Publications of Andrea L Bertozzi

Books

  1. Andrew J. Majda and Andrea L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Univ. Press, 2002. [catalogue.asp].

Preprints

  1. D. Marthaler, A. Bertozzi, and I. Schwartz, Levy searches based on a priori information: The Biased Levy Walk, 2004.
Papers Submitted
  1. Yifei Lou, Xiaoqun Zhang, Stanley Osher and Andrea Bertozzi, Image Recovery via Nonlocal Operators, submitted to IEEE Trans. Image Proc.
  2. Andrea L. Bertozzi, Ning Ju, and Hsiang-Wei Lu, A biharmonic modified forward time stepping method for fourth order nonlinear diffusion equations, submitted to Nonlinearity, 2008.
  3. Wen Yang, Andrea L. Bertozzi, Xiao Fan Wang, Stability of a second order consensus algorithm with time delay, submitted to the 2008 IEEE Conference on Decision and Control.
  4. Ward, T., Wey, C., Hosoi, A. E. & Bertozzi, A. L. 2007 Gravity driven shear thinning of a particle laden fluid down an inclined plane, submitted Physics of Fluids.
  5. Benjamin Cook, Oleg Alexandrov, and Andrea Bertozzi, Linear stability and nonlinear dynamics in particle laden thin films, under review at European Physical Journal, 2007.

Papers Accepted

  1. Andrea L. Bertozzi and Jeremy Brandman, Finite-time blow-up of L^\infty-weak solutions of an aggregation equation accepted in Communications in the Mathematical Sciences, 2008, special issue in honor of Andrew Majda's 60th birthday.
  2. M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi, and L. Chayes, A statistical model of criminal behavior, accepted in M3AS: Mathematical Models and Methods in Applied Sciences, special issue on Traffic, Crowds, and Swarms, 2008.
Papers Published (reverse chronological order)
  1. Julia A. Dobrosotskaya and Andrea L. Bertozzi, A Wavelet-Laplace Variational Technique for Image Deconvolution and Inpainting, IEEE Trans. Imag. Proc., 17(5), pages 657-663, 2008. preprint version.
  2. H.-W. Lu, F. Bottausci, A. L. Bertozzi, C. D. Meinhart, and C.-J. Kim, PIV Investigation of 3-Dimensional Flow in Drops Actuated by EWOD, 21st IEEE Conference on Micro Electro Mechanical Systems, 2008, pages 571-574. preprint version.
  3. B. Cook, A. L. Bertozzi, and A. E. Hosoi, Shock Solutions for Particle-Laden Thin Films, SIAM J. Appl. Math. vol. 88, no. 3, pp. 760-783, 2008, preprint version.
  4. Hsiang-Wei Lu, Frederic Bottausci, Jesse Fowler, Andrea L. Bertozzi, Carl Meinhart, and Chang-Jin "CJ" Kim, A Study of EWOD-Driven Droplets by PIV Investigation, Lab on a Chip, 8, p. 456-461, 2008, DOI: 10.1039/b717141b.
  5. Z. Jin and A. L. Bertozzi, Evironmental Boundary Tracking and Estimation using Multiple Autonomous Vehicles, Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, 2007, pp. 4918-4923. preprint version.
  6. Andrea Bertozzi, Selim Esedoglu, and Alan Gillette, Analysis of a two-scale Cahn-Hilliard model for image inpainting, Multiscale Modeling and Simulation, vol. 6, no. 3, pages 913-936, 2007. Preprint version.
  7. H.-W. Lu, K. Glasner, A. L. Bertozzi, and C.-J. Kim, A Diffuse Interface Model for Electrowetting Droplets in a Hele-Shaw Cell J. Fluid Mech., 590:411-435, 2007. preprint version.
  8. A. L. Bertozzi and T. Laurent, Finite-time blow-up of solutions of an aggregation equation in R^n (springer link), Comm. Math. Phys., 274, p. 717-735, 2007. preprint version
  9. Y. Landa, D. Galkowski, Y. R. Huang, A. Joshi, C. Lee, K. K. Leung, G. Malla, J. Treanor, V. Voroninski, A. L. Bertozzi, and R. Tsai, Robotic path planning and visibility with limited sensor data, in the proceedings of the 2007 American Control Conference. preprint version
  10. Kevin K. Leung, Chung H. Hsieh, Yuan R. Huang, Abhijeet Joshi, Vlad Voroninski, and Andrea L. Bertozzi, A second generation micro-vehicle testbed for cooperative control and sensing strategies, Proceedings of the 2007 American Control Conference, pages 1900-1907. preprint version
  11. Y.-L. Chuang, M. R. D'Orsogna, D. Marthaler, A. L. Bertozzi, and L. Chayes, State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System Physica D, 232, 33-47, 2007.
  12. Yifei Lou, Paolo Favaro, A. L. Bertozzi, and S. Soatto, Autocalibration and uncalibrated reconstruction of shape from defocus, Proceedings of the Conference on Computer Vision and Pattern Recognition, 2007. preprint version
  13. Y.-L. Chuang, Y. R. Huang, M. R. D'Orsogna, and A. L. Bertozzi, Multi-vehicle flocking: scalability of cooperative control algorithms using pairwise potentials, IEEE International Conference on Robotics and Automation, 2007, pp. 2292-2299.
  14. Andrea Bertozzi, Selim Esedoglu, and Alan Gillette, Inpainting of Binary Images Using the Cahn-Hilliard Equation IEEE Trans. Image Proc. 16(1) pp. 285-291, 2007.
  15. Andrea L. Bertozzi, Editorial to UCLA-IPAM-NSF workshop on thin films and fluid interfaces, Applied Mathematics Research eXpress 2006, published online.
  16. Edward Welsh, Bjorn Birnir, and Andrea L. Bertozzi, Shocks in the Evolution of an Eroding Channel, Applied Mathematics Research eXpress 2006, published online.
  17. M. R. D'Orsogna, Y. Chuang, A. Bertozzi, and L. Chayes, Pattern formation, stability and collapse in 2D driven particle systems, in "Device applications of nonlinear dynamics", pages 103-115, edited by A. Bulsara and S. Baglio (Springer-Verlag , Berlin Heidelberg, 2006).
  18. Chung H. Hsieh, Yao-Li Chuang, Yuan Huang, Kevin K. Leung, Andrea L. Bertozzi, and Emilio Frazzoli, An Economical Micro-Car Testbed for Validation of Cooperative Control Strategies, in the Proceedings of the 2006 American Control Conference, Minneapolis, MN, June 14-16, pages 1446-1451.
  19. C.M. Topaz, A.L. Bertozzi, and M.A. Lewis. A nonlocal continuum model for biological aggregation. Bulletin of Mathematical Biology, 68(7), pages 1601-1623, 2006.
  20. John Greer, Andrea Bertozzi, and Guillermo Sapiro, Fourth Order Partial Differential Equations on General Geometries, J. Computational Physics, 216(1), pages 216-246, 2006.
  21. Maria R. D'Orsogna, Yao-Li Chuang, Andrea L. Bertozzi and Lincoln Chayes, Self-propelled particles with soft-core interactions: patterns, stability, and collapse , Physical Review Letters, 96, 104302, 2006.
  22. 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, 191(3-4), pp. 447-468, 2006.
  23. Mark Bowen, Jeanman Sur, Andrea L. Bertozzi, Robert P. Behringer, Nonlinear dynamics of two-dimensional undercompressive shocks, Physica D, Volume 209, Issues 1-4 , 15 September 2005, Pages 36-48.
  24. Chung H. Hsieh, Zhipu Jin, Daniel Marthaler, Bao Q. Nguyen, David J. Tung, Andrea L. Bertozzi, and Richard M. Murray, Experimental Validation of an Algorithm for Cooperative Boundary Tracking , Proceedings of the American Control Conference, Portland 2005, pp. 1078-1083.
  25. B. Q. Nguyen, Y-L Chuang, D. Tung, C. Hsieh, Z. Jin, L. Shi, D. Marthaler, A. L. Bertozzi, R. M. Murray, Virtual attractive-repulsive potentials for cooperative control of second order dynamic vehicles on the Caltech MVWT, Proceedings of the American Control Conference, Portland 2005, pp. 1084-1089.
  26. Junjie Zhou, B. Dupuy, A.L. Bertozzi and A. E. Hosoi, Theory for shock dynamics in particle-laden thin films, Physical Review Letters, March 25, 2005, 117803.
  27. Andrea Bertozzi, John Greer, Stanley Osher, and Kevin Vixie, Nonlinear regularizations of TV based PDEs for image processing , AMS Series of Contemporary Mathematics, vol. 371, pages 29-40, Gui-Qiang Chen, George Gasper, and Joseph Jerome eds, 2005.
  28. M. Kemp, A.L. Bertozzi, D. Marthaler, Multi-UUV perimeter surveillance, edited by C., Brancart, E. An, M. Benjamin, 2004 IEEE/OES Workshop on Autonomous Underwater Vehicles, Sebasco Estates, Maine, pages 102-107. link to online article .
  29. A.L. Bertozzi M. Kemp, and D. Marthaler, Determining Environmental Boundaries: Asynchronous communication and physical scales, Cooperative Control, Lecture Notes in Control and Information Systems, V. Kumar, N. Leonard, and A. S. Morse eds, vol. 309, pages 25-42, 2004.
  30. Chad Topaz and Andrea L. Bertozzi, Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups , SIAM Journal on Applied Mathematics Volume 65, Number 1 pp. 152-174, 2004.
  31. 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. 764-790.
  32. 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. 38-68 [42737].
  33. 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, no. 2, (2004), pp. 223-256.
  34. 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].
  35. 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.
  36. 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].
  37. 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.
  38. 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].
  39. 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 [40140].
  40. 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 .
  41. 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. [ps] [abs].
  42. Andrea L. Bertozzi, Guenther Gruen, and Thomas P. Witelski, Dewetting films: bifurcations and concentrations, Nonlinearity, vol 14, number 6, Nov 2001, pp 1569-1592. [online reprint]
  43. 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 [bladerunner] [abs].
  44. Javier Diez, Lou Kondic, and Andrea Bertozzi, Global models for moving contact lines, Phys. Rev. E. 63, 011208 (January 2001) [available here].
  45. 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 [php].
  46. 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. [35089].
  47. 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.
  48. Andrea L Bertozzi, A. Munch, M. Shearer, Undercompressive Shocks in Thin Film Flow, Physica D, 134(4), 431-464, 1999. [available here].
  49. 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 [getabs].
  50. 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.
  51. A. Munch, A. L. Bertozzi, Rarefaction-Undercompressive Fonts in Driven Films, Physics of Fluids (Letters) 11(10), pp. 2812-2814, 1999 [dbt].
  52. 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.
  53. 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.
  54. 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. postscript document
  55. Andrea L Bertozzi, M. Pugh, Long-Wave Instabilities and Saturation in Thin Film Equations, Comm. Pur. Appl. Math., Vol. LI, pages 625-651, 1998.
  56. 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.
  57. Andrea L Bertozzi, Michael Brenner, Linear Stability and Transient Growth in Driven Contact Lines, Physics of Fluids 9(3) March 1997, pp. 530-539. [dbt].
  58. Robert Almgren, Andrea L Bertozzi, Michael Brenner, Stable and Unstable Singularities in the Unforced Hele-Shaw Cell , Physics of Fluids 8(6), June 1996.
  59. Andrea L Bertozzi, Lubrication Approximations for Surface Tension Driven Interfaces: Some Open Problems, Z. angew. Math. Mech. 76(1996) S2, pp. 373-376 .
  60. 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.
  61. 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.
  62. 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.
  63. 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., Pitman Research Notes in Mathematics Series 323, Longman House, London, 1995.
  64. 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.
  65. 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.
  66. Andrea L Bertozzi, Ashvin B. Chhabra, Cancellation Exponents and Fractal Scaling, Phys. Rev. E., 49(5) May 1, 1994, pp. 4716-9.
  67. 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.
  68. 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.
  69. Andrea L Bertozzi, P. Constantin, Global Regularity for Vortex Patches, Commun. Math. Phys. 152 19-28 (1993).
  70. 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.