Frank Baginski

Phone: (202) 994-6269
Fax: (202) 994-6760
Email: baginski@gwu.edu
 

Spring 2014

Math 6330 Section 10 - Ordinary Differential Equations
  Tu & Th 09:35-10:50 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 light-weight 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 visco-elastic 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, co-authored with R. Croce, S. Gillmor and R. Krause,   Applied Mathematics and Computation, 227 (2014) 399-411.
• The effect of boundary support, aperture size and reflector depth on the performance of inflatable elastic parabolic antenna reflectors, co-authored with K. Brakke,   AIAA J. of Spacecraft and Rockets, 49 No. 5 (2012) 905-914.
• Deployment of Pneumatic Envelopes Including Ascending Balloons and Inflatable Aerodynamic Decelerators, co-authored with M. Coleman and R. Romanofsky,   AIAA J. of Spacecraft and Rockets, 49 No. 2 (2012) 413-421.
• The ExaVolt Antenna: A Large-Aperture, Balloon-embedded Antenna for Ultra-high Energy Particle Detection, co-authored with P. W. Gorham, P. Allison, K. M. Liewer, C. Miki, B. Hill, and G. S. Varner,   Astroparticle Physics, 35 No. 5 (2011) 242-256.
• Solving period problems for minimal surfaces with the support function, co-authored with V. Ramos Batista,   Adv. Appl. Math. Sci.,   9 No. 1 (2011) 85-114.
• Modeling the equilibriium configuration of a piecewise-orthotropic pneumatic envelope with applications to pumpkin-shaped balloons, co-authored with M. Barg and J. Lee,   SIAM Journal on Applied Mathematics,   71 No. 1 (2011) 20-40.
• Exploring the stability landscape of constant-stress pumpkin balloon designs, co-authored with K. Brakke,   AIAA Journal of Aircraft,  47 No. 3 (2010) 849-857.
• Simulating clefts in pumpkin balloons, co-authored with K. Brakke,   Advances in Space Research,  45 (2009) 473-481.
• Existence theorems for tendon-reinforced thin wrinkled membranes subjected to a hydrostatic pressure load, co-authored with M. Barg and W. Collier,   Mathematics and Mechanics of Solids,  13 (2008) 532-570.
• Unstable cyclically symmetric and stable asymmetric pumpkin balloon configurations,  co-authored with K. Brakke and W. Schur,  AIAA Journal of Aircraft, 44 No. 3 (2007) 764-772.
• Stability of cyclically symmetric strained pumpkin balloon configurations and the formation of undesired equilibria, co-authored with K. Brakke and W. Schur,  AIAA Journal of Aircraft,  43 No. 5 (2006) 1414-1423.
• Cleft formation in pumpkin balloons, co-authored with K. Brakke and W. Schur, Advances in Space Research, 37 (2006) 2070-2081.
• On the design and analysis of inflated  membranes, SIAM Journal on Applied Mathematics, 65 No. 3 (2005), 838-857.
• The natural shape balloon and related models, co-authored with J. Winker, Advances in Space Research, 33 No. 10 (2004), 1617-1622
• Structural analysis of  pneumatic envelopes: Variational formulation and optimization-based solution process, co-authored with W. W. Schur, AIAA Journal, 41 No. 2, February 2003, 304-311.
• Special functions on the sphere with applications to  minimal surfaces,   Advances in Applied Mathematics 28 (2002) 360-394.
• Modeling the shapes of constrained partially inflated  high altitude balloons, co-authored with W. Collier,  AIAA Journal 37 No. 9 (2001), 1-11; ``Errata'', AIAA Journal,  40 No. 6 (2002), 1253
• Modeling the  design shape of a large scientific balloon, co-authored with Q. Chen and I. Waldman,  Applied Mathematical Modeling 25 (2001) 953-966
• Modeling ascent configurations of strained high  altitude balloons,  co-authored with K. Brakke, AIAA Journal,  36 No. 10 (1998),  1901-1910.
• A parallel shooting method for determining the natural-shape of a large scientific balloon ,   co-authored with  W. Collier and T. Williams,  SIAM Journal on Applied Mathematics,  58  Number 3, June 1998,   961-974.
• Numerical solutions of boundary value problems for  K-surfaces,  co-authored with N. Whitaker, Numerical Methods for Partial Differential Equations, 12 (1996), 525-546.
• The computation of one-parameter families of bifurcating elastic surfaces,  SIAM Journal on Applied Mathematics, 54  No. 3, (1994), 738-773.
• The buckling of elastic spherical caps, Journal of Elasticity, 25 (1991), 159-192.