Benjamin Vaughan

Benjamin L Vaughan

Associate Professor

Associate Professor

French Hall


A&S Mathematical Sciences - 0025


BS: Wilmington College Wilmington, Ohio, 2001 (Math/Computer Science)

MS: Northwestern University Evanston, IL, 2002 (Applied Mathematics)

PhD: Northwestern University Evanston, IL, 2007 (Applied Mathematics)

Research and Practice Interests

Mathematical biology, mathematical modeling, biofluids, biomechanics, numerical analysis, moving interfaces, pattern formation, CFD, numerical methods for hyperbolic problems, finite element methods, finite difference methods

Positions and Work Experience

2011 -To Present Visiting Researcher, Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan

Abbreviated Publications

Peer Reviewed Publications

Vaughan, BL, and Grotberg, JB. (2016) Splitting of a two-dimensional liquid plug at an airway bifurcation. Journal of Fluid Mechanics 793: 1-20.

Maxwell, A. D., Park, S., Vaughan, B. L., Cain, C. A., Grotberg, J. B., & Xu, Z. (2014). Trapping of embolic particles in a vessel phantom by cavitation-enhanced acoustic streaming. Physics in Medicine and Biology, 59(17), 4927.

Li, Hailong, Fox-Neff, Kristen, Vaughan, Benjamin, French, Donald, Szaflarski, Jerzy P, & Li, Yu (2013). Parallel EPI artifact correction (PEAC) for N/2 ghost suppression in neuroimaging applications. Magnetic resonance imaging, 31(6), 1022-8.

Vaughan, Benjamin L, Galie, Peter A, Stegemann, Jan P, & Grotberg, James B (2013). A poroelastic model describing nutrient transport and cell stresses within a cyclically strained collagen hydrogel. Biophysical Journal, 105(9), 2188-98.

B. L. Vaughan, Jr., R. E. Baker, D. Kay, and P. K. Maini. (2013) A Modified Oster-Murray-Harris Mechanical Model of Morphogenesis. SIAM J. Appl. Math., 73(6), 2124–2142.

Gilmore, Stephen J, Vaughan, Benjamin L, Madzvamuse, Anotida, & Maini, Philip K (2012). A mechanochemical model of striae distensae. Mathematical Biosciences, 240(2), 141-7.

N. J. Douville, P. Zamankhan, Y. C. Tung, R. Li, B. L. Vaughan, C. F. Tai, J. White, P. J. Christensen, J. B. Grotberg, S. Takayama. (2011) Combination of fluid and solid mechanical stresses contribute to cell death and detachment in a microfluidic alveolar model. Lab on a Chip. 11. 609-619.

B. L. Vaughan, Jr., B. G. Smith, & D. L. Chopp. (2010) The Influence of Fluid Flow on Modeling Quorum Sensing in Bacterial Biofilms. Bull. Math. Biol., 72 (5). 1143-1165.

R. A. Barrio, R. E. Baker, B. Vaughan, Jr., K. Tribuzy, M. R. Carvalho, R. Bassanezi, & P. K. Maini. (2009) Modeling the skin pattern of fish. Phys. Rev. E., 2009 March, 79 (3). 031908-1-031908-11.

M. J. Kirisits, J. J. Margolis, B. L. Purevdorj-Gage, B. Vaughan, D. L. Chopp, P. Stoodley, & M. R. Parsek. (2007) The Inuence of the Hydrodynamic Environment on Quorum Sensing in Pseudomonas aeruginosa Biofilms. J. Bacteriol., 189(22): 83578360.

B. G. Smith, B. L. Vaughan, & D. L. Chopp. (2007) The Extended Finite Element Method for Boundary Layer Problems in Biofilm Growth. CAMCoS, 2(1):35-56, 2007.

B. L. Vaughan, Jr., B. G. Smith, and D. L. Chopp.  (2006) A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources. CAMCoS, 1(1):207-228.



B. L. Vaughan and J. B. Grotberg (10-2010). Numerical Simulations of the Propagation of a Liquid . Applied Mathematics Colloquia, Northwestern University. Other Institution. Level:University

B. L. Vaughan and J. B. Grotberg (02-2011). Numerical Simulations of the Propagation of a Liquid . Mathematical Biosciences Seminar, University of Cincinnati.

B. L. Vaughan (05-2011). Introduction to Mathematical Modeling of the Human Circulatory System . Mathematical Biosciences Seminar, University of Cincinnati.

Paper Presentations

B. L. Vaughan, Jr. and J. B. Grotberg (06-2010. ) Propagation of an Air Finger into a Fluid Filled Bifurcation .Naples, Florida.

B. L. Vaughan, Jr., P. Zamankhan, and J. B. Grotberg (06-2010. ) Two-Phase Flow in Pulmonary Airways .University Park, Pennsylvania.

B. L. Vaughan, Jr. and J. B. Grotberg (10-2010. ) Numerical Simulations of the Propagation of a Liquid Plug through a 2D Airway Bifucation .Austin, Texas.


B. L. Vaughan, Jr and D. L. Chopp (2012. ) A Mathematical Model of the Influence of Hydrodynamics on Quorum Sensing in Bacterial Biofilms .Knoxville, Tennessee. Conference.


Physics of Fluids Reviewer

Biomechanics and Modeling in Mechanobiology Reviewer

Bulletin of Mathematical Biology Reviewer

Post Graduate Training and Education

2007-2009 Postdoctoral Researcher, Centre for Mathematical Biology, Mathematical Institute, University of Oxford, , Oxford, United Kingdom

2009-2010 Postdoctoral Researcher, Biofluids Research Laboratory, Department of Biomedical Engineering University of Michigan, , Ann Arbor, Michigan

Courses Taught

Calculus I

Calculus II

Numerical Anlaysis I

Numerical Analysis II

Numerical Analysis III

Applied Mathematics Practicum

Mathematical Modeling

Applied Mathematics Methods

Scientific Computing

Applied ODEs

Dynamical Systems

Advanced Mathematical Modeling

Dynamical Systems