118 citations · 254 across the 16 of their papers we have counts for
18 papers
Exact solution for heat transfer across the Sakiadis boundary layer
W. Cade Reinberger, Nathaniel S. Barlow, Mohamed A. Samaha +1
We consider the problem of convective heat transfer across the laminar boundary-layer induced by an isothermal moving surface in a Newtonian fluid. In previous work (Barlow, Reinbe…
Exact analytical solution for the Sakiadis boundary layer
Nathaniel S. Barlow, W. Cade Reinberger, Steven J. Weinstein
It has recently been established [Naghshineh et al., IMA J. of Appl. Math., 88, 1 (2023)] that a convergent series solution may be obtained for the Sakiadis boundary layer problem…
Asymptotically-consistent analytical solutions for the non-Newtonian Sakiadis boundary layer
Nastaran Naghshineh, Nathaniel S. Barlow, Mohamed A. Samaha +1
The Sakiadis boundary layer induced by a moving wall in a semi-infinite fluid domain is a fundamental laminar flow field relevant to high speed coating processes. This work provide…
On the response of neutrally stable flows to oscillatory forcing with application to liquid sheets
Colin M. Huber, Nathaniel S. Barlow, Steven J. Weinstein
Industrial coating processes create thin liquid films with tight thickness tolerances, and thus models that predict the response to inevitable disturbances are essential. The mathe…
On the shape of an axisymmetric meniscus rising from a static liquid pool
Nastaran Naghshineh, W. Cade Reinberger, Nathaniel S. Barlow +2
We examine the classical problem of the height of a static liquid interface that forms on the outside of a solid vertical cylinder in an unbounded stagnant pool exposed to air. Gra…
On the two-dimensional extension of one-dimensional algebraically growing waves at neutral stability
Colin M. Huber, Nathaniel S. Barlow, Steven J. Weinstein
This work considers two linear operators which yield wave modes that are classified as neutrally stable, yet have responses that grow or decay in time. Previously, King et al. (Phy…
On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs
Nastaran Naghshineh, W. Cade Reinberger, Nathaniel S. Barlow +2
We examine the power series solutions of two classical nonlinear ordinary differential equations of fluid mechanics that are mathematically related by their large-distance asymptot…
On the trajectory of the nonlinear pendulum: Exact analytic solutions via power series
W. Cade Reinberger, Morgan S. Holland, Nathaniel S. Barlow +1
We provide an exact infinite power series solution that describes the trajectory of a nonlinear simple pendulum undergoing librating and rotating motion for all time. Although the…
The Rayleigh collapse of two spherical bubbles
Anthony Harkin, Adam Giammarese, Nathaniel S. Barlow +1
The inertial collapse of two interacting and non-translating spherical bubbles of equal size is considered. The exact analytic solution to the nonlinear ordinary differential equat…
On the shape of air-liquid interfaces with surface tension that bound rigidly-rotating liquids in partially filled containers
Enrique Ramé, Steven J. Weinstein, Nathaniel S. Barlow
The interface shape of a fluid in rigid body rotation about its axis and partially filling the container is often the subject of a homework problem in the first graduate fluids cla…
The effect of pressure fluctuations on the shapes of thinning liquid curtains
Bridget M. Torsey, Steven J. Weinstein, David S. Ross +1
We consider the time-dependent response of a gravitationally-thinning inviscid liquid sheet (a coating curtain) leaving a vertical slot to sinusoidal ambient pressure disturbances.…
Analytic solution of the SEIR epidemic model via asymptotic approximant
Steven J. Weinstein, Morgan S. Holland, Kelly E. Rogers +1
An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in and analytical…
Accurate closed-form solution of the SIR epidemic model
Nathaniel S. Barlow, Steven J. Weinstein
An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48). The…
Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation
Elizabeth R. Belden, Zachary A. Dickman, Steven J. Weinstein +3
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl. Math., 70(1): 21-48) yields accura…
On the stability of waves in classically neutral flows
Colin Huber, Meaghan Hoitt, Nicole Hill +3
This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx {{e}^{i…
Accurate closed-form trajectories of light around a Kerr black hole using asymptotic approximants
Ryne J. Beachley, Morgan Mistysyn, Joshua A. Faber +2
Highly accurate closed-form expressions that describe the full trajectory of photons propagating in the equatorial plane of a Kerr black hole are obtained using asymptotic approxim…
On the summation of divergent, truncated, and underspecified power series via asymptotic approximants
Nathaniel S. Barlow, Christopher R. Stanton, Nicole Hill +2
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order.…
An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes
Nathaniel S. Barlow, Steven J. Weinstein, Joshua A. Faber
An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary sp…