Frank Baginski
Department of Mathematics
The George Washington University
Hall of Government
Room 224
2115 G Street NW
Washington, DC 20052
Phone: (202) 9946269
Fax: (202) 9946760
Email: baginski@gwu.edu
Spring 2014
Math 6330 Section 10  Ordinary Differential Equations
Tu & Th 09:3510:50
in 1957 E, Room 310
Information
on Careers in Mathematics
Previous Courses
Math 6340 (formerly 221) Modern Partial Differential Equations
Math 231 Topics in Applied Mathematics
Research Interests
The advancement of materials and technology
in thin lightweight films has generated great interest in
deployable space structures for a variety
of applications, including inflatable rovers, inflatable antennas,
airbags to cushion landings,
aerobots, planetary and terrestrial balloons. Current research
interests
focus on the development of a mathematical
model for high altitude balloons used by NASA to support
research in the upper atmosphere.
To take full advantage of current balloon technology or develop new
balloon designs, it is important to have
a valid mathematical model for estimating maximum stresses
and strains that are experienced by the
balloon film prior to launch and during its ascent to float altitude.
The problem is complicated by the fact
that the balloon film can fold back upon itself and wrinkle
(see the images below). The balloon problem
generates a wealth of challenging
mathematical problems in differential
geometry, the mechanics of membranes, and direct methods
in the calculus of variations.


A large scientific balloon
at launch

An undesired equilibrium
configuration at float altitude

Recent work on large super pressure pumpkin
balloons, focusing on questions of stability, sensitivity
analysis, the formulation of undesired
stable equilibria (see above), and the deployment problem.
Long term success of the pumpkin
balloon for NASA requires a thorough understanding of the
phenomenon of multiple stable equilibria.
For an ultra long duration balloon (ULDB) mission of 100 days or
longer, there is a need for design criteria
that will enable the designer to arrive at structurally efficient designs
while providing sufficient margins against
the occurrence of instability, and in the case of a viscoelastic
film
also accounting for the service
lifetime configuration changes of the balloon.
For more on scientific ballooning
see the following links:
NASA Balloon Program
Office
NASA Columbia Scientific Balloon
Facility
Selected Publications

Numerical investigations of the role of curvature in strong
segregation problems on a given surface,
coauthored with R. Croce, S. Gillmor and R. Krause, Applied Mathematics and Computation,
227 (2014) 399411.

The effect of boundary support, aperture size and reflector depth on the
performance of inflatable elastic parabolic antenna reflectors,
coauthored with K. Brakke, AIAA J. of Spacecraft and Rockets,
49 No. 5 (2012) 905914.

Deployment of Pneumatic Envelopes Including
Ascending Balloons and Inflatable Aerodynamic Decelerators,
coauthored with M. Coleman and R. Romanofsky, AIAA J. of Spacecraft and Rockets,
49 No. 2 (2012) 413421.

The ExaVolt Antenna: A LargeAperture, Balloonembedded Antenna
for Ultrahigh Energy Particle Detection,
coauthored with P. W. Gorham, P. Allison, K. M. Liewer, C. Miki, B. Hill, and G. S. Varner,
Astroparticle Physics, 35 No. 5 (2011) 242256.

Solving period problems for minimal
surfaces with the support function,
coauthored with V. Ramos Batista, Adv. Appl. Math. Sci.,
9 No. 1 (2011) 85114.

Modeling the equilibriium configuration of a piecewiseorthotropic
pneumatic envelope with applications to pumpkinshaped balloons,
coauthored with M. Barg and J. Lee, SIAM Journal on Applied Mathematics,
71 No. 1 (2011) 2040.

Exploring the stability landscape of constantstress
pumpkin balloon designs, coauthored with K. Brakke, AIAA
Journal of Aircraft, 47 No. 3 (2010) 849857.

Simulating clefts in pumpkin balloons,
coauthored with K. Brakke, Advances in Space Research,
45 (2009) 473481.

Existence theorems for tendonreinforced
thin wrinkled membranes subjected to a hydrostatic pressure load, coauthored
with M. Barg and W. Collier, Mathematics and Mechanics of Solids,
13 (2008) 532570.

Unstable cyclically symmetric and stable
asymmetric pumpkin balloon configurations, coauthored with K.
Brakke and W. Schur, AIAA Journal of Aircraft, 44 No. 3 (2007)
764772.

Stability of cyclically symmetric strained
pumpkin balloon configurations and the formation of undesired equilibria,
coauthored
with K. Brakke and W. Schur, AIAA Journal of Aircraft, 43
No. 5 (2006) 14141423.

Cleft formation in pumpkin balloons, coauthored
with K. Brakke and W. Schur, Advances in Space Research, 37 (2006)
20702081.

On the design and analysis of inflated
membranes, SIAM Journal on Applied Mathematics, 65 No. 3 (2005),
838857.

The natural shape balloon and related models,
coauthored with J. Winker, Advances in Space Research, 33 No. 10
(2004), 16171622

Structural analysis of pneumatic
envelopes: Variational formulation and optimizationbased solution process,
coauthored
with W. W. Schur, AIAA Journal, 41 No. 2, February 2003, 304311.

Special functions on the sphere with applications
to minimal surfaces, Advances in Applied Mathematics
28
(2002) 360394.

Modeling the shapes of constrained partially
inflated high altitude balloons, coauthored with W. Collier,
AIAA Journal 37 No. 9 (2001), 111; ``Errata'', AIAA Journal,
40 No. 6 (2002), 1253

Modeling the design shape of a large
scientific balloon, coauthored with Q. Chen and I. Waldman,
Applied Mathematical Modeling 25 (2001) 953966

Modeling ascent configurations of strained
high altitude balloons, coauthored with K. Brakke, AIAA
Journal, 36 No. 10 (1998), 19011910.

A parallel shooting method for determining
the naturalshape of a large scientific balloon , coauthored
with W. Collier and T. Williams, SIAM Journal on Applied Mathematics,
58 Number 3, June 1998, 961974.

Numerical solutions of boundary value problems
for Ksurfaces, coauthored with N. Whitaker, Numerical
Methods for Partial Differential Equations,
12 (1996), 525546.

The computation of oneparameter families
of bifurcating elastic surfaces, SIAM Journal on Applied Mathematics,
54
No. 3, (1994), 738773.

The buckling of elastic spherical caps,
Journal of Elasticity, 25 (1991), 159192.