Abstract: In order to assess the accuracy
of the mean field approximation to the kinetics of grain growth, we
introduce a one-dimensional model of a polycrystal, in which the grains
are segments in a line, with periodic boundary conditions, each grain
having two adjacent grains. The size of each grain changes with time
according to a given law, the rate of change depending on the size of
the grain and on the sizes of the adjacent grains, in such a way that
small grains shrink, eventually disappearing, and large grains expand,
with conservation of total size. In a mean field approximation, the
adjacent grains are replaced by grains of average size. The evolution
of various initial distributions under the two approaches, i.e. the
discrete and the mean field approaches, is compared. Large differences
between the two approaches are found for particular initial
distributions, while for other distributions the differences are minor.
The kinetics is, in general, faster in the discrete approach, and leads
to broader distributions than in the mean field approximations. Steady
state distributions within the mean field approach are seen to evolve
in the discrete approach. No tendency for a steady state to be reached
has been observed, the distributions becoming in general broader due to
growth. features.
Keywords: Cellular Materials, Grain
Growth, Kinetics, Discrete Simulations, Mean field approximation,
Materials Engineering.
Some
works by the same author:
55. Vitorino Ramos, Pedro
Pina, Exploiting and Evolving Rn
Mathematical Morphology
Feature
Spaces, in Ronse Ch., Najman L., Decencière E. (Eds.), Mathematical Morphology: 40
Years On, pp. 465-474, Springer,
Dordrecht,
The Netherlands, 2005.
53. Vitorino Ramos,
Jonathan Campbell, John Slater, John Gillespie, Ivan F. Bendezu and
Fionn Murtagh, Swarming around Shellfish Larvae
Images, in WCLC-05, 2nd
World
Congress on Lateral Computing, Bangalore,
India, 16-18 Dec., 2005.
63. Vitorino Ramos,
Carlos Fernandes, Agostinho C. Rosa, Social
Cognitive Maps, Swarm
Collective Perception and Distributed Search on Dynamic Landscapes,
submitted to A. Porto, A. Pazos, W. Buno (Eds.), Advancing Artificial
Intelligence through Biological Process Applications, IDEA Group Inc., 2007.
29. Vitorino Ramos,
Filipe Almeida, Artificial Ant Colonies in
Digital Image Habitats - A
Mass Behaviour Effect Study on Pattern Recognition, Proceedings of ANTS´2000 - 2nd
International Workshop on Ant
Algorithms (From Ant
Colonies to Artificial Ants), Marco Dorigo, Martin Middendorf
&
Thomas Stüzle (Eds.), pp. 113-116, Brussels, Belgium, 7-9 Sep.
2000.
59. Carlos Fernandes,
Vitorino Ramos and Agostinho C. Rosa, Self-Regulated
Artificial Ant Colonies on Digital Image Habitats, in Int. Journal of Lateral Computing,
IJLC, vol. 2, nº 1, pp. 1-8, ISSN 0973-208X, Dec. 2005.
70. Ramos, V., Fernandes, C.,
Rosa, A.C., Abraham, A., Computational Chemotaxis
in Ants and Bacteria
over Dynamic
Environments, submitted to CEC´07 -
Congress on Evolutionary
Computation, IEEE Press,
Singapore, 25-28 Sep. 2007.
69. Fernandes, C.,
Rosa, A.C., Ramos V., Binary Ant Algorithm,
to appear in GECCO´07 - Genetic and Evolutionary
Computation Conference, ACM
Press, London, UK, 7-11 July, 2007.
31. Vitorino Ramos,
Fernando Muge, Map Segmentation by Colour Cube
Genetic K-Mean
Clustering, Proc. of ECDL´2000 - 4th European
Conference on Research and Advanced
Technology for Digital Libraries, J. Borbinha and
T. Baker (Eds.), ISBN 3-540-41023-6, Lecture Notes in Computer Science,
Vol. 1923, pp. 319-323, Springer-Verlag
-Heidelberg, Lisbon, Portugal,
18-20 Sep. 2000.
51. Vitorino Ramos, Ajith
Abraham, Evolving a Stigmergic Self-Organized
Data-Mining, in ISDA-04,
4th Int. Conf. on Intelligent Systems, Design and Applications,
Budapest, Hungary, ISBN 963-7154-30-2, pp. 725-730, August 26-28, 2004.
45. Vitorino Ramos, Ajith
Abraham, Swarms on Continuous Data, in
CEC´03 - Congress on Evolutionary
Computation, IEEE Press,
ISBN 078-0378-04-0, pp.1370-1375,
Canberra, Australia, 8-12 Dec. 2003.