Partial CV for Richard J. Braun


Contact Information
Department of Mathematical Sciences
University of Delaware
Newark, DE 19716
Voice: (302) 831-1869, Fax: (302) 831-4511
Email: braun@math.udel.edu
Web: http://www.math.udel.edu/~braun

Education
Department of Engineering Sciences and Applied Mathematics
Northwestern University, Evanston, IL
Ph.D. in Applied Mathematics, 1991
Advisor: Professor S.H. Davis

Department of Mechanical Engineering
Santa Clara University, Santa Clara, CA
M.S. in Mechanical Engineering, 1987
B.S. in Mechanical Engineering, 1983

Experience
Department of Mathematical Sciences
University of Delaware, Newark, DE
Professor, 2004-
Associate Professor, 1999-2004.
Assistant Professor, 1995-1999.

Institute for Mathematics and its Applications
University of Minnesota, Minneapolis, MN
Associate Director, 2013-2014.

School of Mathematics
University of Minnesota, Minneapolis, MN
Visiting Professor, 2013-2014.

Mathematical and Computational Sciences Division
National Institute of Standards and Technology, Gaithersburg, MD
Guest Researcher, 2007-2011.
Faculty Appointee, 1996-2001, 2001-2006.
Research Mathematician, 1993-1995.
National Research Council Postdoctoral Fellow, 1991-1993.
Advisor: Dr. G.B. McFadden

Institute for Mathematics and Its Applications
University of Minnesota, Minneapolis, MN
Long term visitor, 9/2009-12/2009.

Faculty of Mathematical Studies
University of Southampton, Southampton, UK
EPSRC Visiting Fellow, 1/2002-8/2002.

Hewlett Packard Company, Santa Clara, CA
Manufacturing Engineer and Development Engineer, 1984-1987.

Department of Mechanical Engineering
Santa Clara University, Santa Clara, CA
Teaching Assistant, 1983-1984.

Editorial Positions
Mathematics-in-Industry Case Studies, Editorial Board, 2007-now.
SIAM Journal on Applied Mathematics, Associate Editor, 2009-now.
Journal of Engineering Mathematics, Executive Associate Editor, 2011-now.
Associate Editor, Interfacial Phenomena and Heat Transfer, 2013-now.
Editorial Board Member, Journal of Modeling in Ophthalmology, 2015-now.

Research Interests
My research interests include the theory of phase change and fluid dynamics with free boundaries and the dynamics of the tear film on the ocular surface. The mathematical aspects include nonlinear ordinary and partial differential equations, differential algebraic equations, asymptotic and perturbation methods, and scientific computing.

Publications
  1. Computed Tear Film and Osmolarity Dynamics on an Eye-Shaped Domain," Longfei Li, R.J. Braun, T.A. Driscoll, W.D. Henshaw, J.W. Banks and P.E. King-Smith, Math. Med. Biol., 2015; doi.
  2. The Effects of Increasing Ocular Surface Stimulation on Blinking and Tear Secretion," Ziwei Wu, C.G. Begley, N. Port, A. Bradley, R.J. Braun and P.E. King-Smith, Invest. Ophthalmol. Vis. Sci., 56:4211-4220, 2015; doi
  3. "Tear Film Dynamics with Evaporation, Osmolarity and Surfactant Transport," J. Siddique and R.J. Braun, Appl. Math. Modeling, 39:255-269, 2015; doi.
  4. "Tear film dynamics with evaporation, wetting, and time-dependent flux boundary condition on an eye-shaped domain," Longfei Li, RJ Braun, KL Maki, WD Henshaw, PE King-Smith, Physics of Fluids, 26:052101 (2014); doi
  5. "A Model for Tear Film Thinning With Osmolarity and Fluorescein," RJ Braun, NR Gewecke, CG Begley, PE King-Smith and JI Siddique, Invest. Ophthalmol. Vis. Sci. 55:1133-1142, 201; doi
  6. "Heat transfer and tear film dynamics over multiple blink cycles," Quan Deng, RJ Braun and TA Driscoll, Phys. Fluids, 26:071901 (2014); doi
  7. "A model for the tear film and ocular surface temperature for partial blinks," Quan Deng, RJ Braun, TA Driscoll and PE King-Smith, Interfacial Phenomena and Heat Transfer, 1:357-381, 2013; doi
  8. "Evaporation-driven instability of the precorneal tear film," C-C Peng, C Cerretani, RJ Braun and CJ Radke, Advances in Colloid and Interface Science, 206:250-264, 2014; doi
  9. "Tear Film Breakup and Structure Studied by Simultaneous Video Recording of Fluorescence and Tear Film Lipid Layer Images," PE King-Smith, KS Reuter, RJ Braun, JJ Nichols and KK Nichols, Invest. Ophthalmol. Vis. Sci., 54:4900-09, 2013; doi
  10. "Tear Film Images and Breakup Analyzed Using Fluorescent Quenching," PE King-Smith, P. Ramamoorthy, RJ Braun and JJ Nichols, Invest. Ophthalmol. Vis. Sci. 54:6003-11, 2013; doi
  11. "A Model for the Human Tear Film with Heating from Within the Eye," Longfei Li and R.J. Braun, Phys. Fluids 24, (2012) 062103.
  12. "Dynamics of the Tear Film," R.J. Braun, Annu. Rev. Fluid Mech. 44, (2012) 267-297.
  13. "High resolution microscopy of the lipid layer of the tear film," P.E. King-Smith, J.J. Nichols, R.J. Braun, K.K. Nichols, The Ocular Surface 9(4), (2011) 197-211.
  14. "Continuum Models for the Spread of Alcohol Abuse," D.A. French, Z. Teymuroglu, T.J. Lewis and R.J. Braun, J. Int. Eqns. Appl., 22 (2010) 443-464.
  15. "Thin Film Dynamics on a Prolate Spheroid with Application to the Cornea," R.J. Braun, R. Usha, G.B. McFadden, T.A. Driscoll, L.P. Cook and P.E. King-Smith, J. Engrg. Maths., 73 (2012) 121-138.
  16. "Tear Film Dynamics on an Eye-shaped Domain II. Flux Boundary Conditions," K.L. Maki, R.J. Braun, P. Ucciferro, W.D. Henshaw and P.E. King-Smith, J Fluid Mech 647 (2010) 361-390.
  17. "Tear Film Dynamics on an Eye-shaped Domain I. Pressure Boundary Conditions," K.L. Maki, R.J. Braun, W.D. Henshaw and P.E. King-Smith, Math Med Biol 27, (2010) 227-254.
  18. "A Model for Wetting and Evaporation of a Post-blink Precorneal Tear Film," K.N. Winter, D.M. Anderson and R.J. Braun, Math Med Biol 27, (2010) 211-225.
  19. "The Contribution of Lipid Layer Movement to Tear Film Thinning and Breakup," P.E. King-Smith, B.A. Fink, J.J. Nichols, K.K. Nichols, R.J. Braun and G.B. McFadden, Invest. Ophthalmol. Vis. Sci., 50, (2009) 2747-2756.
  20. "An Overset Grid Method for the Study of Reflex Tearing," K.L. Maki, R.J. Braun, T.A. Driscoll, and P.E. King-Smith, Math. Med. Biol. 25, (2008) 187-214.
  21. "Contributions of Evaporation and Other Mechanisms to Tear Film Thinning and Breakup: A Review," P. Ewen King-Smith, Jason J. Nichols, Kelly K. Nichols, Barbara A. Fink and Richard J. Braun, Optom. Vision Sci. 85(8), (2008) 623-630.
  22. "Single-Equation Models for the Tear Film in a Blink Cycle: Realistic Lid Motion," A. Heryudono, R.J. Braun, T.A. Driscoll, L.P. Cook, K. Maki and P.E. King-Smith, Math. Med. Biol. 24, (2007) 347-377.
  23. "Model Problems for the Tear Film in a Blink Cycle: Single Equation Models," R.J. Braun and P.E. King-Smith, J. Fluid Mech. 586, (2007) 465-490.
  24. "Models for Human Tear Film Dynamics," R.J. Braun, in Wave Dynamics and Thin Film Flow Systems, R. Usha, A. Sharma and B.S. Dandapat, eds., (Narosa, Chennai, India, 2006) pp. 404-434.
  25. "Application of Small-World Network Theory into Alcohol Epidemiology," R.J. Braun, R.A. Wilson, R.A. Buchanan, J.A. Pelesko, and J.A. Gleeson, J. Studies on Alcohol 67 (2006) 591-599.
  26. "Numerical Simulation of Liquid Phase Electro-Epitaxial Selective Area Growth," M. Khenner and R.J. Braun," J. Crystal Growth 279, (2005) 213-228.
  27. "Modelling Drainage of the Precorneal Tear Film After a Blink," R.J. Braun and A.D. Fitt, Mathematical Medicine and Biology 20, (2003) 1-28.
  28. "A1-L1_0 Phase Boundaries and Anisotropy via Multiple-Order-Parameter Theory for an fcc Alloy," G.B. Tanoglu, R.J. Braun, J.W. Cahn and G.B. McFadden, Interfaces and Free Boundaries 5(3), (2003) 275-299.
  29. "A 2+1 Dimensional Insoluble Surfactant Model for Vertical Draining Free Film," S. Naire, R.J. Braun and S.A. Snow, J. Comp. Appl. Math 166, (2004) 385-410.
  30. "A Model for Anisotropic Epitaxial Lateral Overgrowth," M. Khenner, R.J. Braun and M.G. Mauk, J. Crystal Growth 241, (2002) 330-346.
  31. "An Isotropic Model for Crystal Growth from Vapor on a Patterned Substrate," M. Khenner, R.J. Braun and M.G. Mauk, J. Crystal Growth, 235 (2002) 425-438.
  32. "Models for Gravitationally-Driven Free Film Drainage," R.J. Braun, S.A. Snow, and S. Naire, J. Engrg. Math. 43, (2002) 281-314.
  33. "Gravitationally-Driven Drainage of a Bounded Vertical Film with an Insoluble Surfactant," A.H. Heidari, R.J. Braun, A.H. Hirsa, S.A. Snow and S. Naire, J. Colloid Interface Sci 253, (2002) 295--307.
  34. "Model Phase Diagrams for an fcc Alloy," R.J. Braun, J. Zhang, J.W. Cahn, G.B. McFadden and A.A. Wheeler, Proceedings of Interfaces for the Twenty-First Century, (Imperial College Press, London, 2002), pp. 213-230.
  35. "An Insoluble Surfactant Model for a Vertical Draining Free Film with Variable Surface Viscosity," S. Naire, R.J. Braun, and S.A. Snow, Physics of Fluids 13, (2001) 2492-2502.
  36. "An Insoluble Surfactant Model for a Vertical Draining Free Film," S. Naire, R.J. Braun, and S.A. Snow, J. Colloid Interface Sci., 230 (2000) 91-106.
  37. "Modelling the Stabilising Behaviour of Silicone Surfactants During the Processing of Polyurethane Foam: The Use of Thin Liquid Films," Steven A. Snow, Udo C. Pernisz, Benjamin M. Nugent, Robert E. Stevens, Richard J. Braun and Shailesh Naire, in Advances in Urethane Science and Technology, ed. by D. Klempner and K.C. Frisch (Rapra Technology Ltd., Shawsbury, UK, 2001) pp. 213-260 (book chapter).
  38. "Limiting Cases of Gravitational Drainage of a Vertical Free Film for Evaluating Surfactants," S. Naire, R.J. Braun, and S.A. Snow, SIAM J. Appl. Math., 61 (2000) 889-913.
  39. "A Perspective on Phase-Field Models of Solidification," R.J. Braun, American Association for Crystal Growth Newsletter, Winter, 1999 (solicited review article).
  40. "Gravitational Drainage of a Tangentially Immobile Thick Film," R.J. Braun, S.A. Snow and U.C. Pernisz, J. Colloid Interface Sci. 219 (1999) 225-240.
  41. "Perturbation Analysis of a Problem of Carrier," A.D. MacGillivray, R.J. Braun and G.B. Tanoglu, Stud. Appl. Math., 104 (2000) 293-311.
  42. "Adaptive Finite-Difference Computations of Dendritic Growth Using a Phase-Field Model," R.J. Braun, B.T. Murray and J. Soto, Model. Sim. Mat. Sci. Eng. 5 (1997) 365-380.
  43. "Adaptive Phase-Field Computations of Dendritic Crystal Growth," R.J. Braun and B.T. Murray, J. Crystal Growth 177 (1997) 41-53.
  44. "Anisotropic Equilibrium and Growth Shapes in a Multiple-Order-Parameter Model of an fcc Alloy," R.J. Braun, J.W. Cahn, G.B. McFadden, H.E. Rushmeier and A.A. Wheeler, Acta mater. 46 (1997) 1-12.
  45. "Anisotropy of Interfaces in an Ordered Alloy: A Multiple-Order-Parameter Model," R.J. Braun, J.W. Cahn, G.B. McFadden, and A.A. Wheeler, Trans. Roy. Soc. London A 355 (1997) 1787-1833.
  46. "Anisotropic Interfaces and Ordering in fcc Alloys: A Multiple-Order-Parameter Continuum Theory," R.J. Braun, J.W. Cahn, J. Hagedorn, G.B. McFadden and A.A. Wheeler, Mathematics of Microstructure Evolution, ed. L-Q. Chen et al., (TMS/SIAM, Philadelphia, 1996) 225-244.
  47. "Lubrication Theory for the Reactive Spreading of Thin Drops," R.J. Braun, B.T. Murray, W.J. Boettinger and G.B. McFadden, Physics of Fluids 7 (1995) 1797-1810.
  48. "Recent Developments in Phase-Field Models of Solidification," A.A. Wheeler, N.A. Ahmad, W.J. Boettinger, R.J. Braun, G.B. McFadden and B.T. Murray, Advances in Space Research 16 (1995) pp. (7)163-(7)172.
  49. "Morphological Instability in Phase Field Models of Solidification," R. J. Braun, G. B. McFadden and S. R. Coriell, Phys. Rev. E 49 (1994) 4336-4352.
  50. "Thermodynamically-Consistent Phase-Field Models for Solidification," S. L. Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun and G. B. McFadden, Physica D 69 (1993) 189-200.
  51. "Phase-Field Models for Anisotropic Interfaces," G. B. McFadden, A. A. Wheeler, R. J. Braun, S. R. Coriell and R. F. Sekerka, Phys. Rev. E 48 (1993) 2016-2024.
  52. "Asymptotic Behavior of Modulated Taylor-Couette Flows with a Crystal-Melt Interface," R.J. Braun, G.B. McFadden, B.T. Murray, S.R. Coriell, M.E. Glicksman and M.E. Selleck, Phys. Fluids A 5 (1993) 1891-1903.
  53. "Effect of Modulated Taylor-Vortex Flows on Crystal-Melt Interfaces," G.B. McFadden, R.J. Braun, B.T. Murray, S.R. Coriell and M.E. Glicksman, Proceedings of the NATO Advanced Research Workshop on Interactive Dynamics of Convection and Solidification, (Kluwer Scientific, Amsterdam, 1992) pp. 19-21.
  54. "Pulsatile Instability in Rapid Directional Solidification: Strongly Nonlinear Analysis," R.J. Braun, G.J. Merchant, K. Brattkus and S.H. Davis, Proceedings of the VIIIth European Symposium on Materials and Fluid Sciences in Microgravity, Vol. II, (ESA Publications Division, Noordwijk, 1992) pp. 559-562.
  55. "Pulsatile Instability in Rapid Directional Solidification: Strongly Nonlinear Analysis," G. J. Merchant, R. J. Braun, K. Brattkus and S. H. Davis, SIAM J. Appl. Math. 52 (1992) 1279-1302.
  56. "Pulsatile and Cellular Mode Interaction in Rapid Directional Solidification," R. J. Braun, G. J. Merchant and S. H. Davis, Phys. Rev. B 45 (1992) 7002-7016.
  57. "Cellular Instability in Rapid Directional Solidification: Bifurcation Theory," R.J. Braun and S.H. Davis, Acta metall. mater. 40 (1992) 2617-2638.
  58. "Oscillatory Instabilities in Rapid Directional Solidification: Bifurcation Theory," R.J. Braun and S.H. Davis, J. Crystal Growth 112 (1991) 670-690.

Funding History

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Visiting Professors

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Selected Professional Activities

Recent Invited Talks

Recent Contributed Talks

Honors and Awards

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Personal Information
Citizenship: U.S.A.
Hobbies: Bicycling, running and hiking.


Richard Braun 9/29/15