Table of Contents
ISRN Nanomaterials
Volume 2013, Article ID 981616, 6 pages
http://dx.doi.org/10.1155/2013/981616
Research Article

The 3D Kuramoto-Sivashinsky Equation for Nonequilibrium Defects Interacting through Self-Consisting Strain and Nanostructuring of Solids

Physics Faculty, Lomonosov Moscow State University, Moscow 119991, Russia

Received 25 June 2013; Accepted 2 September 2013

Academic Editors: R. Hong, G. Jin, and A. Pyatenko

Copyright © 2013 V. I. Emel’yanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer, Berlin, Germany, 1984.
  2. G. I. Sivashinsky, “Instabilities, pattern formation, and turbulence in flames,” Annual Review of Fluid Mechanics, vol. 15, pp. 179–199, 1983. View at Google Scholar · View at Scopus
  3. J. M. Garcia, L. Vazquez, R. Cuerno, J. A. Garcia, M. Castro, and R. Gago, “Self-organized surface nanopatterning by ion beam sputtering,” in Lecture Notes on Nanoscale Science and Technology 5, Z. Wang, Ed., pp. 323–398, Springer, Heidelberg, Germany, 2009. View at Google Scholar
  4. A. G. Limonov, “Numeric simulation of the formation of hexagonal nanoscale structure arrays in Anodic Aluminum Oxide,” Mathematical Models and Computer Simulations, vol. 3, no. 2, pp. 149–157, 2011. View at Google Scholar
  5. V. I. Emel’yanov, “Mechanisms of laser-induced self-organization of nano- and microstructures of surface relief in air and in liquid environment,” in Laser Ablation in Liquids, Principles and Applications in the Preparation of Nanomaterials, G. Yang, Ed., chapter 1, pp. 1–109, Pan Stanford, Singapore, 2012. View at Google Scholar
  6. V. I. Emel'yanov and I. M. Panin, “Formation of nanometer ordered defect-deformational structures induced by energy fluxes in solids,” Physics of the Solid State, vol. 39, no. 11, pp. 1815–1820, 1997. View at Google Scholar · View at Scopus
  7. K. Arakawa, K. Ono, M. Isshiki, K. Mimura, M. Uchikoshi, and H. Mori, “Observation of the one-dimensional diffusion of nanometer-sized dislocation loops,” Science, vol. 318, no. 5852, pp. 956–959, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. I. A. Kunin, Theory of Elastic Media with Microstructure, Springer, New York, NY, USA, 1982.
  9. A. C. Eringen, Nonlocal Continuum Field Theories, Springer, New York, NY, USA, 2002.
  10. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon, New York, NY, USA, 1986.
  11. R. Z. Valiev, R. K. Islamgaliev, and I. V. Alexandrov, “Bulk nanostructured materials from severe plastic deformation,” Progress in Materials Science, vol. 45, no. 2, pp. 103–189, 2000. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Pippan, S. Scheriau, A. Taylor, M. Hafok, A. Hohenwarter, and A. Bachmaier, “Saturation of fragmentation during severe plastic deformation,” Annual Review of Materials Research, vol. 40, pp. 319–343, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. E. Schafler, G. Steiner, E. Korznikova, E. Kerber, and M. J. Zehetbauer, “Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry,” Materials Science and Engineering A, vol. 410411, pp. 169–173, 2005. View at Google Scholar
  14. D. Setman, E. Schafler, E. Korznikova, and M. J. Zehetbauer, “The presence and nature of vacancy type defects in nanometals detained by severe plastic deformation,” Materials Science and Engineering A, vol. 493, no. 1-2, pp. 116–122, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. Y. Y. Zhang, C. M. Wang, W. H. Duan, Y. Xiang, and Z. Zong, “Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes,” Nanotechnology, vol. 20, no. 39, Article ID 395707, 2009. View at Publisher · View at Google Scholar · View at Scopus