Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Modeling the flash-heat experiment on porous domains


Authors: H. T. Banks, D. Cioranescu, A. K. Criner and W. P. Winfree
Journal: Quart. Appl. Math. 70 (2012), 53-67
MSC (2000): Primary 35B27, 76R50, 78M40
Published electronically: September 16, 2011
MathSciNet review: 2920615
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss a mathematical model for the flash-heat experiment in homogeneous isotropic media. We then use this model to investigate the use of homogenization techniques in approximating models for interrogation via flash-heating in porous materials. We represent porous materials as both randomly perforated domains and periodically perforated domains.


References [Enhancements On Off] (What's this?)

  • 1. H.T. Banks, B. Boudreaux, A. K. Criner, K. Foster, C. Uttal, T. Vogel, A.K. Criner and W.P. Winfree, Thermal based damage detection in porous materials, Tech. Rep. CRSC-TR08-11, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, September, 2008; Inverse Probl. Sci. Engr., 18 (2009), 835-851.
  • 2. H.T. Banks, D. Cioranescu, A.K. Criner and W.P. Winfree, Modeling the flash-heat experiment on porous domains, Tech. Rep. CRSC-TR10-06, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May, 2010.
  • 3. H. T. Banks, N. L. Gibson and W. P. Winfree, Void detection in complex geometries, Tech. Rep. CRSC-TR08-09, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May, 2008.
  • 4. H. T. Banks, Michele L. Joyner, Buzz Wincheski, and William P. Winfree, Nondestructive evaluation using a reduced-order computational methodology, Inverse Problems 16 (2000), no. 4, 929–945. MR 1776475, 10.1088/0266-5611/16/4/304
  • 5. H. T. Banks and Fumio Kojima, Boundary shape identification problems in two-dimensional domains related to thermal testing of materials, Quart. Appl. Math. 47 (1989), no. 2, 273–293. MR 998101
  • 6. H. T. Banks and F. Kojima, Identification of material damage in two-dimensional domains using the SQUID-based nondestructive evaluation system, Inverse Problems 18 (2002), no. 6, 1831–1855. Special section on electromagnetic and ultrasonic nondestructive evaluation. MR 1955921, 10.1088/0266-5611/18/6/324
  • 7. H. T. Banks, Fumio Kojima, and W. P. Winfree, Boundary estimation problems arising in thermal tomography, Inverse Problems 6 (1990), no. 6, 897–921. MR 1082231
  • 8. D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in domains with holes, to appear.
  • 9. Doina Cioranescu and Jeannine Saint Jean Paulin, Homogenization of reticulated structures, Applied Mathematical Sciences, vol. 136, Springer-Verlag, New York, 1999. MR 1676922
  • 10. Doina Cioranescu and Patrizia Donato, An introduction to homogenization, Oxford Lecture Series in Mathematics and its Applications, vol. 17, The Clarendon Press, Oxford University Press, New York, 1999. MR 1765047
  • 11. Patrizia Donato and Aïssam Nabil, Homogenization and correctors for the heat equation in perforated domains, Ricerche Mat. 50 (2001), no. 1, 115–144. MR 1941824
  • 12. The Mathworks, Inc., Partial Differential Equation Toolbox 1: User's Guide, The Mathworks, Inc., Natick, MA, 2008.
  • 13. W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbott, Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity, J. Appl. Phys. 32 (9):1679-1684, 1961.
  • 14. Pavel Šolín, Partial differential equations and the finite element method, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. MR 2180081
  • 15. Wenping Wang, Jiaye Wang, and Myung-Soo Kim, An algebraic condition for the separation of two ellipsoids, Comput. Aided Geom. Design 18 (2001), no. 6, 531–539. MR 1843064, 10.1016/S0167-8396(01)00049-8

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35B27, 76R50, 78M40

Retrieve articles in all journals with MSC (2000): 35B27, 76R50, 78M40


Additional Information

H. T. Banks
Affiliation: Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8212

D. Cioranescu
Affiliation: Laboratoire J. L. Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France

A. K. Criner
Affiliation: Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8212

W. P. Winfree
Affiliation: Nondestructive Evaluation Science Branch, NASA Langley Research Center, MS 231, Hampton, Virginia 23681

DOI: https://doi.org/10.1090/S0033-569X-2011-01230-8
Keywords: Modeling porous media, thermal diffusion, homogenization
Received by editor(s): May 16, 2010
Published electronically: September 16, 2011
Article copyright: © Copyright 2011 Brown University


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website