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NUMERICAL SOLUTION OF A 2D- DIFFUSION REACTION PROBLEM MODELLING THE DENSITY OF DI-VACANCIES AND VACANCIES IN A METAL

Year 2017, Volume: 7 Issue: 1, 165 - 172, 01.06.2017

Abstract

A decomposition solution of a diffusion reaction problem, which models the density of di-vacancies and vacancies in a metal is presented. The results are compared with the numerical solutions. Zero - diffusion solutions are obtained numerically and some figures are illustrated..

References

  • Adomian,G., (1994), Solving Frontier Problems of Physics: the Decomposition Method, Kluwer
  • Academic Publishers, Boston. Ali,E.J., (2012), A New Technique of Initial Boundary Value Problems Using Adomian Decompo- sition Method, Int. Math. Forum., 7 (17), pp. 799–814.
  • Brandes,E.A. and Brook,G.B., (1992), Smithells Metals Reference Book, Seventh Edition
  • Butterworth-Heinemann, Oxford. Cherruault,Y. and Adomian,G., (1993), Decomposition methods: a new proof of convergence, Math. Comp. Model., 18, pp.103-106.
  • Dieter,G.E., (1986), Mechanical Metallurgy, Third Edition, McGraw-Hill, New York.
  • Dudarev,S.L., (2013), Density Functional Theory Models for Radiation Damage , Annu. Rev. Mater. Res., 43, pp.35-61.
  • Hare,G. and Roelofs,L.D., (2002), Diffusion of vacancies and adatoms on stepped crystalline sur- faces , Surface Science., 511, pp.283-293.
  • Hoang,S., Baraille,R., Talagrand,O., Nguyen,T.L., and De Mey,P., (1997), Approximation approach for nonlinear filtering problem with time dependent noises, Kybernetika., 33(5), pp.557-576.
  • Kailas,S.V., Material Science: Diffusion.pdf. Retrieved from http://www.nptel.ac.in/courses/ /pdf/LectureNotes/MLN05.pdf Kaya,D. and Yokus,A., (2002), A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations, Math. Comput. Simulat., 60, pp.507
  • Kaya,D. and Aassila,M., (2002), An application for a generalized KdV equation by the decompo- sition method, Phys.Lett. A., 299, pp.201-206.
  • Malik,R., Burch,D., Bazant,M., and Ceder,G. , Particle Size Dependence of the Ionic Diffusivity, DOI: 10.1021/nl1023595, Retrieved from pubs.acs.org/NanoLett.
  • Pamuk,S. , (2005), The decomposition method for continuous population models for single and interacting species, Applied Mathematics and Computation., 163(1), pp.79-88.
  • Pamuk,S., (2005), An application for linear and nonlinear heat equations by Adomians decompo- sition method, Applied Mathematics and Computation, 163(1), pp.89-96.
  • Pamuk,S., (2005), Solution of the porous media equation by Adomians decomposition method
  • Physics Letters A., 344 (2-4), pp.184-188. Sewell,G., (1988), The numerical Solution of Ordinary and Partial Differential Equations. Aca- demic Press, New York.
  • Shewmon,P.G., (1989), Diffusion in Solids, Second Edition, The Minerals, Metals and Materials
  • Society, Warrendale, PA. Sterne,P.A., J. van Ek, and Howell,R.H., (1997), Electronic Structure Calculations of Vacancies and Their Influence on Materials Properties, UCRL-JC-127349, Preprint.
  • Serdal Pamuk, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.3, No.2, 2013.
Year 2017, Volume: 7 Issue: 1, 165 - 172, 01.06.2017

Abstract

References

  • Adomian,G., (1994), Solving Frontier Problems of Physics: the Decomposition Method, Kluwer
  • Academic Publishers, Boston. Ali,E.J., (2012), A New Technique of Initial Boundary Value Problems Using Adomian Decompo- sition Method, Int. Math. Forum., 7 (17), pp. 799–814.
  • Brandes,E.A. and Brook,G.B., (1992), Smithells Metals Reference Book, Seventh Edition
  • Butterworth-Heinemann, Oxford. Cherruault,Y. and Adomian,G., (1993), Decomposition methods: a new proof of convergence, Math. Comp. Model., 18, pp.103-106.
  • Dieter,G.E., (1986), Mechanical Metallurgy, Third Edition, McGraw-Hill, New York.
  • Dudarev,S.L., (2013), Density Functional Theory Models for Radiation Damage , Annu. Rev. Mater. Res., 43, pp.35-61.
  • Hare,G. and Roelofs,L.D., (2002), Diffusion of vacancies and adatoms on stepped crystalline sur- faces , Surface Science., 511, pp.283-293.
  • Hoang,S., Baraille,R., Talagrand,O., Nguyen,T.L., and De Mey,P., (1997), Approximation approach for nonlinear filtering problem with time dependent noises, Kybernetika., 33(5), pp.557-576.
  • Kailas,S.V., Material Science: Diffusion.pdf. Retrieved from http://www.nptel.ac.in/courses/ /pdf/LectureNotes/MLN05.pdf Kaya,D. and Yokus,A., (2002), A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations, Math. Comput. Simulat., 60, pp.507
  • Kaya,D. and Aassila,M., (2002), An application for a generalized KdV equation by the decompo- sition method, Phys.Lett. A., 299, pp.201-206.
  • Malik,R., Burch,D., Bazant,M., and Ceder,G. , Particle Size Dependence of the Ionic Diffusivity, DOI: 10.1021/nl1023595, Retrieved from pubs.acs.org/NanoLett.
  • Pamuk,S. , (2005), The decomposition method for continuous population models for single and interacting species, Applied Mathematics and Computation., 163(1), pp.79-88.
  • Pamuk,S., (2005), An application for linear and nonlinear heat equations by Adomians decompo- sition method, Applied Mathematics and Computation, 163(1), pp.89-96.
  • Pamuk,S., (2005), Solution of the porous media equation by Adomians decomposition method
  • Physics Letters A., 344 (2-4), pp.184-188. Sewell,G., (1988), The numerical Solution of Ordinary and Partial Differential Equations. Aca- demic Press, New York.
  • Shewmon,P.G., (1989), Diffusion in Solids, Second Edition, The Minerals, Metals and Materials
  • Society, Warrendale, PA. Sterne,P.A., J. van Ek, and Howell,R.H., (1997), Electronic Structure Calculations of Vacancies and Their Influence on Materials Properties, UCRL-JC-127349, Preprint.
  • Serdal Pamuk, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.3, No.2, 2013.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Serdal Pamuk This is me

Publication Date June 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

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