An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering

International Journal of Modern Physics B

Volumn 22, Issue 21, 2008, Pages 3487-3578

  He, Ji Huan ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

Carbon nanotube; Electrospinning; Exp function method; Fractal spacetime; Homotopy perturbation method; Lagrange multiplier; Nanofiber; Nanohydrodynamics; Optimization; Parameter expansion method; Spider; Variational iteration method; Variational principle

Indexed keywords

EID: 50949112266     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979208048668     Document Type: Review

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186. A. Beléndez, C. Pascual, D. I. Méndez, M. L. Álvarez and C. Neipp, Application of He's Homotopy Perturbation Method to the relativistic (An)harmonic oscillator. II: A more accurate approximate solution, Int. J. Nonlinear Sci. 8, 493 (2007).
187. A. Beléndez, A. Hernandez, T. Belendez et al., An improved "heuristic" approximation for the period of a nonlinear pendulum: Linear analysis of a classical nonlinear problem, Int. J. Nonlinear Sci. 8, 329 (2007).
188. A. Beléndez, A. Hernandez, T. Beléndez et al., Application of He's homotopy perturbation method to the Duffing-harmonic oscillator, Int. J. Nonlinear Sci. 8, 79 (2007).
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190. A. Beléndez, C. Pascual, S. Gallego, M. Ortuño and C. Neipp, Application of a modified He's homotopy perturbation method to obtain higher-order approximations of an x1/3 force nonlinear oscillator, Phys. Lett. A 371(5-6), 421 (2007).
191. J. Biazar, M. Eslami and H. Ghazvini, Homotopy perturbation method for systems of partial differential equations, Int. J. Nonlinear Sci. 8, 413 (2007).
192. J. Biazar and H. Ghazvini, Exact solutions for non-linear Schrodinger equations by He's homotopy perturbation method, Phys. Lett. A 366, 79 (2007).
193. M. S. H. Chowdhury, I. Hashim and O. Abdulaziz, Application of homotopy-perturbation method to nonlinear population dynamics models, Phys. Lett. A 368, 251 (2007).
194. M. S. H. Chowdhury and I. Hashim, Solutions of time-dependent Emden-Fowler type equations by homotopy-perturbation method, Phys. Lett. A 368, 305 (2007).
195. M. S. H. Chowdhury and I. Hashim, Solutions of a class of singular second-order IVPs by homotopy-perturbation method, Phys. Lett. A 365, 439 (2007).
196. C. Chun, Integration using He's homotopy perturbation method, Chaos Soliton. Fract. 34, 1130 (2007).
197. L. Cveticanin, Homotopy-perturbation method for pure nonlinear differential equation, Chaos Soliton. Fract. 30, 1221 (2006).
198. G. Domairry, M. Ahangari and M. Jamshidi, Exact and analytical solution for non-linear dispersive K (m, p) equations using homotopy perturbation method, Phys. Lett. A 368, 266 (2007).
199. X. C. Cai, W. Y. Wu and M. S. Li, Approximate period solution for a kind of non-linear oscillator by He's perturbation method, Int. J. Nonlinear Sci. 7, 109 (2006).
200. M. Dehghan and F. Shakeri, Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method, Phys. Scrip. 75, 778 (2007).
201. M. A. El-Tawil and A. S. Al-Jihany, On the solution of stochastic oscillatory quadratic nonlinear equations using different techniques, a comparison study, Topological Methods in Nonlinear Analysis Topological Methods in Nonlinear Analysis 31(2), 315 (2008).
202. D. D. Ganji, G. A. Afrouzi, H. Hosseinzadeh et al., Application of homotopy-perturbation method to the second kind of nonlinear integral equations, Phys. Lett. A 371, 20 (2007).
203. D. D. Ganji, M. J. Hosseini and J. Shayegh, Some nonlinear heat transfer equations solved by three approximate methods, Int. Commun. Heat Mass Trans. 34, 1003 (2007).
204. D. D. Ganji and A. Sadighi, Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J. Comput. Appl. Math. 207, 24 (2007).
205. D. D. Ganji and A. Sadighi, Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, Int. J. Nonlinear Sci. 7, 411 (2006).
206. D. D. Ganji and M. Rafei, Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method, Phys. Lett. A 356, 131 (2006).
207. D. D. Ganji, The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. Lett. A 355, 337 (2006).
208. D. D. Ganji, M. Nourollahi and E. Mohseni, Application of He's methods to nonlinear chemistry problems, Comput. Math. Appl. 54, 1122 (2007).
209. Z. Z. Ganji, D. D. Ganji, M. Rostamian and M. Hossaini, Application of homotopy perturbation method to coupled systems of partial differential equations with time fractional derivatives, Topological Methods in Nonlinear AnalysisTopological Methods in Nonlinear Analysis 31(2), 341 (2008).
210. M. Gorji, D. D. Ganji and S. Soleimani, New application of He's homotopy perturbation method, Int. J. Nonlinear Sci. 8, 319 (2007).
211. M. Ghasemi, M. T. Kajani and E. Babolian, Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput. 188, 446 (2007).
212. M. Ghasemi, M. T. Kajani and E. Babolian, Numerical solutions of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation method, Appl. Math. Comput. 188, 450 (2007).
213. M. Ghasemi, M. T. Kajani and E. Babolian, Application of He's homotopy perturbation method to nonlinear integro-differential equations, Appl. Math. Comput. 188, 538 (2007).
214. M. Ghasemi, M. T. Kajani and A. Davari, Numerical solution of two-dimensional nonlinear differential equation by homotopy perturbation method, Appl. Math. Comput. 189, 341 (2007).
215. A. Ghorbani and J. Saberi-Nadjafi, He's homotopy perturbation method for calculating adomian polynomials, Int. J. Nonlinear Sci. 8, 229 (2007).
216. Q. K. Ghori, M. Ahmed and A. M. Siddiqui, Application of homotopy perturbation method to squeezing flow of a Newtonian fluid, Int. J. Nonlinear Sci. 8, 179 (2007).
217. A. M. Siddiqui, R. Mahmood and Q. K. Ghori, Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method, Int. J. Nonlinear Sci. 7, 7 (2006).
218. A. M. Siddiqui, M. Ahmed and Q. K. Ghori, Couette and Poiseuille flows for non-Newtonian fluids, Int. J. Nonlinear Sci. 7, 15 (2006).
219. M. Inc and Y. Ugurlu, Numerical simulation of the regularized long wave equation by He's homotopy perturbation method, Phys. Lett. A 369, 173 (2007).
220. S. Momani, Z. Odibat and I. Hashim, Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods, Topological Methods in Nonlinear Analysis 31(2), 211 (2008).
221. S. Momani and Z. Odibat, Numerical approach to differential equations of fractional order, J. Comput. Appl. Math. 207, 96 (2007).
222. S. Momani and Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A 365, 345 (2007).
223. S. Momani and Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Soliton. Fract. 31, 1248 (2007).
224. S. Momani and Z. Odibat, Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations, Comput. Math. Appl. 54, 910 (2007).
225. Z. Odibat and S. Momani. Applications of variational iteration and homotopy perturbation methods to fractional evolution equations, Topological Methods in Nonlinear Analysis 31(2), 227 (2008).
226. Z. Odibat and S. Momani, Numerical solution of Fokker-Planck equation with space-and time-fractional derivatives, Phys. Lett. A 369, 349 (2007).
227. Z. Odibat and S. Momani, Numerical methods for nonlinear partial differential equations of fractional order, Appl. Math. Model. 32, 28 (2008).
228. Z. Odibat and S. Momani, A reliable treatment of homotopy perturbation method for Klein-Gordon equations, Phys. Lett. A 365, 351 (2007).
229. Z. M. Odibat, Solitary solutions for the nonlinear dispersive K (m, n) equations with fractional time derivatives, Phys. Lett. A 370, 295 (2007).
230. Q. Ma, R. Y. Xing and S. L. Mei, Application of homotopy perturbation method to regularization of scalar images, Topological Methods in Nonlinear Analysis 31(2), 230 (2008).
231. S. L. Mei, C. J. Du and S. W. Zhang, Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems, Chaos Soliton. Fract. 35, 536 (2008).
232. S. L. Mei and S. W. Zhang, Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations, Comput. Math. Appl. 54, 1092 (2007).
233. T. Ozis and A. Yidirim, A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity, Chaos Soliton. Fract. 34, 989 (2007).
234. T. Ozis and A. Yidirim, Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method, Int. J. Nonlinear Sci. 8, 239 (2007).
235. T. Ozis and A. Yidirim, A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities, Int. J. Nonlinear Sci. 8, 243 (2007).
236. T. Ozis and A. Yidirim, Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators, Chaos Soliton. Fract. 32, 445 (2007).
237. T. Ozis and A. Yildirim, Determination of limit cycles by iterated homotopy perturbation method for nonlinear oscillators with strong nonlinearity, Topological Methods in Nonlinear Analysis 31(2), 349 (2008).
238. A. Molabahrami, F. Khani and S. Hamedi-Nezhad, Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method, Phys. Lett. A 370, 433 (2007).
239. H. Jafari and S. Momani, Solving fractional diffusion and wave equations by modified homotopy perturbation method, Phys. Lett. A 370, 388 (2007).
240. M. Javidi and A. Golbabai, A numerical solution for solving system of Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput. 189, 1921 (2007).
241. M. A. Rana, A. M. Siddiqui, Q. K. Ghori et al., Application of He's homotopy perturbation method to Sumudu transform, Int. J. Nonlinear Sci. 8, 185 (2007).
242. M. Rubner. Zeitschrift fur Biologie 19, 536 (1883).
243. A. Sadighi and D. D. Ganji, Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods, Int. J. Nonlinear Sci. 8, 435 (2007).
244. F. Shakeri and M. Dehghan, Inverse problem of diffusion equation by He's homotopy perturbation method, Phys. Scrip. 75, 551 (2007).
245. V. Marinca, Application of modified homotopy perturbation method to nonlinear oscillations, Archives of Mechanics Archives of Mechanics 58(3), 241 (2006).
246. L. Xu, He's homotopy perturbation method for the temperature distribution in convective straight fins with temperature-dependent thermal conductivity, Topological Methods in Nonlinear Analysis 31(2), 253 (2008).
247. L. Xu, He's homotopy perturbation method for a boundary layer equation in unbounded domain, Comput. Math. Appl. 54, 1067 (2007).
248. E. Yusufoglu, Homotopy perturbation method for solving a nonlinear system of second order boundary value problems, Int. J. Nonlinear Sci. 8, 353 (2007).
249. D. H. Shou and J. H. He, Application of parameter-expanding method to strongly nonlinear oscillators, Int. J. Nonlinear Sci. 8, 121 (2007).
250. S. Q. Wang and J. H. He, Nonlinear oscillator with discontinuity by parameter-expansion method, Chaos Soliton. Fract. 35, 688 (2008).
251. L. Xu, Application of He's parameter-expansion method to an oscillation of a mass attached to a stretched elastic wire, Phys. Lett. A 368, 259 (2007).
252. L. Xu, Determination of limit cycle by He's parameter-expanding method for strongly nonlinear oscillators, J. Sound Vib. 302, 178 (2007).
253. L. N. Zhang and L. Xu, Determination of the limit cycle by He's parameter-expansion for oscillators in a u(3)/(1+u(2)) potential, Z. Naturforsch. A 62, 396 (2007).
254. Z. L. Tao, Frequency-amplitude relationship of the Duffing-harmonic oscillator, Topological Methods in Nonlinear Analysis 31(2), 279 (2008).
255. Z. L. Tao, Frequency-amplitude relationship of nonlinear oscillators by He's parameter-expansion method, Chaos Solitions and Fractal, in press doi:10.1016/j.chaos.2008.02.036.
256. J. H. He, Electrospinning: The big world of small fibers, Polym. Int. 56(11), 1321 (2007).
257. J. H. He, L. Xu, Y. Wu et al., Mathematical models for continuous electrospun nanofibers and electrospun nanoporous microspheres, Polym. Int. 56(11), 1323 (2007).
258. S. Tan, X. Huang and B. Wu, Some fascinating phenomena in electrospinning processes and applications of electrospun nanofibers, Polym. Int. 56(11), 1330 (2007).
259. S. Sell, C. Barnes, M. Smith et al., Extracellular matrix regenerated: Tissue engineering via electrospun biomimetic nanofibers, Polym. Int. 56(11), 1349 (2007).
260. S. Park, K. Park, H. Yoon et al. Apparatus for preparing electrospun nanofibers: Designing an electrospinning process for nanofiber fabrication, Polym. Int. 56(11), 1361 (2007).
261. Y. Q. Wan, J. H. He and J. Y. Yu, Carbon nanotube-reinforced polyacrylonitrile nanofibers by vibration-electrospinning, Polym. Int. 56(11), 1367 (2007).
262. J. Sutasinpromprae, S. Jitjaicham, M. Nithitanakul et al., Preparation and characterization of ultrafine electrospun polyacrylonitrile fibers and their subsequent pyrolysis to carbon fibers, Polym. Int. 55(8), 825 (2006).
263. H. R. Allcock, L. B. Steely and A. Singh, Hydrophobic and superhydrophobic surfaces from polyphosphazenes, Polym. Int. 55(6) 621 (2006).
264. S. Pracek, Theory of string motion in the textile process of yarn unwinding, Int. J. Nonlinear Sci. 8(3), 451 (2007).
265. J. H. He, Y. Liu, L. Xu et al., Micro sphere with nanoporosity by electrospinning, Chaos Soliton. Fract. 32(3), 1096 (2007).
266. J. H. He, Y. Liu, L. Xu et al., Micro sphere with nanoporosity by electrospinning, Chaos Soliton. Fract. 32, 1096 (2007).
267. L. Xu, J. H. He and Y. Liu, Electrospun nanoporous spheres with Chinese drug, Int. J. Nonlinear Sci. 8(2): 199 (2007).
268. J. H. He, Y. Q. Wan and L. Xu, Nano-effects, quantum-like properties in electrospun nanofibers, Chaos Soliton. Fract. 33(1), 26 (2007).
269. J. H. He, Nano bubble dynamics in spider spinning system, J. Animal and Veterinary Adv. 7, 207 (2008).
270. Y. Liu and J. H. He, Bubble electrospinning for mass production of nanofibers, Int. J. Nonlinear Sci. 8(3), 393 (2007).
271. J. H. He, Y. Liu, L. Xu et al., Biomimic fabrication of electrospun nanofibers with high-throughput, Chaos Soliton. Fract. 37(3), 643 (2008) doi:10.1016/j.chaos.2007.11.028
272. Y. Liu, J.-H. He and J.-Y. Yu, Bubble-electrospinning: A novel method for making nanofibers, J. Phys.: Conf. Series 96, 012001 (2008).
273. Y. Liu, J.-H. He, L. Xu and J.-Y. Yu, The principle of bubble electrospinning and its experimental verification, J. Polym. Eng. 28, 55 (2008).
274. Y. Liu and L. Xu, Controlling air vortex in air-vortex spinning by Zeng-He model, Int. J. Nonlinear Sci. 7, 389 (2006).
275. Y. C. Zeng, Y. Wu, Z. G. Pei et al., Numerical approach to electrospinning, Int. J. Nonlinear Sci. 7, 385 (2006).
276. Y. C. Zeng and C. W. Yu, A flexible fiber model for dynamic simulation of fibers in high speed air flows, Int. J. Nonlinear Sci. 7, 427 (2006).
277. J.-H. He, Application of Sirofil Technology to Electrospinning, J. Polym. Eng. 28(1-2, 119 (2008).
278. G. Lukaszewicz, Micropolar Fluids: Theory and Applications (Birkhauser, Boston, 1999).
279. J. H. He, A variational model for 2-D micropolar blood flow, J. Hydrodynamics B 15(3), 119 (2003).
280. J. H. He, A new mathematical model for yarn motion in tube, in Proc. Fourth Int. Conf. Fluid Mech., eds. F. Zhuang and J. C. Li (Tsinghua University Press, Beijing, 2004), 621-622.
281. J. H. He, Allometric scaling law in conductive polymer, Polymer 45, 9067 (2004).
282. J. H. He, Resistance in cell membrane and nerve fiber, Neurosci. Lett. 373, 48 (2005).
283. J. H. He and X. H. Wu, A modified Morris-Lecar model for interacting ion channels, Neurocomputing 64, 543 (2005).
284. J.-H. He, A new resistance formulation for carbon nonotubes, Journal of Nanomaterials 954874 (2008) doi:10.1155/2008/954874.
285. J.-H. He and Y. Liu, A hierarchy of motion in electrospinning process and E-infinity nanotechnology, J. Polym. Eng. 28, 101 (2008).
286. J.-H. He and L. Xu, Super-carbon nanotubes: An E-infinity approach, Int. J. Electrospun Nanofibers and Applications 1(3), 161 (2007).
287. V. R. Coluci, N. M. Pugno, S. O. Dantas et al., Atomistic simulations of the mechanical properties of "super" carbon nanotubes, Nanotechnology 18, 335702 (2007).
288. V. R. Coluci, D. S. Galvao and A. Jorio, Geometric and electronic structure of carbon nanotube networks: "super"-carbon nanotubes, Nanotechnology 17, 617 (2006).
289. V. R. Coluci, S. B. Legoas, M. de Aguiar et al., Chaotic signature in the motion of coupled carbon nanotube oscillators, Nanotechnology 16, 583 (2005).
290. J. H. He and S. D. Zhu, Differential-difference model for nanotechnology, J. Phys.: Conf. Series 96, 012189 (2008).
291. A. Yildirim, Exact solutions of nonlinear differential-difference equations by He's homotopy perturbation method, Int. J. Nonlinear Sci. 9(2), 111 (2008).
292. R. Mokhtari, Variational iteration method fof solving nonlinear differential-difference. Int. J. Nonlinear Sci. 9(1), 19 (2008).