Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
Volume 22, Issue 21, Pages 3487-3578Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217979208048668
Keywords
variational principle; Lagrange multiplier; optimization; variational iteration method; homotopy perturbation method; exp-function method; parameter-expansion method; nanofiber; electrospinning; spider; nanohydrodynamics; carbon nanotube; fractal spacetime; E-infinity theory
Funding
- National Natural Science Foundation of China [10772054, 10572038]
- New Century Excellent Talents in University [NCET-05-0417]
- [B07024]
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This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references.
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