@article{blake_griffith_pierce_levy_parker_huebner_2024, title={Tell your story: Metrics of success for academic data science collaboration and consulting programs}, volume={13}, ISSN={["2049-1573"]}, DOI={10.1002/sta4.686}, abstractNote={Measuring success plays a central role in justifying and advocating for a statistical or data science consulting or collaboration program (SDSP) within an academic institution. We present several specific metrics to report to targeted audiences to tell the story for success of a robust and sustainable program. While gathering such metrics includes challenges, we discuss potential data sources and possible practices for SDSPs to inform their own approaches. Emphasizing essential metrics for reporting, we also share the metric gathering and reporting practices of two programs in greater detail. New or existing SDSPs should evaluate their local environments and tailor their practice to gathering, analysing and reporting success metrics accordingly. This approach provides a strong foundation to use success metrics to tell compelling stories about the SDSP and enhance program sustainability. The area of success metrics provides ample opportunity for future research projects that leverage qualitative methods and consider mechanisms for adapting to the changing landscape of data science.}, number={2}, journal={STAT}, author={Blake, Mara Rojeski and Griffith, Emily and Pierce, Steven J. and Levy, Rachel and Parker, Micaela and Huebner, Marianne}, year={2024}, month={Jun} }
 @book{voigt_hagman_gehrtz_ratliff_alexander_levy_2022, title={Justice through the lens of calculus: Framing new Possibilities for diversity, equity, and inclusion}, url={http://arxiv.org/abs/2111.11486.}, author={Voigt, M. and Hagman, J. and Gehrtz, J. and Ratliff, B. and Alexander, N. and Levy, R.}, year={2022} }
 @book{voigt_hagman_gehrtz_ratliff_alex_er_levy_2022, title={Justice through the lens of calculus: Framing new Possibilities for diversity, equity, and inclusion}, url={http://arxiv.org/abs/2111.11486.}, author={Voigt, M. and Hagman, J. and Gehrtz, J. and Ratliff, B. and Alex and er, N. and Levy, R.}, year={2022} }
 @misc{stankiewicz-van der zanden_brown_levy_2021, title={A Window into Mathematical Modeling in Kindergarten}, ISBN={9783030638993 9783030639006}, ISSN={2213-9273 2213-9281}, url={http://dx.doi.org/10.1007/978-3-030-63900-6_12}, DOI={10.1007/978-3-030-63900-6_12}, abstractNote={Authentic mathematical modeling in the kindergarten classroom becomes feasible by recognizing and building on children’s ideas, which they construct, discuss, and represent in developmentally appropriate forms. This chapter present a case of mathematical modeling teaching and learning in a kindergarten classroom.}, journal={Early Mathematics Learning and Development}, publisher={Springer International Publishing}, author={Stankiewicz-Van Der Zanden, Robyn and Brown, Stacy and Levy, Rachel}, year={2021}, pages={267–310} }
 @article{stankiewitz-van der zanden_levy_2021, title={Three questions from CCTM teachers about Mathematical Modeling}, volume={54}, number={1}, journal={Colorado Mathematics Teacher}, author={Stankiewitz-Van der Zanden, R. and Levy, R.}, year={2021}, month={Oct}, pages={1} }
 @article{z stankiewitz-van_en_levy_2021, title={Three questions from CCTM teachers about Mathematical Modeling}, volume={54}, number={1}, journal={Colorado Mathematics Teacher}, author={Z Stankiewitz-Van and en, R. and Levy, R.}, year={2021}, pages={1} }
 @book{critchell_2020, title={The Privilege of Flight}, ISBN={9780578691275}, publisher={Iris Cummings Critchell}, author={Critchell, Iris Cummings}, editor={Levy, RachelEditor}, year={2020} }
 @article{levy_2019, title={Tondeur Initiative Builds Career Activities at MAA Sections}, volume={39}, number={6}, journal={MAA Focus}, author={Levy, R.}, year={2019}, month={Dec}, pages={14–15} }
 @book{levy_laugesen_santosa_2018, place={Philadelphia, PA}, title={BIG Jobs Guide: Business, Industry, and Government Careers for Mathematical Scientists, Statisticians, and Operations Researchers}, ISBN={9781611975284}, publisher={SIAM - Society for Industrial and Applied Mathematics}, author={Levy, R. and Laugesen, R. and Santosa, F.}, year={2018} }
 @book{bliss_kavanagh_galluzzo_levy_2018, place={Philadelphia, PA}, title={Math Modeling: Computing and Communicating}, ISBN={9781611975239}, publisher={SIAM - Society for Industrial and Applied Mathematics}, author={Bliss, K. and Kavanagh, K. and Galluzzo, B. and Levy, R.}, year={2018} }
 @article{levy_2017, title={Birth of the BIG Math Network}, volume={37}, number={6}, journal={MAA Focus}, author={Levy, R.}, year={2017}, month={Dec}, pages={17–19} }
 @inbook{levy_2017, place={Santa Barbara, CA}, title={Euphemia Haynes Lofton}, ISBN={9781610696029 9781610696036}, booktitle={Women in American History: A Social, Political, and Cultural Encyclopedia and Document Collection}, publisher={ABC-CLIO}, author={Levy, R.}, editor={Lamphier, Peg A. and Welch, RosanneEditors}, year={2017} }
 @article{levy_chow_kwon_socha_mccarthy_turner_2017, title={SIAM Education Subcommittee Report on Undergraduate Degree Programs in Applied Mathematics}, volume={59}, ISSN={0036-1445 1095-7200}, url={http://dx.doi.org/10.1137/15m1008002}, DOI={10.1137/15m1008002}, abstractNote={The SIAM Education Committee has released a report called Undergraduate Degree Programs in Applied Mathematics. The report describes the general and specific features of undergraduate education in applied mathematics, based on interviews with 12 diverse but representative programs, and offers commentary based on the experience of the committee. This article summarizes the key findings of the SIAM report, focusing on curricular requirements, the role of industry, undergraduate research, student recruitment, and starting a new program. The goal of the report and this article is to provide guidance to new programs, existing programs, and the development of policy.}, number={1}, journal={SIAM Review}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Levy, Rachel and Chow, Edmond and Kwon, Byong and Socha, Katherine and McCarthy, Maeve and Turner, Peter R.}, year={2017}, month={Jan}, pages={199–204} }
 @article{sinclair_levy_daniels_2017, title={Simulating surfactant spreading: Influence of a physically motivated equation of state}, volume={29}, ISSN={0956-7925 1469-4425}, url={http://dx.doi.org/10.1017/s095679251700002x}, DOI={10.1017/s095679251700002x}, abstractNote={In this paper, we present numerical simulations that demonstrate the effect of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension in surfactant-driven thin liquid films. Previous choices of the model EoS have been an ad-hoc decreasing function. Here, we instead propose an empirically motivated EoS; this provides a route to resolve some discrepancies and raises new issues to be pursued in future experiments. In addition, we test the influence of the choice of initial conditions and values for the non-dimensional groups. We demonstrate that the choice of EoS improves the agreement in surfactant distribution morphology between simulations and experiments, and influences the dynamics of the simulations. Because an empirically motivated EoS has regions with distinct gradients, future mathematical models may be improved by considering more than one timescale. We observe that the non-dimensional number controlling the relative importance of gravitational versus capillary forces has a larger influence on the dynamics than the other non-dimensional groups, but is nonetheless not a likely cause of discrepancy between simulations and experiments. Finally, we observe that the experimental approach using a ring to contain the surfactant could affect the surfactant and fluid dynamics if it disrupts the intended initial surfactant distribution. However, the fluid meniscus itself does not significantly affect the dynamics.}, number={1}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={Sinclair, Dina and Levy, Rachel and Daniels, Karen E.}, year={2017}, month={Mar}, pages={30–54} }
 @inbook{levy_2017, place={Santa Barbara, CA}, title={The Association for Women in Mathematics}, ISBN={9781610696029 9781610696036}, booktitle={Women in American History: A Social, Political, and Cultural Encyclopedia and Document Collection}, publisher={ABC-CLIO}, author={Levy, R.}, editor={Lamphier, P. and Welch, R.Editors}, year={2017} }
 @article{venkataramanan_levy_kolata_2016, title={Careers Outside Academia: How Should Math and Applied Math Students Prepare?}, volume={49}, number={7}, journal={SIAM News}, author={Venkataramanan, L. and Levy, R. and Kolata, B.}, year={2016}, month={Sep}, pages={6} }
 @book{garfunkel_montgomery_bliss_fowler_galluzzo_giordano_godbold_gould_levy_libertini_et al._2016, place={Bedford, MA}, title={GAIMME :
Guidelines for assessment & instruction in mathematical modeling education}, ISBN={9781611974430 9781611974447}, publisher={Consortium for Mathematics and Its Applications & Society for Industrial and Applied Mathematics}, author={Garfunkel, S.A. and Montgomery, M. and Bliss, K. and Fowler, K. and Galluzzo, B. and Giordano, F. and Godbold, L. and Gould, H. and Levy, R. and Libertini, K. and et al.}, year={2016} }
 @book{garfunkel_montgomery_bliss_fowler_galluzzo_giordano_godbold_gould_levy_libertini_et al._2016, title={GAIMME : Guidelines for assessment & instruction in mathematical modeling education}, publisher={Consortium for Mathematics and Its Applications & Society for Industrial and Applied Mathematics}, author={Garfunkel, S.A. and Montgomery, M. and Bliss, K. and Fowler, K. and Galluzzo, B. and Giordano, F. and Godbold, L. and Gould, H. and Levy, R. and Libertini, K. and et al.}, year={2016} }
 @article{kwon_levy_2016, title={Launch of the Center for Mathematical Modeling: Carlos Castillo-Chavez in El Salvador}, volume={49}, number={4}, journal={SIAM News}, author={Kwon, B. and Levy, R.}, year={2016}, month={May}, pages={11} }
 @article{hernández_levy_felton-koestler_zbiek_2016, title={Mathematical Modeling in the High School Curriculum}, volume={110}, ISSN={0025-5769 2330-0582}, url={http://dx.doi.org/10.5951/mathteacher.110.5.0336}, DOI={10.5951/mathteacher.110.5.0336}, abstractNote={Ideas from the GAIMME report illustrate how teachers can engage students in the modeling process.}, number={5}, journal={The Mathematics Teacher}, publisher={National Council of Teachers of Mathematics}, author={Hernández, Maria L. and Levy, Rachel and Felton-Koestler, Mathew D. and Zbiek, Rose Mary}, year={2016}, month={Dec}, pages={336–342} }
 @misc{levy_2016, title={Mathematics Society Presidents Endorse Active Learning Statement}, url={https://sinews.siam.org/Details-Page/mathematics-society-presidents-endorse-active-learning-statement}, journal={SIAM News Blog}, author={Levy, R.}, year={2016}, month={Dec} }
 @article{levy_2016, title={Mathematics Society Presidents Endorse Active Learning Statement}, url={https://sinews.siam.org/Details-Page/mathematics-society-presidents-endorse-active-learning-statement}, journal={SIAM News Blog}, author={Levy, R.}, year={2016} }
 @article{levy_2016, title={NSF-IPAM Workshop Tackles Workforce Issues}, volume={49}, number={3}, journal={SIAM News}, author={Levy, R.}, year={2016}, month={Apr}, pages={4} }
 @inproceedings{lape_levy_yong_hankel_eddy_2016, title={Probing the Flipped Classroom: Results of A Controlled Study of Teaching and Learning Outcomes in Undergraduate Engineering and Mathematics}, url={http://dx.doi.org/10.18260/p.25958}, DOI={10.18260/p.25958}, abstractNote={Rachel Levy is an Associate Professor of Mathematics and the Associate Dean of Faculty Development at Harvey Mudd College. In addition to her work on fluid mechanics, she is an investigator on two NSF-funded education projects: one studying flipped classrooms and the other preparing teachers for mathematical modeling in the elementary grades. She is the Vice President for Education for SIAM, the Society for Industrial and Applied Mathematics and the founder of the blog Grandma got STEM.}, booktitle={2016 ASEE Annual Conference & Exposition Proceedings}, publisher={ASEE Conferences}, author={Lape, Nancy and Levy, Rachel and Yong, Darryl and Hankel, Nancy and Eddy, Rebecca}, year={2016}, month={Jul} }
 @article{levy_2016, title={Teaching Mathematical Modeling to Students: From Kindergarten Through College and Beyond}, volume={49}, number={4}, journal={SIAM News}, author={Levy, R.}, year={2016}, month={May}, pages={5} }
 @inbook{teague_fowler_levy_2016, place={Reston, VA}, series={Annual perspectives in mathematics education}, title={The GAIMME Report: Mathematical Modeling in the K-16 Curriculum}, ISBN={9780873539739 9780873539746}, booktitle={Mathematical modeling and modeling mathematics}, publisher={National Council of Teachers of Mathematics}, author={Teague, D. and Fowler, K. and Levy, R.}, editor={Hirsch, C.R. and McDuffie, A.R.Editors}, year={2016}, collection={Annual perspectives in mathematics education} }
 @misc{levy_2015, title={5 Reasons to Teach Mathematical Modeling}, url={https://www.americanscientist.org/blog/macroscope/5-reasons-to-teach-mathematical-modeling}, journal={American Scientist Macroscope Blogs}, author={Levy, R.}, year={2015}, month={May} }
 @article{levy_2015, title={5 Reasons to Teach Mathematical Modeling}, url={https://www.americanscientist.org/blog/macroscope/5-reasons-to-teach-mathematical-modeling}, journal={American Scientist Macroscope Blogs}, author={Levy, R.}, year={2015} }
 @article{turner_levy_fowler_2015, title={Collaboration in the Mathematical Sciences Community on Mathematical Modeling Across the Curriculum}, volume={28}, ISSN={0933-2480 1867-2280}, url={http://dx.doi.org/10.1080/09332480.2015.1120122}, DOI={10.1080/09332480.2015.1120122}, abstractNote={12 As representatives of the Society for Industrial and Applied Mathematics (SIAM) who are engaged in education outreach, we are working to bring together the mathematical sciences communities to help facilitate mathematical modeling in the K–12 arena. This effort embraces all aspects of modeling: mathematical, statistical, computational, and data-based, as well as science-/physics-based. Indeed, for most interesting applications, these aspects interweave and no one sphere of expertise will have all the answers. We will use the term “modeling” as an umbrella for all of these. The emergence of data science—and data-enabled science—as a major area of research and study makes this blending of skills and understanding from the entire mathematical sciences spectrum critically important. When we say “mathematical sciences,” we include statistics, operations research, data science, and algorithmic approaches—pure, industrial, and applied mathematics. Certainly, modeling will be a key element of educational programs that prepare students for work in data-rich environments. Arguably, modeling is key to moving from data to information and making good decisions. Another major motivation for this article is the fact that applied mathematics and statistics share much of the raison d’être for K–12 education in the mathematical sciences in the first place. (See also the Usiskin article, “The Relationships Between Statistics and Other collaboration in the mathematical sciences community on mathematical modeling Across the curriculum}, number={4}, journal={CHANCE}, publisher={Informa UK Limited}, author={Turner, Peter R. and Levy, Rachel and Fowler, Kathleen}, year={2015}, month={Oct}, pages={12–18} }
 @article{levy_maki_fowler_2015, title={How Can the SIAM Community Help Embed Math Modeling in K–16 Curricula?}, volume={48}, number={3}, journal={SIAM News}, author={Levy, R. and Maki, K. and Fowler, K.}, year={2015}, month={Apr}, pages={6–7} }
 @inbook{levy_2015, place={Princeton, NJ}, title={Industrial Mathematics Inspires Mathematical Modeling Tasks with High Cognitive Demand}, ISBN={9780691150390}, booktitle={The Princeton Companion to Applied Mathematics}, publisher={Princeton University Press}, author={Levy, R.}, editor={Higham, N.J. and Dennis, M.R.Editors}, year={2015} }
 @misc{levy_2015, title={Internships Connect Math Students to New Career Paths}, url={https://www.americanscientist.org/blog/macroscope/internships-connect-math-students-to-new-career-paths}, journal={American Scientist Macroscope Blogs}, author={Levy, R.}, year={2015}, month={Jul} }
 @article{levy_2015, title={Internships Connect Math Students to New Career Paths}, url={https://www.americanscientist.org/blog/macroscope/internships-connect-math-students-to-new-career-paths}, journal={American Scientist Macroscope Blogs}, author={Levy, R.}, year={2015} }
 @book{levy_2015, title={Mathematical Sciences Internships:  Building Career Pathways}, url={http://www.ipam.ucla.edu/wp-content/uploads/2015/10/NSF-IPAM-industry-internship-workshop-report.pdf}, author={Levy, R.}, year={2015} }
 @book{levy_2015, title={Mathematical Sciences Internships:  Building Career Pathways}, url={http://www.ipam.ucla.edu/wp-content/uploads/2015/10/NSF-IPAM-industry-internship-workshop-report.pdf}, author={Levy, R.}, year={2015} }
 @book{shearer_levy_2015, place={Princeton, NJ}, title={Partial Differential Equations: an Introduction to Theory and Applications}, ISBN={9780691161297}, publisher={Princeton University Press}, author={Shearer, M. and Levy, R.}, year={2015} }
 @article{kwon_levy_2015, title={SIAM at the National Math Festival}, volume={48}, number={6}, journal={SIAM News}, author={Kwon, B. and Levy, R.}, year={2015}, month={Jul}, pages={1,6} }
 @article{levy_2015, title={Should Your Research Be on YouTube?}, volume={48}, number={5}, journal={SIAM News}, author={Levy, R.}, year={2015}, month={Jun}, pages={3} }
 @article{levy_2015, title={The Moody’s Mega Math Challenge Marks 10th Year}, volume={48}, number={5}, journal={SIAM News}, author={Levy, R.}, year={2015}, month={Jun}, pages={6–7} }
 @article{yong_levy_lape_2015, title={Why No Difference? A Controlled Flipped Classroom Study for an Introductory Differential Equations Course}, volume={25}, ISSN={1051-1970 1935-4053}, url={http://dx.doi.org/10.1080/10511970.2015.1031307}, DOI={10.1080/10511970.2015.1031307}, abstractNote={Abstract Flipped classrooms have the potential to improve student learning and metacognitive skills as a result of increased time for active learning and group work and student control over pacing, when compared with traditional lecture-based courses. We are currently running a 4-year controlled study to examine the impact of flipping an Introductory Differential Equations course at Harvey Mudd College. In particular, we compare flipped instruction with an interactive lecture with elements of active learning rather than a traditional lecture. The first two years of this study showed no differences in learning, metacognitive, or affective gains between the control and flipped sections. We believe that contextual factors, such as a strong group-work culture at Harvey Mudd College, contribute to the similar performance of both sections. Additionally, to maintain a rigorous experimental design, we maintained identical content across the control and flipped section; relaxing this requirement in a non-study setting would allow us to take further advantage of educational opportunities afforded by flipping, and may therefore improve student learning.}, number={9-10}, journal={PRIMUS}, publisher={Informa UK Limited}, author={Yong, Darryl and Levy, Rachel and Lape, Nancy}, year={2015}, month={Oct}, pages={907–921} }
 @article{levy_2014, title={AFTERMATH: Every Math Major Should Take a Public-Speaking Course}, volume={21}, ISSN={1072-4117 1947-6213}, url={http://dx.doi.org/10.4169/mathhorizons.21.4.34}, DOI={10.4169/mathhorizons.21.4.34}, abstractNote={"AFTERMATH: Every Math Major Should Take a Public-Speaking Course." Math Horizons, 21(4), p. 34 Additional informationNotes on contributorsRachel LevyRachel Levy is an associate professor of mathematics at Harvey Mudd College and editor-in-chief of SIAM Undergraduate Research Online (SIURO). Email:levy@hmc.edu}, number={4}, journal={Math Horizons}, publisher={Informa UK Limited}, author={Levy, Rachel}, year={2014}, month={Apr}, pages={34–34} }
 @misc{lape_levy_yong_2014, title={Can Flipped Classrooms Help Students Learn? We're Trying to Find Out}, url={https://slate.com/technology/2014/04/flipped-classrooms-can-they-help-students-learn.html}, journal={Slate Future Tense blog}, author={Lape, N.K. and Levy, R. and Yong, D.}, year={2014}, month={Apr} }
 @article{lape_levy_yong_2014, title={Can Flipped Classrooms Help Students Learn? We're Trying to Find Out}, url={https://slate.com/technology/2014/04/flipped-classrooms-can-they-help-students-learn.html}, journal={Slate Future Tense blog}, author={Lape, N.K. and Levy, R. and Yong, D.}, year={2014} }
 @book{turner_crowley_humpherys_levy_socha_wasserstein_2014, place={Philadelphia, PA}, title={Modeling Across the Curriculum II}, url={http://evoq-eval.siam.org/Portals/0/Publications/Reports/ModelingAcross%20Curr_2014.pdf?ver=2018-03-19-103126-827}, institution={Society for Industrial and Applied Mathematics}, author={Turner, P.R. and Crowley, J.M. and Humpherys, J. and Levy, R. and Socha, K. and Wasserstein, R.}, year={2014} }
 @book{turner_crowley_humpherys_levy_socha_wasserstein_2014, title={Modeling Across the Curriculum II}, url={http://evoq-eval.siam.org/Portals/0/Publications/Reports/ModelingAcross%20Curr_2014.pdf?ver=2018-03-19-103126-827}, publisher={Society for Industrial and Applied Mathematics}, author={Turner, P.R. and Crowley, J.M. and Humpherys, J. and Levy, R. and Socha, K. and Wasserstein, R.}, year={2014} }
 @article{levy_2014, title={Postdoc Mentorship Can Launch Careers}, volume={102}, ISSN={0003-0996 1545-2786}, url={http://dx.doi.org/10.1511/2014.111.418}, DOI={10.1511/2014.111.418}, number={6}, journal={American Scientist}, publisher={Sigma Xi}, author={Levy, Rachel}, year={2014}, pages={418} }
 @inproceedings{lape_levy_yong_haushalter_eddy_hankel_2014, title={Probing the Inverted Classroom: A Controlled Study of Teaching and Learning Outcomes in Undergraduate Engineering and Mathematics}, url={http://dx.doi.org/10.18260/1-2--22939}, DOI={10.18260/1-2--22939}, abstractNote={Rachel Levy Mathematics She MA in Instructional Design and a MA/PhD in Applied Mathematics In addition to mathematics, she regularly teaches first-year writing. She serves on the Society for Industrial and Applied Mathematics (SIAM) Education Committee, as Editor-in-chief of SIURO, SIAM Undergraduate Research Online, and as an Associate Editor of Math Horizons. Levy facilitates project-based learning for students at all levels, from end-of-class projects in first-year differential equations to yearlong industrial projects for teams of seniors. She encourages her research students to share mathematical fluid mechanics with a variety of audiences through conferences, outreach programs, and formal research papers. Her online project Grandma got STEM shares the power and talent of geeky grannies with its international readership.}, booktitle={2014 ASEE Annual Conference & Exposition Proceedings}, publisher={ASEE Conferences}, author={Lape, Nancy and Levy, Rachel and Yong, Darryl and Haushalter, Karl and Eddy, Rebecca and Hankel, Nancy}, year={2014} }
 @article{levy_hill_forest_grotberg_2014, title={Pulmonary Fluid Flow Challenges for Experimental and Mathematical Modeling}, volume={54}, ISSN={1540-7063 1557-7023}, url={http://dx.doi.org/10.1093/icb/icu107}, DOI={10.1093/icb/icu107}, abstractNote={Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make.}, number={6}, journal={Integrative and Comparative Biology}, publisher={Oxford University Press (OUP)}, author={Levy, R. and Hill, D. B. and Forest, M. G. and Grotberg, J. B.}, year={2014}, month={Aug}, pages={985–1000} }
 @article{levy_turner_2014, title={SIAM Education Committee Releases Timely Report on Undergraduate Programs}, volume={47}, number={5}, journal={SIAM News}, author={Levy, R. and Turner, P.}, year={2014}, month={Jun}, pages={2} }
 @book{levy_2014, place={Philadelphia, PA}, title={SIAM Education Committee Report on Undergraduate Degree Programs in Applied Mathematics}, url={https://www.siam.org/reports/undergraduate_14.pdf}, institution={SIAM - Society for Industrial and Applied Mathematics}, author={Levy, R.}, year={2014} }
 @book{levy_2014, title={SIAM Education Committee Report on Undergraduate Degree Programs in Applied Mathematics}, url={https://www.siam.org/reports/undergraduate_14.pdf}, publisher={SIAM - Society for Industrial and Applied Mathematics}, author={Levy, R.}, year={2014} }
 @article{strickland_hin_sayanagi_gaebler_daniels_levy_2014, title={Self-healing dynamics of surfactant coatings on thin viscous films}, volume={26}, ISSN={1070-6631 1089-7666}, url={http://dx.doi.org/10.1063/1.4872020}, DOI={10.1063/1.4872020}, abstractNote={We investigate the dynamics of an insoluble surfactant on the surface of a thin viscous fluid spreading inward to fill a surfactant-free region. During the initial stages of surfactant self-healing, Marangoni forces drive an axisymmetric ridge inward to coalesce into a growing central distension; this is unlike outward spreading, in which the ridge only decays. In later dynamics, the distension slowly decays and the surfactant concentration equilibrates. We present results from experiments in which we simultaneously measure the surfactant concentration (using fluorescently tagged lipids) and the fluid height profile (via laser profilometry). We compare the results to simulations of a mathematical model using parameters from our experiments. For surfactant concentrations close to but below the critical monolayer concentration, we observe agreement between the height profiles in the numerical simulations and the experiment, but disagreement in the surfactant distribution. In experiments at lower concentrations, the surfactant spreading and formation of a Marangoni ridge are no longer present, and a persistent lipid-free region remains. This observation, which is not captured by the simulations, has undesirable implications for applications where uniform coverage is advantageous. Finally, we probe the generality of the effect, and find that distensions of similar size are produced independent of initial fluid thickness, size of initial clean region, and surfactant type.}, number={4}, journal={Physics of Fluids}, publisher={AIP Publishing}, author={Strickland, Stephen L. and Hin, Matthew and Sayanagi, M. Richard and Gaebler, Cameron and Daniels, Karen E. and Levy, Rachel}, year={2014}, month={Apr}, pages={042109} }
 @article{bourouiba_hu_levy_2014, title={Surface-Tension Phenomena in Organismal Biology: An Introduction to the Symposium}, volume={54}, ISSN={1540-7063 1557-7023}, url={http://dx.doi.org/10.1093/icb/icu113}, DOI={10.1093/icb/icu113}, abstractNote={Flows driven by surface tension are both ubiquitous and diverse, involving the drinking of birds and bees, the flow of xylem in plants, the impact of raindrops on animals, respiration in humans, and the transmission of diseases in plants and animals, including humans. The fundamental physical principles underlying such flows provide a unifying framework to interpret the adaptations of the microorganisms, animals, and plants that rely upon them. The symposium on "Surface-Tension Phenomena in Organismal Biology" assembled an interdisciplinary group of researchers to address a large spectrum of topics, all articulated around the role of surface tension in shaping biology, health, and ecology. The contributions to the symposium and the papers in this issue are meant to be a starting point for novices to familiarize themselves with the fundamentals of flows driven by surface tension; to understand how they can play a governing role in many settings in organismal biology; and how such understanding of nature's use of surface tension can, in turn, inspire humans to innovate.}, number={6}, journal={Integrative and Comparative Biology}, publisher={Oxford University Press (OUP)}, author={Bourouiba, L. and Hu, D. L. and Levy, R.}, year={2014}, month={Sep}, pages={955–958} }
 @article{levy_lichtman_hu_2014, title={The Scientist-Reporter Collaboration: A Guide to Working with the Press}, volume={47}, number={3}, journal={SIAM News}, author={Levy, R. and Lichtman, F. and Hu, D.}, year={2014}, month={Apr}, pages={5–7} }
 @misc{strait_shearer_levy_cueto-felgueroso_juanes_2014, title={Two Fluid Flow in a Capillary Tube}, volume={109}, ISBN={9783319111247 9783319111254}, ISSN={2194-1009 2194-1017}, url={http://dx.doi.org/10.1007/978-3-319-11125-4_14}, DOI={10.1007/978-3-319-11125-4_14}, journal={Collaborative Mathematics and Statistics Research}, publisher={Springer International Publishing}, author={Strait, Melissa and Shearer, Michael and Levy, Rachel and Cueto-Felgueroso, Luis and Juanes, Ruben}, year={2014}, month={Oct}, pages={149–161} }
 @article{levy_2013, title={Activities for Students: Soap and Slope: Mathematical Adventures in Fluid Dynamics}, volume={107}, ISSN={0025-5769 2330-0582}, url={http://dx.doi.org/10.5951/mathteacher.107.5.0378}, DOI={10.5951/mathteacher.107.5.0378}, abstractNote={The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.}, number={5}, journal={The Mathematics Teacher}, publisher={National Council of Teachers of Mathematics}, author={Levy, Rachel}, year={2013}, month={Dec}, pages={378–384} }
 @article{levy_2013, title={Grandma Got STEM turns 100 posts old!}, volume={3}, ISSN={2159-8118}, url={http://dx.doi.org/10.5642/jhummath.201302.15}, DOI={10.5642/jhummath.201302.15}, abstractNote={The Grandma Got STEM blog celebrates the contributions of senior women to Science, Technology, Engineering and Mathematics. This announcement discusses the origins of the blog and describes the submission process for the ongoing project.}, number={2}, journal={Journal of Humanistic Mathematics}, publisher={Claremont Colleges Library}, author={Levy, Rachel}, year={2013}, month={Jul}, pages={149–152} }
 @article{williams_levy_2013, title={Hitting the Target: Connecting Parents to STEM}, volume={33}, number={6}, journal={MAA Focus}, author={Williams, T. and Levy, R.}, year={2013}, month={Dec}, pages={15–17} }
 @article{levy_2013, title={Quantitative Approaches to Sustainability Seminars}, volume={60}, ISSN={0002-9920 1088-9477}, url={http://dx.doi.org/10.1090/noti979}, DOI={10.1090/noti979}, abstractNote={How can mathematicians contribute to education about sustainability? Mathematicians study climate change, energy-related technologies, models of energy availability, production and consumption, and even the political and social aspects of sustainable legislation and practices. However, at this point, few courses on sustainability can be found in mathematics department offerings. When we consider problems that our current and future students will face, energy sustainability certainly seems important. But how many of these ideas reach our classrooms? We can incorporate sustainability into our existing courses through problem sets, projects, capstones, or independent studies. We can also reach a broad audience through the topical seminars offered at many colleges and universities. These seminars, sometimes specially designed for first-year students, tend to be characterized by small class size, discussion, and project-based learning, and perhaps by speakers and field trips. When students of all majors enter these courses they bring a wide range of mathematical preparation, confidence, and enthusiasm, which can make mathematical versions of these seminars challenging to design. A seminar in sustainability offered by mathematicians can provide students with an attractive path toward quantitative literacy. In this article I will explore how David MacKay’s free online textbook, Sustainable Energy Without the Hot Air (SEWTHA), could be used in a seminar to introduce students to principles of sustainability.}, number={04}, journal={Notices of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Levy, Rachel}, year={2013}, month={Apr}, pages={1} }
 @article{levy_turner_2013, title={SIURO: A Flourishing Home for Undergraduate Research}, volume={46}, number={8}, journal={SIAM News}, author={Levy, R. and Turner, P.}, year={2013}, month={Oct}, pages={5} }
 @misc{keeter_moore_muller_nieters_flenner_martonosi_bertozzi_percus_levy_2012, title={Cooperative search with autonomous vehicles in a 3D aquatic testbed}, url={http://dx.doi.org/10.1109/acc.2012.6314965}, DOI={10.1109/acc.2012.6314965}, abstractNote={We consider the problem of cooperative search using autonomous aquatic vehicles, giving a proof-of-concept demonstration in an aquatic testbed. We implement a point-to-point controller for remote-controlled submarines with severe control and buoyancy limitations, develop software to track their motion and establish reliable communication and control. We then propose multiple randomized algorithms, based on Lévy flights, for locating sparse targets in a three-dimensional bounded environment. These algorithms are tested in simulation, showing that they are competitive with nonrandom systematic search, while likely also more robust. The simulations are combined with in-tank tests to display performance under real physical conditions.}, journal={2012 American Control Conference (ACC)}, publisher={IEEE}, author={Keeter, M. and Moore, D. and Muller, R. and Nieters, E. and Flenner, J. and Martonosi, S. E. and Bertozzi, A. L. and Percus, A. G. and Levy, R.}, year={2012}, month={Jun} }
 @misc{levy_uminsky_2012, title={Formation of Ocean Surface Patterns by Cetacean Fluke Oscillations}, ISBN={9781461439967 9781461439974}, ISSN={0940-6573}, url={http://dx.doi.org/10.1007/978-1-4614-3997-4_11}, DOI={10.1007/978-1-4614-3997-4_11}, abstractNote={This paper presents a theory describing the fluid mechanics of whale flukeprints. It contains excerpts of a longer paper recently published in the International Journal of Non-Linear Mechanics special issue on biological structures. Whale flukeprints are smooth oval-shaped water patches that form on the surface of the ocean behind a swimming or diving whale. The prints persist up to several minutes and can be used to track whales cruising near the ocean surface. The motion of the fluke provides a mechanism for shedding vortex rings. The subsequent interaction of the vortex ring with the ocean surface damps the short wavelength capillary waves in the print. The theory suggests that the role of natural surfactants are of secondary importance in the early formation of flukeprints. We describe potential directions for future research, including collection of quantitative data from real flukeprints.}, journal={Natural Locomotion in Fluids and on Surfaces}, publisher={Springer New York}, author={Levy, Rachel and Uminsky, David}, year={2012}, pages={159–166} }
 @article{levy_uminsky_park_calambokidis_2011, title={A theory for the hydrodynamic origin of whale flukeprints}, volume={46}, ISSN={0020-7462}, url={http://dx.doi.org/10.1016/j.ijnonlinmec.2010.12.009}, DOI={10.1016/j.ijnonlinmec.2010.12.009}, abstractNote={Abstract Whale flukeprints are an often observed, but poorly understood, phenomenon. Used by whale researchers to locate whales, flukeprints refer to a strikingly smooth oval-shaped water patch which forms behind a swimming or diving whale on the surface of the ocean and persists up to several minutes. In this paper we provide a description of hydrodynamic theory and related experiments explaining the creation and evolution of these “whale footprints.” The theory explains that the motion of the fluke provides a mechanism for shedding of vortex rings which subsequently creates a breakwater that damps the short wavelength capillary waves. The theory also suggests that the role of natural surfactants are of secondary importance in the early formation of these prints.}, number={4}, journal={International Journal of Non-Linear Mechanics}, publisher={Elsevier BV}, author={Levy, R. and Uminsky, D. and Park, A. and Calambokidis, J.}, year={2011}, month={May}, pages={616–626} }
 @article{levy_rosenthal_wong_2010, title={Engineering flow states with localized forcing in a thin Marangoni-driven inclined film}, volume={82}, ISSN={1539-3755 1550-2376}, url={http://dx.doi.org/10.1103/physreve.82.056320}, DOI={10.1103/physreve.82.056320}, abstractNote={Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections to theory for hyperbolic conservation laws predicting wave fronts from Marangoni-driven thin films without forcing. We demonstrate how a variety of forcing profiles, such as gaussian, rectangular, and triangular, affect the formation of downstream transient structures, including an N wave not commonly discussed in the context of thin films. Simulations employing a controlled approximation of a compressive-undercompressive wave pair demonstrate possibilities for applications of localized forcing as microfluidic valve. In the simulations, localized forcing provides a control parameter that can be used to determine mass flux and film profiles.}, number={5}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Levy, Rachel and Rosenthal, Stephen and Wong, Jeffrey}, year={2010}, month={Nov} }
 @article{grunewald_levy_mata_ward_bertozzi_2009, title={Self-similarity in particle-laden flows at constant volume}, volume={66}, ISSN={0022-0833 1573-2703}, url={http://dx.doi.org/10.1007/s10665-009-9345-4}, DOI={10.1007/s10665-009-9345-4}, abstractNote={This paper deals with the evolution of a localized, constant-volume initial condition on an incline into a spreading descending thin-film solution. Clear fluids in this geometry are known to have a front position that moves according to a t 1/3 scaling law, based on similarity-solution analysis by Huppert (Nature 300:427–429, 1982). The same dynamics are investigated for particle-laden flow using a recently proposed lubrication model and physical experiments. The analysis includes the role of a precursor in the model. In the lubrication model, the height of the precursor significantly influences the position of the fluid front, independent of particles settling in the direction of flow. By comparing theory with experiments it is shown that the t 1/3 scaling law persists, to leading order, for particle-laden flows with particle settling. However, additional physics is needed in the existing lubrication models to quantitatively explain departures from clear-fluid self-similarity due to particle settling.}, number={1-3}, journal={Journal of Engineering Mathematics}, publisher={Springer Science and Business Media LLC}, author={Grunewald, Natalie and Levy, Rachel and Mata, Matthew and Ward, Thomas and Bertozzi, Andrea L.}, year={2009}, month={Oct}, pages={53–63} }
 @misc{peterson_shearer_witelski_levy_2009, title={Stability of traveling waves in thin liquid films driven by gravity and surfactant}, volume={67}, ISSN={0160-7634 2324-7088}, url={http://dx.doi.org/10.1090/psapm/067.2/2605281}, DOI={10.1090/psapm/067.2/2605281}, abstractNote={A thin lay er of fluid flowing down a solid planar surface has a free sur face height described by a nonlinear POE derived via the lubrication ap­ proximat ion from the Navi er St okes equations. For th in films , sur face tension plays an important rol e both in providing a significant driving force and in smoothi ng the free surface. Sur fac tant molecules on the free surface tend to reduce surfac e tensio n, set t ing up grad ients that modify th e shape of the free surface. In ear lier work [12, 13J a traveling wave was found in which the free sur fac e undergoes three sharp transitions, or in ternal layers , and the surfactant is d istributed ove r a bounded region . T his triple-step traveling wave sa t is fies a system of POE, a hyperbolic conservation law for the free sur face height , and a degenerate parabolic equation descr ibing t he surfac t ant distribution. As such, th e traveling wave is overco rnpressive. An ex am ination of the lin­ earized equat ions indicates the direction and growt h rates of one-dimensiona l waves generated by small perturbat ion s in va r ious parts of the wave. Numeri­ cal si mulat ions o f the nonlinea r eq uat ions o ffer further evide nce of stability t o one-d ime nsiona l perturbations.}, journal={Hyperbolic Problems: Theory, Numerics and Applications}, publisher={American Mathematical Society}, author={Peterson, Ellen and Shearer, Michael and Witelski, Thomas P. and Levy, Rachel}, year={2009}, pages={855–868} }
 @article{levy_shearer_taylor_2007, title={Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics}, volume={17}, ISSN={1051-1970 1935-4053}, url={http://dx.doi.org/10.1080/10511970601131555}, DOI={10.1080/10511970601131555}, abstractNote={Abstract We describe a program that provides structured practice of prerequisite material to students in an ordinary differential equations course using an existing automated homework system originally designed for precalculus and calculus classes. The goal of the program is to improve students' comprehension of material presented in class by timing the review to occur just before the prerequisite material is relevant in class. The review is designed to gain class time that would otherwise be dedicated to review, with minimal involvement of the instructor. We report positive responses from both instructors and students in two sections of the course.}, number={2}, journal={PRIMUS}, publisher={Informa UK Limited}, author={Levy, Rachel and Shearer, Michael and Taylor, Padraic}, year={2007}, month={May}, pages={167–180} }
 @article{levy_shearer_witelski_2007, title={Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves}, volume={18}, ISSN={0956-7925 1469-4425}, url={http://dx.doi.org/10.1017/s0956792507007218}, DOI={10.1017/s0956792507007218}, abstractNote={The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerate-parabolic, and admits traveling wave solutions in which the free-surface height is piecewise constant, and the surfactant concentration is piecewise linear and continuous. The jumps and corners in the traveling waves are regularized when the small parameters are nonzero; their structure is revealed through a combination of analysis and numerical simulation.}, number={6}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={Levy, Rachel and Shearer, Michael and Witelski, Thomas P.}, year={2007}, month={Dec}, pages={679–708} }
 @article{finkel_kuster_lasater_levy_reese_ipsen_2006, title={Communicating Applied Mathematics: Four Examples}, volume={48}, ISSN={0036-1445 1095-7200}, url={http://dx.doi.org/10.1137/s0036144504443523}, DOI={10.1137/s0036144504443523}, abstractNote={Communicating Applied Mathematics is a writing- and speaking-intensive graduate course at North Carolina State University. The purpose of this article is to provide a brief description of the course objectives and the assignments. Parts A--D of of this article represent the class projects and illustrate the outcome of the course: 
* The Evolution of an Optimization Test Problem: From Motivation to Implementation, by Daniel E. Finkel and Jill P. Reese 
* Finding the Volume of a Powder from a Single Surface Height Measurement, by Christopher Kuster 
* Finding Oscillations in Resonant Tunneling Diodes, by Matthew Lasater 
* A Shocking Discovery: Nonclassical Waves in Thin Liquid Films, by Rachel Levy 
We introduce a water-supply problem considered by the optimization and hydrology communities for benchmarking purposes. The objective is to drill five wells so that the cost of pumping water out of the ground is minimized. Using the implicit filtering optimization algorithm to locate the wells, we save approximately $2,500 over the cost of a given initial well configuration. 
 
The volume of powder poured into a bin with obstructions is found by calculating the height of the surface at every point. This is done using the fast marching algorithm. We look at two different bin geometries and determine the volumes as a function of the powder height under the spout. The surface of the powder satisfies a two-dimensional eikonal equation. This equation is solved using the fast marching method. 
 
Resonant tunneling diodes (RTDs) are ultrasmall semiconductor devices that have potential as very high-frequency oscillators. To describe the electron transport within these devices, physicists use the Wigner--Poisson equations which incorporate quantum mechanics to describe the distribution of electrons within the RTD. Continuation methods are employed to determine the steady-state electron distributions as a function of the voltage difference across the device. These simulations predict the operating state of the RTD under different applied voltages and will be a tool to help physicists understand how changing the voltage applied to the device leads to the development of current oscillations. 
 
When a thin film flows down an inclined plane, a bulge of fluid, known as a capillary ridge, forms on the leading edge and is subject to a fingering instability in which the fluid is channeled into rivulets. This process is familiar to us in everyday experiments such as painting a wall or pouring syrup over a stack of pancakes. It is also observed that changes in surface tension due to a temperature gradient can draw fluid up an inclined plane. Amazingly, in this situation the capillary ridge broadens and no fingering instability is observed. Numerical and analytical studies of a mathematical model of this process led to the discovery that these observations are associated with a nonclassical shock wave previously unknown to exist in thin liquid films.}, number={2}, journal={SIAM Review}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Finkel, Daniel E. and Kuster, Christopher and Lasater, Matthew and Levy, Rachel and Reese, Jill P. and Ipsen, Ilse C. F.}, year={2006}, month={Jan}, pages={359–389} }
 @article{witelski_shearer_levy_2006, title={Growing surfactant waves in thin liquid films driven by gravity}, volume={1}, ISSN={1687-1200 1687-1197}, url={http://dx.doi.org/10.1155/amrx/2006/15487}, DOI={10.1155/amrx/2006/15487}, abstractNote={The dynamics of a gravity-driven thin film flow with insoluble surfactant are described in the lubrication approximation by a coupled system of nonlinear PDEs. When the total quantity of surfactant is fixed, a traveling wave solution exists. For the case of constant flux of surfactant from an upstream reservoir, global traveling waves no longer exist as the surfactant accumulates at the leading edge of the thin film profile. The dynamics can be described using matched asymptotic expansions for t →∞ . The solution is constructed from quasistatically evolving traveling waves. The rate of growth of the surfactant profile is shown to be O( √ t) and is supported by numerical simulations.}, journal={Applied Mathematics Research eXpress}, publisher={Oxford University Press (OUP)}, author={Witelski, T. P. and Shearer, M. and Levy, R.}, year={2006}, month={Jan} }
 @article{levy_shearer_2006, title={The Motion of a Thin Liquid Film Driven by Surfactant and Gravity}, volume={66}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/050637030}, DOI={10.1137/050637030}, abstractNote={We investigate wave solutions of a lubrication model for surfactant-driven flow of a thin liquid film down an inclined plane. We model the flow in one space dimension with a system of nonlinear PDEs of mixed hyperbolic-parabolic type in which the effects of capillarity and surface diffusion are neglected. Numerical solutions reveal distinct patterns of waves that are described analytically by combinations of traveling waves, some with jumps in height and surfactant concentration gradient. The various waves and combinations are strikingly different from what is observed in the case of flow on a horizontal plane. Jump conditions admit new shock waves sustained by a linear surfactant wave traveling upstream. The stability of these waves is investigated analytically and numerically. For initial value problems, a critical ratio of upstream to downstream height separates two distinct long-time wave patterns. Below the critical ratio, there is also an exact solution in which the height is piecewise constant and ...}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Levy, R. and Shearer, M.}, year={2006}, month={Jan}, pages={1588–1609} }
 @article{levy_shearer_2005, title={Kinetics and nucleation for driven thin film flow}, volume={209}, ISSN={0167-2789}, url={http://dx.doi.org/10.1016/j.physd.2005.07.003}, DOI={10.1016/j.physd.2005.07.003}, abstractNote={The lubrication theory of thin liquid films, driven by a constant surface stress opposing gravity, is described by a scalar fourth order PDE for the film height h:ht+(h2−h3)x=−γ(h3hxxx)x, in which γ is a positive constant related to surface tension. In this paper, the wave structure of solutions observed in numerical simulations with γ>0 is related to the recent hyperbolic theory of the underlying scalar conservation law, in which γ=0. This theory involves a kinetic relation, describing possible undercompressive shocks, and a nucleation condition, governing the transition from classical to non-classical solution of the Riemann problem. The kinetic relation and nucleation condition are derived from consideration of traveling wave solutions (with γ>0). The kinetic relation is identified with a codimension-one bifurcation of the corresponding vector field, for which there is a traveling wave approximating an undercompressive shock. The nucleation condition is identified as a transition in the vector field at which there is no traveling wave connecting upstream and downstream heights. The thresholds defined by these conditions are incorporated into a Riemann solver map, which is tested for initial value problems for the full PDE. It is found that the parameter γ determines a limit to the applicability of the hyperbolic theory, in which the fourth order diffusion can dominate short-time transients, resulting in long-time convergence to the classical solution when the hyperbolic theory would predict a non-classical solution.}, number={1-4}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier BV}, author={Levy, Rachel and Shearer, Michael}, year={2005}, month={Sep}, pages={145–163} }
 @article{levy_shearer_2004, title={Comparison of two dynamic contact line models for driven thin liquid films}, volume={15}, ISSN={0956-7925 1469-4425}, url={http://dx.doi.org/10.1017/s0956792504005741}, DOI={10.1017/s0956792504005741}, abstractNote={The modeling of the motion of a contact line, the triple point at which solid, liquid and air meet, is a major outstanding problem in the fluid mechanics of thin films [2, 9]. In this paper, we compare two well-known models in the specific context of Marangoni driven films. The precursor model replaces the contact line by a sharp transition between the bulk fluid and a thin layer of fluid, effectively pre-wetting the solid; the Navier slip model replaces the usual no-slip boundary condition by a singular slip condition that is effective only very near the contact line. We restrict attention to traveling wave solutions of the thin film PDE for a film driven up an inclined planar solid surface by a thermally induced surface tension gradient. This involves analyzing third order ODE that depend on several parameters. The two models considered here have subtle differences in their description, requiring a careful treatment when comparing traveling waves and effective contact angles. Numerical results exhibit broad agreement between the two models, but the closest comparison can be done only for a rather restricted range of parameters. The driven film context gives contact angle results quite different from the case of a film moving under the action of gravity alone. The numerical technique for exploring phase portraits for the third order ODE is also used to tabulate the kinetic relation and nucleation condition, information that can be used with the underlying hyperbolic conservation law to explain the rich combination of wave structures observed in simulations of the PDE and in experiments [3, 15].}, number={6}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={Levy, Rachel and Shearer, Michael}, year={2004}, month={Dec}, pages={625–642} }