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

Yıl 2017, Cilt: 7 Sayı: 1, 165 - 172, 01.06.2017

Öz

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..

Kaynakça

  • 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.
Yıl 2017, Cilt: 7 Sayı: 1, 165 - 172, 01.06.2017

Öz

Kaynakça

  • 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.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Serdal Pamuk Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 1

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