Multiscale modeling requires multiscale mathematics.

Introduction. In 1999 multiscale modeling / multiscale mathematics seemed to burst into Multiscalethe academic world.  Mark F. Horstemeyer of Mississippi State University cites the exponential increase of published titles that included the word “multiscale.”  Today, the SIAM journal, Multiscale Modeling and Simulation, cites editors and authors from the most prestigious schools and research laboratories from around the world.

Perspective. Notwithstanding, none of the work done to date within this domain of study starts with infinitesimal Planck units of length and time. These two physical computations by Max Planck in 1899 are abstractions too far removed from practical applications. That this Planck scale could be pervasive throughout all time and space has not been a consideration within the multiscale paradigm.

To  date, only Jack Xin and Pingwen Zhang have been asked about its relevance.  With this writing, all the associate editors of the SIAm publication, Multiscale Modeling and Simulation, will be asked for their opinions. Of particular interest at this stage of our exploration is any multiscale research within particle physics.

Scholarship. Out of thousands of articles, we lift out the following for review:

Multiscale Modeling and Simulation
Editor-in-Chief, Jack Xin, University of California, Irvine
Associate Editors

  1. Andrea L. Bertozzi, University of California, Los Angeles
  2. Liliana Borcea, University of Michigan
  3. Russel Caflisch, Courant Institute of Mathematical Sciences, New York University
  4. Eric Cances, CERMICS
  5. José A. Carrillo, Imperial College London
  6. Hector Ceniceros, University of California, Santa Barbara
  7. Long Chen, University of California Irvine
  8. Tom Chou, University of California, Los Angeles
  9. Daan Crommelin, CWI
  10. Yalchin Efendiev, Texas A&M University
  11. Albert Fannjiang, University of California, Davis
  12. Susan Friedlander, University of Southern California
  13. Gero Friesecke, Technical University Munich
  14. Roger Ghanem, University of Southern California
  15. Cory Hauck, Oak Ridge National Laboratory
  16. Michael Herty, RWTH Aachen
  17. Thomas Hou, California Institute of Technology
  18. Shi Jin, Shanghai Jiao Tong University
  19. Ralf Kornhuber, Freie Universitaet Berlin
  20. Frederic Legoll, ENPC
  21. Guang Lin, Purdue University West Lafayette
  22. Robert Lipton, Louisiana State University
  23. Jianfeng Lu, Duke University
  24. Mitchell Luskin, University of Minnesota
  25. Peter Markowich, University of Vienna
  26. Alexander B. Movchan, University of Liverpool
  27. Barbara Niethammer, Universitaet Bonn
  28. Yasumasa Nishiura, Tohoku University
  29. Stanley Osher, University of California, Los Angeles
  30. Lorenzo Pareschi, University of Ferrara
  31. Grigorios A. Pavliotis,Imperial College London
  32. Petr Plechac, University of Delaware
  33. Zuowei Shen, National University of Singapore
  34. Mary Silber, University of Chicago
  35. James Sneyd, University of Auckland
  36. Jared Tanner, Oxford University
  37. Hamdi Tchelepi, Stanford University
  38. Richard Tsai, University of Texas, Austin
  39. Mark Tuckerman, New York University
  40. Rachel Ward University of Texas, Austin
  41. Pingwen Zhang, Peking University
  42. Hongkai Zhao, University of California, Irvine

Horstemeyer, M. F. (2009). “Multiscale Modeling: A Review”. In Leszczyński, Jerzy; Shukla, Manoj K. Practical Aspects of Computational Chemistry: Methods, Concepts and Applications. pp. 87–135. ISBN 978-90-481-2687-3.