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Research

Research Interests

Study and research in nonlinear partial differential equations arising in the theory of elasticity and differential geometry with applications to membranes, minimal surfaces, and elastic shells; mathematical modeling of balloons, aerostats, airships, antennas, aerodynamic decelerators and other inflatable structures; research in cell membranes, lipid bilayers and equilibrium shapes that minimize bending energy; research in inhibitory systems and related diblock copolymer problems; functional analysis and bifurcation theory applied to nonlinear partial differential equations; special functions.

Articles

  1. F. Baginski and V. Ramos Batista, Closed geodesics on the mylar balloon, Am. Math. Monthly, 131 No. 9 (2024).
  2. F. Baginski and V. Ramos Batista, Closed Geodesics on Weingarten Surfaces with k1/k2 = c > 0, SIAM J. Applied Dynamical Systems, 23 No. 3 (2024) 1705-1719.
  3. F. Baginski and J. Liu, Numerical investigations of pattern formation in binary systems with inhibitory long-range interaction, J. Electronic Research Archive, 2022, 30(5): 1606-1631. DOI: 10.3934/era.2022081.
  4. J. Liu, F. Baginski, X. Ren, Equilibrium Configurations of Boundary Droplets in a Self-organizing Inhibitory System, SIAM Journal on Applied Dynamical Systems, 17 No. 1 (2018) 1353-1376.
  5. P. Gorham, et. al, Shape Analysis and Deployment of the ExaVolt Antenna, Journal of Astronomical Instrumentation,  6 No. 2 (2017) 174004.
  6. F. Baginski, K. Brakke, J. Cruz, Estimating the Collapse Pressure of a Tension-Cone Aerodynamic Decelerator, AIAA Journal of Spacecraft and Rockets, 51 (4) (2014) 1368-1373.
  7. F. Baginski, R. Croce, S. Gillmor, R. Krause, Numerical investigations of the role of curvature in strong segregation problems on a given surface. Applied  Mathematics and Computation, 227  (2014)  399-411.
  8. M. Coleman, F. Baginski, R. Romanofsky, The effect of boundary support, aperture size and reflector depth on the performance of inflatable elastic parabolic antenna reflectors. AIAA Journal of Spacecraft and Rockets,  49 No. 5 (2012) 905-914.
  9. F. Baginski and K. Brakke, Deployment of Pneumatic Envelopes with Applications to Ascending Balloons and Inflatable Aerodynamic Decelerators, AIAA Journal of Spacecraft and Rockets, 49 No. 2 (2012) 413-421.
  10. P. W. Gorham, F. E. Baginski, P. Allison, K. M. Liewer, C. Miki, B. Hill, and G. S. Varner, The ExaVolt Antenna: A Large-Aperture, Balloon-embedded Antenna for Ultra-high Energy Particle Detection, Astroparticle Physics, 35 No. 5 (2011) 242-256.
  11. V. Ramos Batista and F. Baginski, Solving period problems for minimal surfaces with the support function, Adv. Appl. Math. Sci. 9(1), 85-114 (2011).
  12. M. Barg, J. Lee, and F. Baginski, Modeling the equilibrium  configuration of a piecewise-orthotropic pneumatic envelope with applications to pumpkin-shaped balloons. SIAM Journal of Applied Mathematics, Vol. 71 No. 1, (2011) 20-40.
  13. F. Baginski and K. Brakke, Estimating the deployment pressure in pumpkin balloons, AIAA Journal of Aircraft, 48  No. 1 (2011) 235-247.
  14. F. Baginski and K. Brakke, Exploring the stability landscape of constant-stress pumpkin balloon designs. AIAA Journal of Aircraft, 47  No.3 (2010) 849-857.
  15. F. Baginski and K. Brakke, Simulating clefts in  pumpkin balloons. Adv. Space Res. 45  No. 4 (2010) 473-481.
  16. M. Barg, W. Collier, and F. Baginski, Existence Theorems For  Tendon-Reinforced Thin Wrinkled Membranes Subjected to a Hydrostatic Pressure Load, Mathematics and the Mechanics of Solids, 13  No. 6 (2008),  532-570.
  17. F. Baginski, K. Brakke, and W. Schur, Unstable cyclically symmetric and stable asymmetric pumpkin  balloon configurations, AIAA Journal of Aircraft, 44  No. 3 (2007) 764-772.
  18. F. Baginski, K. Brakke, and W. Schur, Stability of cyclically symmetric strained pumpkin balloon configurations  and the formation of undesired equilibria, AIAA Journal of Aircraft. 43  No. 5 (2006) 1414-1423.
  19. F. Baginski, W. Schur, and K. Brakke, Cleft formation in pumpkin balloons, Adv. Space Res., 37  (2006) 2070-2081.
  20. F. Baginski and W. W. Schur,  Undesired equilibria of self-deploying pneumatic envelopes, AIAA Journal of Aircraft,  42  No. 6 (2005), 1639-1642.
  21. F. Baginski, On the design and analysis of inflated membranes: natural and pumpkin shaped balloons, SIAM Journal on Applied Mathematics. 65  No. 3 (2005) 838-857.
  22. F. Baginski and J. Winker, The natural shape balloon and related models, Adv. Space Res., 33 No. 10 (2004), 1617-1622.
  23. F. Baginski, Nonuniqueness of strained ascent shapes of high altitude balloons,  Adv. Space Res., 33  No. 10 (2004), 1705-1710.
  24. F. Baginski, W. W. Schur, Structural analysis of pneumatic envelopes: A variational formulation and optimization-based solution process, AIAA Journal, 41  No. 2 (2003), 304-311.
  25. F. Baginski, A mathematical model for a partially inflated balloon with a periodic lobe structure, Adv. Space Res., 30 No. 5 (2002),  1167-1171.
  26. Q. Chen, lan Waldman, F. Baginski, Modeling the  design shape of a large scientific balloon, Applied Mathematical Modelling, Vol. 25/11, November 2001, p. 953-966.
  27. W. Collier and F. Baginski, Modeling the shapes of constrained partially inflated high altitude balloons , AIAA Journal, 39  No. 9 (2001), 1662-1672.
  28. W. Collier and F. Baginski, A mathematical model for the strained shape of a large scientific balloon at float altitude, ASME Jour. of Appl. Mechanics, 67  No.1 (2000), 6-16.
  29. F. Baginski and K. Brakke, Modeling ascent configurations of strained high altitude balloons , AIAA J., 36  No.10 (1998),  1901-1910.
  30. W. Collier and F. Baginski, Energy minimizing shapes of partially inflated large scientific balloons. Advances in Space Research, 21  No. 7 (1998) 975-978.
  31. F. Baginski, W. Collier, T. Williams, A parallel shooting method for determining the natural-shape of a large scientific balloon, SIAM Journal on Applied Mathematics, 58  No. 3 (1998), 961-974.
  32. F. Baginski and N. Whitaker, Numerical solutions of boundary value problems for  K-surfaces in R^3, Numerical Methods for Partial Differential Equations, 12  (1996), 525-546.
  33. F. Baginski, Modeling non-axisymmetric off-design shapes of large scientific balloons, AIAA Journal, 34  No. 2 (1996), 400-407.
  34. F. Baginski,  A variational principle for the ascent shape of large scientific balloons ,  Advances in Space Research, 17  No. 9 (1996), (9)15-(9)18.
  35. F. Baginski and S. Ramamurti, Variational principles for ascent shapes of large scientific balloons , AIAA Journal, 33  No. 4 (1995), 764-768.
  36. F. Baginski, The computation of one-parameter families of bifurcating elastic surfaces, SIAM Journal on Applied Mathematics, 54 No. 3 (1994), 738-773.
  37. F. Baginski, The buckling of  elastic spherical caps, Journal of Elasticity, Vol. 25 (1991), 159-192.
  38. F. Baginski, Comparison theorems for the nu-zeroes of Legendre functions P^m_nu(z_0) for -1< z_0 <1, Proceedings  of the American Mathematical Society, 111(2) (1991), 395-402.
  39. F. Baginski, Ordering the zeroes of Legendre functions P^m_nu(z_0) when considered as a function of nu,  Journal of Mathematical Analysis and Applications, Vol. 147, No. 1 (1990), 296-308.
  40. F. Baginski, Upper and lower bounds for eigenvalues of the Laplacian on spherical cap domains, Quarterly of Applied Mathematics, Vol. 48 No. 3 (1990), 569--573; Errata: Vol. 49 No. 2 (1991), 399.
  41. F. Baginski, Axisymmetric and nonaxisymmetric buckled states of a shallow spherical cap, Quarterly of Applied Mathematics, 46  No. 2 (1988), 331-351.

Ph.D Students

  • Debdeep Bhattacharya, Harmonic Analysis Techniques in Nonlinear Dispersive Equations and Signal Processing, Spring 2020.
  • Jiajun Lu, Pattern Formation in Binary Systems with Inhibitory Long-range Interaction, Spring 2018.
  • Michael Coleman, Surface Accuracy Analysis and Mathematical Modeling of Deployable Large Aperture Inflatable Elastic Antenna Reflectors, August 2010.
  • Jieun Lee, Modeling the Equilibrium Configuration of a Piecewise Orthotropic Pneumatic Envelope and the Phase Separation in a Membrane, co-advised with X. Ren, August 2010.
  • Michael Barg, Direct Methods in the Calculus of Variations with Applications to Tendon-Reinforced Piecewise-Isotropic Membranes, August 2007.
  • William Collier, Applications of Variational Principles to Modeling a Partially Inflated Scientific Research Balloon, January 2000.

Grants, Fellowships and Awards

  • ExaVolt Antenna: Supporting Technology for Suborbital Ultra-high Energy Particle Observatories, George Washington University, Co-I, NASA Astrophysics Research and Analysis, NASA Award NNX12AC54G, Period: 01/10/2012-12/31/2015.
  • 2011 NASA Glenn Faculty Fellowship, Antenna and Optical System Branch, NASA Glenn Research Center, Cleveland, Ohio, June 6, 2010 - August 12, 2011.
  • Research in Shape Optimization and Accuracy of Large Aperture Deployable Antennas II, Antenna, Microwave, and Optical Systems Branch, NASA Award: NNX09AH08G, NASA John H. Glenn Research Center, Cleveland, OH; Award Period: 05/01/2009 - 12/31/2009.
  • Modeling S-Clefts in Pumpkin Balloons, NASA Award: NNX07AQ49G, Balloon Program Office, NASA Goddard Space Flight Center/Wallops Flight Facility, Wallops Island, VA; Period: 08/13/2007–08/31/2008.
  • Research in Shape Optimization and Accuracy of Large Aperture Deployable Antennas, NASA Award: NNX07AR67G, Antenna, Microwave, and Optical Systems Branch, NASA John H. Glenn Research Center, Cleveland, OH. Award Period: 08/23/2007–08/29/2008.
  • The Analysis of Nonstandard Pumpkin Balloon Configurations: Undesired Stable Equilibria and Tendon Failure Modes, NASA Goddard Space Flight Center/Wallops Flight Facility, NASA Award NAG5-5353. Period: 01/01/03 - 12/31/05.
  • The Shape of a Statically Determinate Pressurized Pumpkin Balloon and the Analysis of Related Undesired Stable Equilibria, NASA Goddard Space Flight Center/Wallops Flight Facility, NASA Award NAG5-5353, Period: 10/10/01 - 12/31/02.
  • The Shape of a Descending Balloon. Experiments with Partially Inflated Balloons and Model Validation, NASA Goddard Space Flight Center/Wallops Flight Facility, NASA Award NAG5-5292, Period: 5/18/2000 - 11/30/2001.
  • Strained Ascent Shapes and Other Off-Design Configurations of Large Scientific Balloons, National Aeronautics and Space Administration, NASA Award NAG5-697, Period: 7/1998 - 7/2000.
  • Modeling Partially Inflated High Altitude Strained Balloon Shapes. Ascent Shapes and Constrained Configurations from Launch to Float Altitude, NASA Goddard Space Flight Center/Wallops Flight Facility, NASA Award NAG5-697. Period: 4/97-5/98.
  • Strain Energy Methods for the Analysis of Partially Inflated High Altitude Balloons II. Ascent and Constrained Configurations, NASA Goddard Space Flight Center/Wallops Flight Facility, Award NAG5-697. Period: 4/96–3/97.
  • Strain Energy Methods for the Analysis of Partially Inflated High Altitude Balloons, NASA Goddard Space Flight Center/Wallops Flight Facility, NASA Award NAG5-697. Period: 3/95–2/96.
  • Mathematical Modeling of Energy Minimizing Off-design Shapes of Large Scientific Balloons. Variational Principles for Strain Energy, NASA Goddard Space Flight Center/Wallops Flight Facility, NASA Award NAG5-697. Period: 3/94–2/95.
  • Mathematical Modeling of Energy Minimizing Off-design Shapes of Large Scientific Balloons, National Aeronautics and Space Administration, NASA Award NAG5-697. Period: 2/93–1/94.

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