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My Research
My research interests fall into two major categories:
fluid dynamics, and computational/molecular biology. I am
focusing on the former as I am currently pursuing a PhD in
applied
mathematics at MIT. At the moment, under the supervision
of Professor John
Bush, I am studying several poorly understood
free-surface flow phenomena: polygonal hydraulic jumps,
polygonal fluid sheets, and cusped fluid sheets. In fact,
polygonal sheets and cusped sheets were discovered in our
laboratory, and the collage to the right (winner of the
first
MIT student mural competition) illustrates several
interesting flows also studied in the lab (by myself and
others).
Our goal is to obtain a fundamental understanding of
these flows and therefore predict when they will occur. Each
flow may have a multitude of engineering applications but
must first be carefully studied. This involves developing
theoretical models to explain the observed behavior. We are
very fortunate to have a
fluids
laboratory in the math department
(1
of 9 in the US) where we are able to conduct experiments
to support theoretical findings. In addition, much of the
research requires computational analysis. Equipped with
experimental, theoretical, and computational tools, we
investigate these three intriguing phenomena.
 We
have studied polygonal hydraulic jumps since 2002. An early
discovery led to a publication in the Journal of Fluid
Mechanics in 2003:
The influence of surface tension on the circular hydraulic
jump. A second paper, An
experimental investigation of the stability of the circular
hydraulic jump,
answers the questions of both why and when do
polygonal hydraulic jumps occur. A preview of our findings can be found on the
jump web page, although it is more of
a teaser. In addition, you can view our
winning Gallery of Fluid Motion entry,
Viscous Hydraulic Jumps.
 This
past summer, with the experimental help of undergraduates
Erica and Chad, I studied cusped fluid sheets. One such
example is shown to the right. Surface tension normally
prevents the appearance of sharp curvature, but I was able
to theoretically predict the existence and stability of the
cusped sheets. The full results of the study are being
withheld until publication, but I will be presenting some
details during a
SPAMS
talk on November 1, 2005, which is open to the general
public.
 Ongoing
research includes the polygonal sheet phenomenon which was
first described by Robbie Buckingham and John Bush in 2001,
and described in the Gallery of Fluid Motion article:
Fluid Polygons. You
can also visit their web page, by clicking on the picture to
the left.
Just recently, the two graduate students who work in the
fluids lab have become "famous." You can read about the
RoboSnail or even the water strider paradox in CNN or in
NATURE if you wish. You can also view
Dave's water strider
page. In addition, a second Nature paper on
meniscus climbing has just been published.
As for my older research interests, computational/molecular biology, I have had the opportunity to do
biological research during three out of four of my college
summers. I have worked at Pfizer and the
Cincinnati
Children's Hospital on a variety of projects.
Publications
Aristoff, J.M., Lieberman, C., Chan, E., Bush, J.W.M. “Water
bell and sheet instabilities.”
Gallery of Fluid
Motion, Physics of Fluids.
18,
(2006).
Bush, J.W.M.,
Aristoff, J.M., Hosoi, A.E. “An Experimental Investigation of
the
Stability of the Circular Hydraulic Jump .”
Journal of Fluid
Mechanics. 558, 33-52,
(2006).
KirchBach, C., Zheng,
H., Aristoff, J., Kavanagh, J., Villac, B., Lo, M.
“Trajectories Leaving a Sphere in the Restricted 3-Body
Problem.” Proceedings of the
AAS/AIAA Space Flight Mechanics Meeting. 120,
1875-1902, (2005).
Peacock, T.,
Stocker, R., Aristoff, J. “An Experimental Investigation of
the Angular Dependence of Diffusion-Driven Flow.”
Physics of Fluids.
16,
3503-3505, (2004).
Aristoff, J.M., Leblanc, J.D., Hosoi, P., Bush, J.W.M.
“Viscous Hydraulic Jumps.”
Gallery of Fluid Motion,
Physics of Fluids,
16,
(2004).
Aristoff, J.M. “The Diffusion-Limited Aggregate.”
MIT Undergraduate
Journal of Mathematics.
MIT Department of Mathematics, Cambridge MA,
6,
1-9, (2004).
Bush,
J.W.M. & Aristoff, J.M. “The Influence of Surface Tension on
the Circular Hydraulic Jump.”
Journal of Fluid
Mechanics.
489,
229-238, (2003).
Peacock, T., Stocker, R., Aristoff, J. “An Experimental
Investigation of Diffusion Driven Flow.” Abstract. The
American Physical Society, 56th Meeting of the Division of
Fluid Dynamics. November 23rd, (2003).
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