Nathaniel Barlow Headshot

Nathaniel Barlow

Associate Professor

School of Mathematical Sciences
College of Science

Office Location

Nathaniel Barlow

Associate Professor

School of Mathematical Sciences
College of Science


BS, Ph.D., Clarkson University


Nate received his Ph.D. in 2009 from Clarkson University in Mechanical Engineering. His research background is in hydrodynamic stability analysis (particularly absolute/convective instability classification) and the long-time behavior of dispersive waves in fluids. From 2010-2014, Nate was an NSF CI-TraCS Postdoctoral Fellow, splitting his time between the Chemical Engineering Department and the Center for Computational Research at SUNY Buffalo. As a post-doc, Nate helped create the method of asymptotic approximants, a re-summation technique used to analytically continue truncated and/or divergent series. Since joining RIT, Nate has partnered with his long-time collaborator and co-creator of asymptotic approximants, Steve Weinstein, to build a research group of students and faculty with the goal of progressing efforts in asymptotic analysis in general.

Teaching is an underlying theme in Nate's career. During the first two years of his Ph.D., Nate was an NSF G-K12 graduate teaching fellow, running weekly science and engineering lessons in K-12 classrooms across NY from the Adirondacks to the Bronx. During the last few years of his Ph.D., Nate was a full-time instructor in the Math Department at Clarkson University; In 2009, he won Clarkson's Outstanding Teaching Award for Graduate Students. Continuing on a path of teaching excellence at  RIT, Nate has 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 more information on his joint research group with Steve Weinstein, news items, and an updated publication list, go here. For pictures of Nate's 3D Math prints check out his instagram site. For other fun math/teaching stuff, check out Nate's personal site.

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...


Areas of Expertise

Select Scholarship

Journal Paper
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

3 Credits
This course is an introduction to the study of ordinary differential equations and their applications. Topics include solutions to first order equations and linear second order equations, method of undetermined coefficients, variation of parameters, linear independence and the Wronskian, vibrating systems, and Laplace transforms.
3 Credits
This course covers the algebra of complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of real-valued integrals by complex-variable methods.
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.
1 - 3 Credits
This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.
0 - 9 Credits
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
0 Credits
Continuation of Thesis
1 - 3 Credits
Independent Study

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