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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 (to appear).
  2. 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.
  3. 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.
  4. P. Gorham, et. al, Shape Analysis and Deployment of the ExaVolt Antenna, Journal of Astronomical Instrumentation,  6 No. 2 (2017) 174004.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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).
  11. 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.
  12. F. Baginski and K. Brakke, Estimating the deployment pressure in pumpkin balloons, AIAA Journal of Aircraft, 48  No. 1 (2011) 235-247.
  13. 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.
  14. F. Baginski and K. Brakke, Simulating clefts in  pumpkin balloons. Adv. Space Res. 45  No. 4 (2010) 473-481.
  15. 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.
  16. 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.
  17. 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.
  18. F. Baginski, W. Schur, and K. Brakke, Cleft formation in pumpkin balloons, Adv. Space Res., 37  (2006) 2070-2081.
  19. F. Baginski and W. W. Schur,  Undesired equilibria of self-deploying pneumatic envelopes, AIAA Journal of Aircraft,  42  No. 6 (2005), 1639-1642.
  20. 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.
  21. F. Baginski and J. Winker, The natural shape balloon and related models, Adv. Space Res., 33 No. 10 (2004), 1617-1622.
  22. F. Baginski, Nonuniqueness of strained ascent shapes of high altitude balloons,  Adv. Space Res., 33  No. 10 (2004), 1705-1710.
  23. 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.
  24. F. Baginski, A mathematical model for a partially inflated balloon with a periodic lobe structure, Adv. Space Res., 30 No. 5 (2002),  1167-1171.
  25. 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.
  26. W. Collier and F. Baginski, Modeling the shapes of constrained partially inflated high altitude balloons , AIAA Journal, 39  No. 9 (2001), 1662-1672.
  27. 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.
  28. F. Baginski and K. Brakke, Modeling ascent configurations of strained high altitude balloons , AIAA J., 36  No.10 (1998),  1901-1910.
  29. W. Collier and F. Baginski, Energy minimizing shapes of partially inflated large scientific balloons. Advances in Space Research, 21  No. 7 (1998) 975-978.
  30. 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.
  31. 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.
  32. F. Baginski, Modeling non-axisymmetric off-design shapes of large scientific balloons, AIAA Journal, 34  No. 2 (1996), 400-407.
  33. 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.
  34. F. Baginski and S. Ramamurti, Variational principles for ascent shapes of large scientific balloons , AIAA Journal, 33  No. 4 (1995), 764-768.
  35. F. Baginski, The computation of one-parameter families of bifurcating elastic surfaces, SIAM Journal on Applied Mathematics, 54 No. 3 (1994), 738-773.
  36. F. Baginski, The buckling of  elastic spherical caps, Journal of Elasticity, Vol. 25 (1991), 159-192.
  37. 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.
  38. 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.
  39. 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.
  40. 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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