin liquid films driven
by gravity and surfactant.
Proceedings of Symposia in Applied Mathematics, To appear, 2009.
(with C.M. Dafermos) Finite
time emergence of a shock wave for scalar conservation laws. J. Hype.
Diff. Eqns.,
to appear, 2009. (PDF)
(with N. Giffen) Shock formation
and breaking in particle size-segregation. Discrete and Continuous
Dynamical Systems, submitted.
(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, submitted. (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, submitted. (PDF)
(with L.B.H.
May, N. Giffen and K.E. Daniels) The Gray-Thornton model of granular
segregation. IUTAM Proceedings, submitted. (PDF)