Nathaniel Barlow
Professor, Applied Mathematics
School of Mathematics and Statistics
College of Science
Undergraduate Program Coordinator, Applied and Computational Mathematics
585-475-4077
Office Hours
M 11:30-noon
Th 11-noon
F 11:45-12:30
Office Location
Nathaniel Barlow
Professor, Applied Mathematics
School of Mathematics and Statistics
College of Science
Undergraduate Program Coordinator, Applied and Computational Mathematics
Education
BS, Ph.D., Clarkson University
Bio
Nate received his Ph.D. in 2009 from Clarkson University in Mechanical Engineering, where he began his research on long-time behavior of dispersive waves in fluids. From 2010-2014, Nate was an NSF CI-TraCS Postdoctoral Fellow, hosted by Chemical Engineering Department and the Center for Computational Research at SUNY Buffalo. It was here that Nate and Steve Weinstein began developing methods for the re-summing divergent and slowly convergent series. Since joining RIT, Nate has partnered with Steve to build a research group of students and faculty with the goal of progressing efforts in asymptotic analysis in general. More info on their research group can be found on the Barlow-Weinstein Group website. Their book "Power Series Solutions to Nonlinear Ordinary Differential Equations" can be found online.
Nate won the 2017/2018 RIT Innovative Teaching with Technology Award, the 2017/2018 Richard and Virginia Eisenhart Provost's Award for Excellence in Teaching, and an Eisenhart Award for Outstanding Teaching (2020/2021).
For pictures of Nate's 3D Math prints check out his instagram site. For other fun math/teaching stuff, check out Nate's (out of date) personal site. For some of his original music, search Nate Barlow on Spotify, Apple Music or other distributors.
When not doing math research, Nate can be found writing sentences in the third person, such as "When not doing math research, Nate can be found writing sentences in the third person, such as "When not doing math research...
585-475-4077
Areas of Expertise
Asymptotic Analysis
Fluid Dynamics
Waves
Instability
Series Analysis
Numerical Methods
Differential Equations
Mathematical Modeling
Computational Relativity and Gravitation
Gravitational Waves
Select Scholarship
Full Length Book
Barlow, Nathaniel S. and Steven J. Weinstein. Power Series Solutions to Nonlinear Ordinary Differential Equations and Related Problems of Physics, Engineering, and Life Sciences. 1 ed. Philadelphia, PA: SIAM, 2025. Print.
Journal Paper
Barlow, Nathaniel S., W. Cade Reinberger, and Steven J. Weinstein. "Exact and explicit analytical solution for the Sakiadis boundary layer." Physics of Fluids 36. 31703 (2024): 1-4. Web.
Naghshineh, Nastaran, et al. "The shape of an axisymmetric meniscus in a static liquid pool: effective implementation of the Euler transformation." IMA Journal of Applied Mathematics 88. 5 (2023): 735-764. Print.
Reinberger, W. Cade, et al. "Exact solution for heat transfer across the Sakiadis boundary layer." Physics of Fluids 36. 7 (2024): 073609:1-13. Print.
Naghshineh, Nastaran, et al. "On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs." IMA Journal of Applied Mathematics 88. 1 (2023): 43-66. Print.
Naghshineh, Nastaran, et al. "Asymptotically consistent analytical solutions for the non-Newtonian Sakiadis boundary layer." Physics of Fluids 35. 53103 (2023): 1-15. Print.
Huber, Colin M., Nathaniel S. Barlow, and Steven J. Weinstein. "On the response of neutrally stable flows to oscillatory forcing with application to liquid sheets." Physics of Fluids 34. (2022): 104106: 1-20. Print.
Huber, Colin M., Nathaniel S. Barlow, and Steven J. Weinstein. "On the two-dimensional extension of one-dimensional algebraically growing waves at neutral stability." Wave Motion 116. (2022): 103083:1-20. Print.
Reinberger, W. Cade, et al. "On The Power Series Solution to The Nonlinear Pendulum." The Quarterly Journal of Mechanics and Applied Mathematics 75. 4 (2022): 347–369. Print.
Torsey, Bridget M., et al. "The effect of pressure fluctuations on the shapes of thinning liquid curtains." Journal of Fluid Mechanics 910. (2021): A28:1-15. Print.
Rame, Enriquie, Nathaniel S. Barlow, and Steven J. Weinstein. "On the shape of air–liquid interfaces with surface tension that bound rigidly rotating liquids in partially filled containers." IMA Journal of Applied Mathematics 86. (2021): 1266-1286. Print.
Belden, Elizabeth R., et al. "Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation." The Quarterly Journal of Mechanics and Applied Mathematics 73. 1 (2020): 36-50. Print.
Huber, Colin, et al. "On the stability of waves in classically neutral flows." IMA Journal of Applied Mathematics 85. 2 (2020): 309-340. Print.
Barlow, Nathaniel S. and Steven J. Weinstein. "Accurate Closed-form Solution of the SIR Epidemic Model." Physica D: Nonlinear Phenomena 408. (2020): 1-4. Print.
Weinstein, Steven J., et al. "Analytic Solution of the SEIR Epidemic Model via Asymptotic Approximant." Physica D: Nonlinear Phenomena 411. (2020): 132633:1-6. Print.
Weinstein, Steven J., et al. "On Oblique Liquid Curtains." Journal of Fluid Mechanics 876. R3 (2019): 1-9. Print.
Beachley, Ryne J., et al. "Accurate Closed-form Trajectories of Light Around a Kerr Black Hole Using Asymptotic Approximants." Class. Quantum Grav. 35. 205009 (2018): 1-28. Print.
Barlow, Nathaniel S., et al. "On the Summation of Divergent, Truncated, and Underspecified Power Series via Asymptotic Approximants." Quarterly Journal of Mechanics and Applied Math 70. 1 (2017): 21-48. Print.
Barlow, Nathaniel S., Steven J. Weinstein, and Joshua A. Faber. "An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes." Class. Quantum Grav. 34. 135017 (2017): 1-16. Print.
King, Kristina R., et al. "Stability of Algebraically Unstable Dispersive Flows." Physical Review Fluids 1. 7 (2016): 073604:1-19. Web.
Helenbrook, Brian T. and Nathaniel S. Barlow. "Spatial—temporal Stability Analysis of Faceted Growth with Application to Horizontal Ribbon Growth." Journal of Crystal Growth 454. (2016): 35-44. Print.
Barlow, Nathaniel S., et al. "Communication: Analytic continuation of the virial series through the critical point using parametric approximants." Journal of Chemical Physics 143. (2015): 071103 (1-5). Print.
Barlow, Nathaniel S., Brian T. Helenbrook, and Steven J. Weinstein. "Algorithm for Spatio-temporal Analysis of the Signalling Problem." IMA Journal of Applied Mathematics 82. 1 (2017): 1-82. Print.
Barlow, Nathaniel S., et al. "Critical Isotherms from Virial Series Using Asymptotically Consistent Approximants." AIChE Journal 60. 9 (2014): 3336-3349. Print.
Currently Teaching
MATH-199
Mathematics and Statistics Seminar
1 Credit
This course provides an introduction to math and statistics software. The course provides practice in technical writing.
MATH-326
Boundary Value Problems
3 Credits
This course provides an introduction to boundary value problems. Topics include Fourier series, separation of variables, Laplace's equation, the heat equation, and the wave equation in Cartesian and polar coordinate systems.
MATH-495
Undergraduate Research in Mathematical Sciences
1-3 Credits
This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.
MATH-498
Independent Study in Mathematical Sciences
1-3 Credits
This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.
MATH-501
Experiential Learning Requirement in Mathematics
0 Credits
The experimental learning requirement in the Applied Mathematics and Computational Mathematics programs can be accomplished in various ways. This course exists to record the completion of experiential learning activities. Such pre-approval is considered on a case-by-case basis.
MATH-589
Advanced Special Topics
1-4 Credits
Special Topics courses cover content that is not represented in the main curriculum on an experimental or trial basis.
MATH-689
Advanced Special Topics
1-4 Credits
Special Topics courses cover content that is not represented in the main curriculum on an experimental or trial basis.
MATH-790
Research & Thesis
0-9 Credits
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
MATH-799
MATH GRADUATE Independent Study
1-3 Credits
Independent Study