NSF Research Training Group in Applied Differential Equations and Scientific Computing

Andrea Bertozzi, Principal Investigator



(left) Photo from summer 2008. Front Row: Eunice Huang, Nicole Barbaro, Denise Lewis, Mayra Cisneros, Claudia Falcon, Ning Tendo, Daria Merkurjev, Ekaterina Merkurjev, Sheida Rahmani, Rachel Levy. Middle Row: Maria Pavlovkskaya, Jackie Brosamer, Edwin Lei, Andrea Bertozzi, Melissa Strait, Vedika Khemani Back Row: Steve Rosenthal, Alex Honda, Allan Garcia, Nick Meves, Travis Askham, Martin Short, Patrick Foley, Michael Moeller, Oliver Nguyen, Todd Wittman

(right) Photo from summer 2009. Front row: Brittany Dutra,Bryce Lampe, Nizar Almoussa, Kevin Chan, Allan Garcia Second row: Xiadong (Jef) Huang, Sam Lin, Annie Chen, Steve Dai, Kym Louie, Rachel Levy, Jia Yin Seo, Joyce Ho, Sarah Loeb, Sheida Rahmani, Shannon Reid, Daria Merkurjev Third row: Andrea Bertozzi, Paul Latterman, Jeremy Neuman, Michael Egesdal, Alex Honda, Yohannes Fessehatsion, Kate Burger, Kanhui Lin, Oliver Ortlieb, Matthew Mata, Jeff Eldredge, Todd Wittman Back row: Nebo Murisic, Chris Fathauer, Dmitri Skjorshammer, Russell Melick, Trystan Koch, Amit Friedman, Sam Stechmann, Robert Stephens, George Mohler

This Research Training Group supports undergraduates and beginning graduate students doing research in applied differential equations and scientific computing. The group is a consortium of students from UCLA, Harvey Mudd College and from additional universities. This web page gives an overview and research results for the REU portion of the program.

This program is run with the philosophy that there a number of ways to effectively involve undergraduates in research that gives them a meaningful experience beyond the classroom. Being at a large research university like UCLA allows for many modalities of interaction. Bringing students from four year colleges to UCLA allows them to have an experience working alongside PhD students and postdocs that they would not obtain in their college environment. In some cases, we place individual students in regular research groups where they can contribute a valuable role that is suitable for their level of experience yet contributes ultimately to part of a research paper. In other instances, we have formed small focus groups with a single faculty mentor working together with a small team of undergraduates. The latter type of group is modelled somewhat on the IPAM RIPS program but where the research projects are suggested by UCLA faculty members rather than by corporations. Finally, we have benefitted from interdisciplinary interactions through the Applied Mathematics Laboratory which bring together students, postdocs, and faculty in engineering and science to work on problems where mathematics can make a significant impact. The possibility of having students work on hands-on experiments provides a larger array of research opportunities suitable for students at the undergraduate level.

In addition to providing a valuable research experience for undergraduates, we try to heavily involve young faculty, postdocs, and advanced PhD students in the mentoring process, while maintaining oversight by senior faculty. These interactions provides the REU students with a viewport into the steps needed to develop a research career. Moreover, it provides invaluable mentoring experience for our junior researchers, often enabling them to advance their careers through broader access to tenure track positions and through additional research publications and products brought about by projects involving the undergraduate researchers.

While NSF RTG support is crucial for funding the undergraduates, to maintain a program of this size and scope, we are indebted to support from regular research grants through a number of agencies, including NSF, ARO, ONR, DOE, NIH, other DoD support, and some industrial partners. The large majority of support for faculty mentors and PhD students assisting with this program comes from these regular research grants.

Here is a recent article on undergraduate research. It is based on studies that were largely done at four year colleges, rather than at research universities.

What Good Is Undergraduate Research, Anyway? , The Chronicle of Higher Education, Aug. 17, 2007.

Mentors 2006

Mentors 2007

Mentors 2008

Mentors 2009

Mentors 2010

List of Undergraduate Participants, Summer 2006

List of Undergraduate Participants, Summer 2007

List of Undergraduate Participants, Summer 2008

List of Undergraduate Participants, Summer 2009

List of Undergraduate Participants, Summer 2010

Harvey Mudd student projects in this program

Selected reports, papers, presentations and videos

2010 REU projects

  • publication - M. Gonzalez and X. Huang and B. Irvine :

    M. Gonzalez, X. Huang, B. Irvine, D. S. Hermina Martinez, C. H. Hsieh, Y. R. Huang, M. B. Short, and A. L. Bertozzi A Third Generation Micro-vehicle Testbed for Cooperative Control and Sensing Strategies published in ICINCO 2011.

  • Jef Huang and Kevin Thompson, project report ``Atomic Force Microscopy: Algorithms for Efficient Sampling", 15 pages, 2010.
  • Christian Blanco, Ian Drayer, Hannah Kim, Ryan Wilson, project reports, George Mohler and Maria-Grazie Ascenzi mentors: A Mathematical Approach to Chondrocyte Data Collection and Columnar Organization, and Mathematically Modeling Chondrocyte Orientation and division in Relation to Primary Cilium

    Poster presentation: M.-G. Ascenzi, C. Blanco, I. Drayer, H. Kim, R. Wilson, K. Retting, K. Lyons, and G. Mohler, Primary cilium function in murine growth plate organization: a mathematical model, 2011 annual meeting Orthopaedic Research Society, Long Beach, California.

    Paper published: M.-G. Ascenzi, C. Blanco, I. Drayer, H. Kim, R. Wilson, K. Retting, K. Lyons, and G. Mohler, (2011) Effect of localization, length and orientation of chondrocytic primary cilium on murine growth plate organization Journal of Theoretical Biology 285 (2011) 147-155.

  • Chris Lee, Alex Livenson, Jackson Newhouse, Eshed Ohn-Bar, project report (Alex Chen and Todd Wittman mentors) Correlation Effects in Stock Market Volatility
  • Jake Bouricius, Trystan Koch, Paul Latterman, Brian Le, and Samantha Mesuro, project report, Nebo Murisic mentor Flow of Particle-Laden Thin Films
  • Mark Allenby, Kym Louie, and Marina Masaki, project report, Tim Lucas mentor, A Point Process Model for Simulating Gang-on-Gang Violence

    -Also presentation (same title) at the Joint Mathematics Meetings New Orleans, 2011, by Mark Allenby

    2009 REU projects

  • Dimitri Skjorshammer - paper published in Theoretical and Computational Fluid Dynamics, Convectively coupled wave-environment interactions by Samuel N. Stechmann, Andrew J. Mada, and Dmitri Skjorshammer, 2012.
  • Nizar Almoussa, Brittany Dutra, Bryce Lampe, Pascal Getreuer, Todd Wittman, Carolyn Salafia, and Luminita Vese, Automated Vasculature Extraction from Placenta Images, Proc. SPIE Medical Imaging Conference. San Diego, CA. February 2011.
  • Joyce Ho, Vincent Hu, Paul Latterman, Trystan Koch, Kanhui Lin, preprint accepted in Physica D, special issue in honor of Steve Childress: N. Murisic, J. Ho, V. Hu, P. Latterman, T. Koch, K. Lin, M. Mata, and A. Bertozzi, Particle-laden viscous thin-film flows on an incline: experiments compared with an equilibrium theory based on shear-induced migration and particle settling .
  • Kym Louie, talk at AMS Joint meetings San Francisco, AMS Session on Mathematics in the Social Sciences, January 13, 2010, Statistical Modeling of Gang Violence in Los Angeles.
  • Statistical Modeling of Gang Violence in Los Angeles Mike Egesdal, Chris Fathauer, Kym Louie, Jeremy Neuman, published in SIAM J. Undergraduate Research Online, 2010.
  • Contributed talks by Kanhui Lin, Vincent Hu, Joyce Ho, Paul Latterman, Trystan Koch, APS Division of Fluid Dynamics Annual Meeting, Minneapolis, MN, November 2009.

    2008 REU projects

  • Disaster Los Angeles reports and videos

  • Link to Pan-sharpening, crime hotspots, and Road Gap Detection reports and presentations

  • Sheida Rahmani, Melissa Strait, Daria Merkurjev, - publication : Sheida Rahmani, Melissa Strait, Daria Merkurjev, Michael Moeller, and Todd Wittman, An Adaptive IHS Pan-sharpening Method, IEEE Trans. Geosci. Remote Sensing Letters, vol. 7, no. 4, 2010.

  • Stephen Rosenthal - publication

    Rachel Levy, Stephen Rosenthal, and Jeffrey Wong Engineering flow states with localized forcing in a thin Marangoni-driven inclined film Phys. Rev. E 82, 056320 (2010) 12 pages.

    2007 REU projects

  • Trevor Ashley 2007 - Boundary estimation and video tracking , powerpoint presentation and video clips

    ``Experimental Validation of Environmental Boundary Tracking with On-Board Sensors'', by Abhijeet Joshi, Trevor Ashley, Yuan R. Huang, and Andrea L. Bertozzi, 2009 American Control Conference, St. Louis, MO. - publication

  • Arash Fayz and Ying Vuong 2007 - Crime modelling and data, powerpoint presentation
  • Meiching Fong 2007 - Dimension reduction on hyperspectral images, presentation and report
  • Zhong Hu 2007 - Gradient Free Boundary Tracking, presentation and report
  • Vicknesh Selvam 2007 - Hyperspectral TV Denoising and Inpainting, presentation and report
  • Kenn Tevin 2007 - Realistic movement of burglars in crime simulation code, PDF presentation
  • Ani Asatryan, Kate Jaffe, Tracy Nguyen, and Ilina Sandler, MATLAB Implementation of Statistical Condition Estimation, faculty advisors- Alan J. Laub and Jianlin Xia
  • William Hourigan 2007 - Experimental investigation of transition to laminar mixing of a homogeneous viscous liquid in a tilted-rotating tank.

    Publication: Experimental investigation of transition to laminar mixing of a homogeneous viscous liquid in a tilted-rotating tank, by T. Ward and W. Hourigan, Chemical Engineering Science Volume 64, Issue 23, 1 December 2009, Pages 4919-4928.

  • Parousia Rockstroh (HMC) 2007 - A thin-film liquid bridge model of adhesion. Manuscript in preparation for submission, with mentor Thomas Ward (now at NCSU).
  • Mario Lopez 2007 - Electrohydrostatically driven syphoning from a reservoir with a radial Hele-Shaw cell. Manuscript in preparation for submission, with mentor Thomas Ward (now at NCSU).

    2006 REU projects

  • Jeffrey Hyman 2006 - Report on Monte Carlo Sampling - includes personal critique of the summer REU program.

  • Jon Azose 2006 - Video of crime hotspots on Jeff Brantingham's website

  • Jason Reich 2006 - publication

    J.M. Reich, X.B. Niu, Y.-J., R.E. Caflisch, and C. Ratsch, Lateral alloy segregation in thin heteroepitaxial films, Phys. Rev. B 79, 073405 (2009).

  • Asher Metchik 2006 - publication

    Thomas Ward and Asher Metchik, Viscous fluid mixing in a tilted tank by periodic shear, Chemical Engineering Science, 62 (22), 6274-6284, 2007. preprint version

  • James von Brecht 2006 - publication

    James H. von Brecht, Seshadri R. Thiruvenkadam, and Tony F. Chan, Occlusion tracking with Logic Models , IASTED Conference on Signal and Image Processing 2007

  • Vlad Voroninski and Abhijeet Joshi 2006 - publication

    Y. Landa, D. Galkowski, Y. R. Huang, A. Joshi, C. Lee, K. K. Leung, G. Mall a, 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.

  • Vlad Voroninski and Abhijeet Joshi 2006 - publication

    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, in the proceedings of the 2007 American Control Conference.

  • Wyatt Toolson 2006 - paper published

    Chad M. Topaz, Andrew J. Bernoff, Sheldon Logan, and Wyatt Toolson, A model for rolling swarms of locusts European Physical Journal - Special Topics, vol. 157, pages 93-109, 2008.

  • Ani Asatryan, Vatche Attarian, Abhijeet Joshi, Vlad Voroninski, Meghdi Aboulian, and Krystle McBride 2006 - paper published

    Carmeliza Navasca, Ani Asatryan, Vatche Attarian, Abhijeet Joshi, Vlad Voroninski, Meghdi Aboulian, and Krystle McBride Implementations of control laws for motion camouflage in a pursuit-evasion system , Proceedings of the 23rd IFIP Conference on System Modeling and Optimization, Krakow, Poland 2007.