Math @ Duke
- Andrew J. Majda and Andrea L. Bertozzi, Vorticity and Incompressible Flow,
Cambridge Univ. Press, 2002.
- Andrea L. Bertozzi, Heteroclinic orbits and chaotic dynamics in planar fluid flows,
SIAM J. Math. Anal., vol. 19, no. 6, November 1988, pp. 1271-1294. pp 41-76.
- Michael Brenner and Andrea L. Bertozzi, Spreading of Droplets on a Solid Surface,
Physical Review Letters, 71 No. 4 pp. 593-596, July 26, 1993.
- Andrea L Bertozzi, James McKenna, Multidimensional Residues, Generating Functions, and Their Application To Queueing Networks,
SIAM Review, 35, No. 2, pp. 239-268, June 1993.
- Andrea L Bertozzi, P. Constantin, Global Regularity for Vortex Patches,
Commun. Math. Phys. 152 19-28 (1993).
- Andrea L Bertozzi, M. Pugh, The Lubrication Approximation for Thin Viscous Films: The Moving Contact Line with a 'Porous Media' cut off of Van der Waals Interactions,
Nonlinearity. 7(6)November, 1994, pp. 1535-64.
- Andrea L Bertozzi, Michael P. Brenner, Todd F. Dupont, Leo P. Kadanoff, Singularities and Similarities in Interface Flows,
Trends and Perspectives in Applied Mathematics, pp. 155-208, L. Sirovich, ed. volume 100, Springer-Verlag Applied Mathematical Sciences, 1994.
- Andrea L Bertozzi, Ashvin B. Chhabra, Cancellation Exponents and Fractal Scaling,
Phys. Rev. E., 49(5) May 1, 1994, pp. 4716-9.
- A. J. Bernoff, Andrea L Bertozzi, Singularities in a Modified Kuramoto-Sivashinsky Equation Describing Interface Motion for Phase Transition,
Physica D 85 (1995) 375-404.
- Andrea L Bertozzi, Loss and Gain of Regularity in a Lubrication Equation for Thin Viscous Films,
Free Boundary Problems: Theory and Applications, pp. 72-85, J. I. Diaz, M. Herrero, A. Linan, J. L. Vazquez, eds.
- Robert Almgren, Andrea L Bertozzi, Michael Brenner, Stable and Unstable Singularities in the Unforced Hele-Shaw Cell,
Physics of Fluids 8(6), June 1996.
- Andrea L Bertozzi, Lubrication Approximations for Surface Tension Driven Interfaces: Some Open Problems,
Z. angew. Math. Mech. 76(1996) S2, pp. 373-376
- Andrea L Bertozzi, Symmetric Singularity Formation in Lubrication-Type Equations for Interface Motion, 34 pp,
SIAM J. Applied Math. Vol. 56, No. 3, pp. June 1996, pp. 681-714
- Andrea L Bertozzi, M. Pugh, The Lubrication Approximation for Thin Viscous Films: Regularity and Long Time Behavior of Weak Solutions,
Comm. Pure. Appl. Math., February, 49(2), 1996, pp. 85-123.
- Andrea L Bertozzi, Michael Brenner, Linear Stability and Transient Growth in Driven Contact Lines,
Physics of Fluids 9(3) March 1997, pp. 530-539.
- Andrea L Bertozzi, The Mathematics of Moving Contact Lines in Thin Liquid Films,
Notices Am. Math. Soc., 45(6), pp. 689-697, June/July 1998
- Andrea L Bertozzi, M. Pugh, Long-Wave Instabilities and Saturation in Thin Film Equations,
Comm. Pur. Appl. Math., Vol. LI, pages 625-651, 1998.
- Andrew Bernoff, Andrea L Bertozzi, Thomas Witelski, Axisymmetric Surface Diffusion: Dynamics and Stability of Self-Similar Pinch-Off,
J. Stat. Phys., 93(3/4), November 1998, pp. 725-776
- Andrea L Bertozzi, A. Munch, X. Fanton, A.M. Cazabat, Contact Line Stability and 'Undercompressive Shocks' In Driven Thin Film Flow,
Physical Review Letters, 81(23), pp. 5169-5l72. December 7, 1998
- Andrea L. Bertozzi,A. Münch and M. Shearer, Undercompressive waves in driven thin film flow: Theory, Computation, and Experiment,
Proceedings of the Conference on Trends in Mathematical Physics, Knoxville,
TN, Oct. 14-17, 1998. editors: V.Alexiades and G.Siopsis, AMS/IP Studies in Advanced Mathematics,
Volume 13, AMS and International Press, 1999, pp. 43-68.
- A. Munch, A. L. Bertozzi, Rarefaction-Undercompressive Fonts in Driven Films,
Physics of Fluids (Letters) 11(10), pp. 2812-2814, 1999
- L. Kondic and A. L. Bertozzi, Nonlinear Dynamics and Transient Growth of Driven Contact Lines,
Physics of Fluids, vol. 11, number 11, pages 3560-3562, 1999
- L. Kondic and A. L. Bertozzi, Thin Liquid Films: Instabilities of Driven Coating Flows On A Rough Surface,
Dynamics in Small Confined Systems IV, ed. J. M. Drake, G. S. Grest, J. Klafter, and R. Kopelman, Materials Research Society Symposium Proceedings, Vol. 543, pages 213-218, 1999.
- Andrea L Bertozzi, A. Munch, M. Shearer, Undercompressive Shocks in Thin Film Flow,
Physica D, 134(4), 431-464, 1999.
- L. Zhornitskaya and A. L. Bertozzi, Positivity Preserving Numerical Schemes for Lubrication-Type Equations,
S.I.A.M. J. Num Anal., Vol. 37, No. 2, pp. 523-555, 2000.
- Andrea L. Bertozzi and Michael Shearer, Existence of undercompressive traveling waves in thin film equations,
SIAM J. Math. Anal., vol 32, no. 1, pp. 194-213, 2000.
- Andrea L. Bertozzi and Mary C. Pugh, Finite-time blow-up of solutions of some long-wave unstable thin film equations,
Indiana Univ. Mathematics J. 49(4), pp. 1323-1366, 2000
- Javier Diez, Lou Kondic, and Andrea Bertozzi, Global models for moving contact lines,
Phys. Rev. E. 63, 011208 (January 2001)
- Andrea Bertozzi, Andreas Munch, Michael Shearer, and Kevin Zumbrun, Stability of compressive and undercompressive thin film travelling waves,
European J. of Appl. Math., 12(3), pp.253-291, 2001
- Andrea L. Bertozzi, Guenther Gruen, and Thomas P. Witelski, Dewetting films: bifurcations and concentrations,
Nonlinearity, vol 14, number 6, Nov 2001, pp 1569-1592.
- M. Bertalmio, A. L. Bertozzi, and G. Sapiro, Navier-Stokes, Fluid Dynamics, and Image and Video Inpainting,
Proceedings of the International Conference on Computer Vision and Pattern Recognition , IEEE, Dec. 2001, Kauai, HI, volume I, pp. I-355-I362.
- Andrea L. Bertozzi and Mark Bowen, Thin films and moving contact lines,
Modern Methods in Scientific Computing and Applications, Proceedings of the Nato Adv. Study Institute, Montreal Canada, 2001, pp. 31-79.Anne Bourlioux, Martin J. Gander, and Gert Sabidussi, eds., Nato Science Series II, Vol. 75, Kluwer, Dordrecht, 2002
- R. Buckingham, M. Shearer, and A. L. Bertozzi, Thin film traveling waves and the Navier slip condition,
SIAM J. Appl. Math.Volume 63, Number 2, pp. 722-744, 2003
- Jeanman Sur, Andrea L. Bertozzi, Robert P. Behringer, Reverse undercompressive shock structures in driven thin film flow,
Phys. Rev. Lett. 90 (12) 126105, 2003
- B. Cook, D. Marthaler, C. Topaz, A. Bertozzi, and M. Kemp, Fractional bandwidth reacquisition algorithms for VSW-MCM,
Multi-Robot Systems: From Swarms to Intelligent Automata, Volume II, 2003, Kluwer Academic Publishers, Dordrecht, A.C. Schultz et al. eds. 77-86
- Daniel Marthaler and Andrea L. Bertozzi, Tracking environmental level sets with autonomous vehicles,
S. Butenko, R. Murphey and P.M. Pardalos (editors), ``Recent Developments in Cooperative Control and Optimization'', Kluwer Academic Publishers, 2003
- B. A. Wagner, A. L. Bertozzi, and L. E. Howle, Positive Feedback Control of Rayleigh-Benard Convection,
Discrete and Continuous Dynamical Systems Series B, 2003, special issue in honor of David Schaeffer, vol. 3 no. 4
pp. 619-642 [html]
- John B. Greer and Andrea L. Bertozzi, H1 Solutions of a class of fourth order nonlinear equations for image processing,
Discrete and continuous dynamical systems 2004, special issue in honor of Mark Vishik, Editors: V. Chepyzhov, M. Efendiev, Alain Miranville, and Roger Temam, web page , vol. 1-2 no. 10
pp. 349-366 [html] [abs]
- A. L. Bertozzi, Heteroclinic orbits and chaotic dynamics in planar fluid-flows,
Siam Journal On Mathematical Analysis, vol. 19 no. 6
pp. 1271 -- 1294
- A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films - the moving contact line with a porous-media cutoff of van-der-waals interactions,
Nonlinearity, vol. 7 no. 6
pp. 1535 -- 1564
- A. J. Bernoff and A. L. Bertozzi, Singularities in a modified kuramoto-sivashinsky equation describing interface motion for phase-transition,
Physica D, vol. 85 no. 3
pp. 375 -- 404
- A. L. Bertozzi, Lubrication approximations for surface tension driven interfaces: Some open problems,
Zeitschrift Fur Angewandte Mathematik Und Mechanik, vol. 76
pp. 373 -- 376
- A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films: Regularity and long-time behavior of weak solutions,
Communications On Pure And Applied Mathematics, vol. 49 no. 2
pp. 85 -- 123
- A. L. Bertozzi, Symmetric singularity formation in lubrication-type equations for interface motion,
Siam Journal On Applied Mathematics, vol. 56 no. 3
pp. 681 -- 714
- A. J. Bernoff and A. L. Bertozzi and T. P. Witelski, Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff,
Journal Of Statistical Physics, vol. 93 no. 3-4
pp. 725 -- 776
- A. L. Bertozzi and A. Munch and X. Fanton and A. M. Cazabat, Contact line stability and "undercompressive shocks" in driven thin film flow,
Physical Review Letters, vol. 81 no. 23
pp. 5169 -- 5172
- A. Munch and A. L. Bertozzi, Rarefaction-undercompressive fronts in driven films,
Physics Of Fluids, vol. 11 no. 10
pp. 2812 -- 2814
- A. L. Bertozzi and A. Munch and M. Shearer, Undercompressive shocks in thin film flows,
Physica D, vol. 134 no. 4
pp. 431 -- 464
- L. Zhornitskaya and A. L. Bertozzi, Positivity-preserving numerical schemes for lubrication-type equations,
Siam Journal On Numerical Analysis, vol. 37 no. 2
pp. 523 -- 555
- J. B. Greer and A. L. Bertozzi, H-1 solutions of a class of fourth order nonlinear equations for image processing,
Discrete And Continuous Dynamical Systems, vol. 10 no. 1-2
pp. 349 -- 366
- Andrea L. Bertozzi and John B. Greer, Low curvature image simplifiers: global regularity of smooth solutions and Laplacian limiting schemes,
Comm. Pure Appl. Math., vol. 57 no. 6
- John B. Greer and Andrea L. Bertozzi, Traveling wave solutions of fourth order PDEs for image processing,
SIAM J. Math. Anal., vol. 36 no. 1
pp. 38-68 
- T.P. Witelski, A. J. Bernoff, A. L. Bertozzi, Blow-up and dissipation in a critical-case unstable thin film equation,
European J. Appl. Math., vol. 15
- C. M. Topaz and A. L. Bertozzi, Swarming patterns in a two-dimensional kinematic model for biological groups,
Siam Journal On Applied Mathematics, vol. 65 no. 1
pp. 152 -- 174
- T. P. Witelski and A. J. Bernoff and A. L. Bertozzi, Blowup and dissipation in a critical-case unstable thin film equation,
European Journal Of Applied Mathematics, vol. 15
pp. 223 -- 256
- A. L. Bertozzi and J. B. Greer, Low-curvature image simplifiers: Global regularity of smooth solutions and Laplacian limiting schemes,
Communications On Pure And Applied Mathematics, vol. 57 no. 6
pp. 764 -- 790
- Andrea Bertozzi, John Greer, Stanley Osher, and Kevin Vixie, Nonlinear regularizations of TV based PDEs for image processing,
AMS Series of Contemporary Mathematics, proceedings of the 2003 Northewestern PDE conference, Gui-Qiang Chen, Joseph Jerome, and George Gasper eds.
- Chad Topaz and Andrea L. Bertozzi, Swarming dynamics and pattern formation in a model for biological group motion,
to appear in SIAM J. Appl. Math.
- A.L. Bertozzi M. Kemp, and D. Marthaler, Determining Environmental Boundaries: Asynchronous communication and physical scales,
in Proceedings of the Block Island Workshop on Cooperative Control 2003, Lecture Notes in Control and Information Systems, edited by V. Kumar, N. Leonard, S. Morse
(September, 2003), Springer-Verlag
- Chuang, Y.L., Oren, R., Bertozzi, A.L., Phillips, N., and Katul, G.G., "The porous media model for the hydraulic system of a tree: from sap flux data to transpiration rate",
- Mark Bowen, Jeanman Sur, Andrea L. Bertozzi, Robert P. Behringer, Nonlinear dynamics of two-dimensional undercompressive shocks,
- M Kemp, A.L. Bertozzi, D. Marthaler, Multi-UUV perimeter surveillance, edited by Sebasco Estates, Maine, C., Brancart, E. An, M. Benjamin
(2004) (IEEE OES Workshop on Multiple AUV Operations.)
- Junjie Zhou, B. Dupuy, A.L. Bertozzi and A. E. Hosoi, Shock dynamics in particle-laden thin films
- Daniel Marthaler and Andrea L. Bertozzi, Collective motion algorithms for determining environmental boundaries
, preprint 2002
Duke University, Box 90320
Durham, NC 27708-0320