Math @ Duke

Books
 Andrew J. Majda and Andrea L. Bertozzi, Vorticity and Incompressible Flow,
Cambridge Univ. Press, 2002.
[catalogue.asp]
Papers Published
 A. L. Bertozzi and J. B. Greer, Lowcurvature image simplifiers: Global regularity of smooth solutions and Laplacian limiting schemes,
Communications On Pure And Applied Mathematics, vol. 57 no. 6
(June, 2004),
pp. 764  790
 T. P. Witelski and A. J. Bernoff and A. L. Bertozzi, Blowup and dissipation in a criticalcase unstable thin film equation,
European Journal Of Applied Mathematics, vol. 15
(April, 2004),
pp. 223  256
 C. M. Topaz and A. L. Bertozzi, Swarming patterns in a twodimensional kinematic model for biological groups,
Siam Journal On Applied Mathematics, vol. 65 no. 1
(2004),
pp. 152  174
 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
(2004),
pp. 764790
 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
(2004),
pp. 3868 [42737]
 T.P. Witelski, A. J. Bernoff, A. L. Bertozzi, Blowup and dissipation in a criticalcase unstable thin film equation,
European J. Appl. Math., vol. 15
(2004),
pp. 223256
 J. B. Greer and A. L. Bertozzi, H1 solutions of a class of fourth order nonlinear equations for image processing,
Discrete And Continuous Dynamical Systems, vol. 10 no. 12
(2004),
pp. 349  366
 L. Zhornitskaya and A. L. Bertozzi, Positivitypreserving numerical schemes for lubricationtype equations,
Siam Journal On Numerical Analysis, vol. 37 no. 2
(January, 2000),
pp. 523  555
 A. L. Bertozzi and A. Munch and M. Shearer, Undercompressive shocks in thin film flows,
Physica D, vol. 134 no. 4
(December, 1999),
pp. 431  464
 A. Munch and A. L. Bertozzi, Rarefactionundercompressive fronts in driven films,
Physics Of Fluids, vol. 11 no. 10
(October, 1999),
pp. 2812  2814
 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
(December, 1998),
pp. 5169  5172
 A. J. Bernoff and A. L. Bertozzi and T. P. Witelski, Axisymmetric surface diffusion: Dynamics and stability of selfsimilar pinchoff,
Journal Of Statistical Physics, vol. 93 no. 34
(November, 1998),
pp. 725  776
 A. L. Bertozzi, Symmetric singularity formation in lubricationtype equations for interface motion,
Siam Journal On Applied Mathematics, vol. 56 no. 3
(June, 1996),
pp. 681  714
 A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films: Regularity and longtime behavior of weak solutions,
Communications On Pure And Applied Mathematics, vol. 49 no. 2
(February, 1996),
pp. 85  123
 A. L. Bertozzi, Lubrication approximations for surface tension driven interfaces: Some open problems,
Zeitschrift Fur Angewandte Mathematik Und Mechanik, vol. 76
(1996),
pp. 373  376
 A. J. Bernoff and A. L. Bertozzi, Singularities in a modified kuramotosivashinsky equation describing interface motion for phasetransition,
Physica D, vol. 85 no. 3
(August, 1995),
pp. 375  404
 A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films  the moving contact line with a porousmedia cutoff of vanderwaals interactions,
Nonlinearity, vol. 7 no. 6
(November, 1994),
pp. 1535  1564
 A. L. Bertozzi, Heteroclinic orbits and chaotic dynamics in planar fluidflows,
Siam Journal On Mathematical Analysis, vol. 19 no. 6
(November, 1988),
pp. 1271  1294
 John B. Greer and Andrea L. Bertozzi, H^{1} 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. 12 no. 10
,
pp. 349366 [html] [abs]
 B. A. Wagner, A. L. Bertozzi, and L. E. Howle, Positive Feedback Control of RayleighBenard Convection,
Discrete and Continuous Dynamical Systems Series B, 2003, special issue in honor of David Schaeffer, vol. 3 no. 4
,
pp. 619642 [html]
 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
[htm]
 B. Cook, D. Marthaler, C. Topaz, A. Bertozzi, and M. Kemp, Fractional bandwidth reacquisition algorithms for VSWMCM,
MultiRobot Systems: From Swarms to Intelligent Automata, Volume II, 2003, Kluwer Academic Publishers, Dordrecht, A.C. Schultz et al. eds. 7786
[available here]
 Jeanman Sur, Andrea L. Bertozzi, Robert P. Behringer, Reverse undercompressive shock structures in driven thin film flow,
Phys. Rev. Lett. 90 (12) 126105, 2003
[GetabsServlet]
 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. 722744, 2003
[40140]
 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. 3179.Anne Bourlioux, Martin J. Gander, and Gert Sabidussi, eds., Nato Science Series II, Vol. 75, Kluwer, Dordrecht, 2002
 M. Bertalmio, A. L. Bertozzi, and G. Sapiro, NavierStokes, 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. I355I362.
[ps] [abs]
 Andrea L. Bertozzi, Guenther Gruen, and Thomas P. Witelski, Dewetting films: bifurcations and concentrations,
Nonlinearity, vol 14, number 6, Nov 2001, pp 15691592.
[accel] [abs]
 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.253291, 2001
[bladerunner] [abs]
 Javier Diez, Lou Kondic, and Andrea Bertozzi, Global models for moving contact lines,
Phys. Rev. E. 63, 011208 (January 2001)
[available here]
 Andrea L. Bertozzi and Mary C. Pugh, Finitetime blowup of solutions of some longwave unstable thin film equations,
Indiana Univ. Mathematics J. 49(4), pp. 13231366, 2000
[php]
 Andrea L. Bertozzi and Michael Shearer, Existence of undercompressive traveling waves in thin film equations,
SIAM J. Math. Anal., vol 32, no. 1, pp. 194213, 2000.
[35089]
 L. Zhornitskaya and A. L. Bertozzi, Positivity Preserving Numerical Schemes for LubricationType Equations,
S.I.A.M. J. Num Anal., Vol. 37, No. 2, pp. 523555, 2000.
[33569]
 Andrea L Bertozzi, A. Munch, M. Shearer, Undercompressive Shocks in Thin Film Flow,
Physica D, 134(4), 431464, 1999.
[available here]
 L. Kondic and A. L. Bertozzi, Nonlinear Dynamics and Transient Growth of Driven Contact Lines,
Physics of Fluids, vol. 11, number 11, pages 35603562, 1999
[getabs]
 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 213218, 1999.
 A. Munch, A. L. Bertozzi, RarefactionUndercompressive Fonts in Driven Films,
Physics of Fluids (Letters) 11(10), pp. 28122814, 1999
[dbt]
 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. 1417, 1998. editors: V.Alexiades and G.Siopsis, AMS/IP Studies in Advanced Mathematics,
Volume 13, AMS and International Press, 1999, pp. 4368.
 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. 51695l72. December 7, 1998
[getabs]
 Andrew Bernoff, Andrea L Bertozzi, Thomas Witelski, Axisymmetric Surface Diffusion: Dynamics and Stability of SelfSimilar PinchOff,
J. Stat. Phys., 93(3/4), November 1998, pp. 725776
 Andrea L Bertozzi, M. Pugh, LongWave Instabilities and Saturation in Thin Film Equations,
Comm. Pur. Appl. Math., Vol. LI, pages 625651, 1998.
 Andrea L Bertozzi, The Mathematics of Moving Contact Lines in Thin Liquid Films,
Notices Am. Math. Soc., 45(6), pp. 689697, June/July 1998
 Andrea L Bertozzi, Michael Brenner, Linear Stability and Transient Growth in Driven Contact Lines,
Physics of Fluids 9(3) March 1997, pp. 530539.
[dbt]
 Robert Almgren, Andrea L Bertozzi, Michael Brenner, Stable and Unstable Singularities in the Unforced HeleShaw Cell,
Physics of Fluids 8(6), June 1996.
[dbt]
 Andrea L Bertozzi, Lubrication Approximations for Surface Tension Driven Interfaces: Some Open Problems,
Z. angew. Math. Mech. 76(1996) S2, pp. 373376
 Andrea L Bertozzi, Symmetric Singularity Formation in LubricationType Equations for Interface Motion, 34 pp,
SIAM J. Applied Math. Vol. 56, No. 3, pp. June 1996, pp. 681714
 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. 85123.
 A. J. Bernoff, Andrea L Bertozzi, Singularities in a Modified KuramotoSivashinsky Equation Describing Interface Motion for Phase Transition,
Physica D 85 (1995) 375404.
 Andrea L Bertozzi, Loss and Gain of Regularity in a Lubrication Equation for Thin Viscous Films,
Free Boundary Problems: Theory and Applications, pp. 7285, J. I. Diaz, M. Herrero, A. Linan, J. L. Vazquez, eds.
 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. 153564.
 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. 155208, L. Sirovich, ed. volume 100, SpringerVerlag Applied Mathematical Sciences, 1994.
 Andrea L Bertozzi, Ashvin B. Chhabra, Cancellation Exponents and Fractal Scaling,
Phys. Rev. E., 49(5) May 1, 1994, pp. 47169.
 Michael Brenner and Andrea L. Bertozzi, Spreading of Droplets on a Solid Surface,
Physical Review Letters, 71 No. 4 pp. 593596, July 26, 1993.
 Andrea L Bertozzi, James McKenna, Multidimensional Residues, Generating Functions, and Their Application To Queueing Networks,
SIAM Review, 35, No. 2, pp. 239268, June 1993.
 Andrea L Bertozzi, P. Constantin, Global Regularity for Vortex Patches,
Commun. Math. Phys. 152 1928 (1993).
 Andrea L. Bertozzi, Heteroclinic orbits and chaotic dynamics in planar fluid flows,
SIAM J. Math. Anal., vol. 19, no. 6, November 1988, pp. 12711294. pp 4176.
Papers Accepted
 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.
(March, 2004)
 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, GuiQiang Chen, Joseph Jerome, and George Gasper eds.
(2004)
Papers Submitted
 Junjie Zhou, B. Dupuy, A.L. Bertozzi and A. E. Hosoi, Shock dynamics in particleladen thin films
(2004)
 M Kemp, A.L. Bertozzi, D. Marthaler, MultiUUV perimeter surveillance, edited by Sebasco Estates, Maine, C., Brancart, E. An, M. Benjamin
(2004) (IEEE OES Workshop on Multiple AUV Operations.)
 Mark Bowen, Jeanman Sur, Andrea L. Bertozzi, Robert P. Behringer, Nonlinear dynamics of twodimensional undercompressive shocks,
Physica D
(2004)
 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",
Ecological modeling
(2004)
 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), SpringerVerlag
Preprints
 Daniel Marthaler and Andrea L. Bertozzi, Collective motion algorithms for determining environmental boundaries
, preprint 2002


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