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Diffusion Path in Ternary One-Phase Systems: An Overview

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Języki publikacji
EN
Abstrakty
EN
In this article, the fundamental questions concerning the diffusion path, in particular, what is the shape of diffusion path in ternary systems and how to approximate it from the initial concentration profile, will be answered. The new rules were found which allow for determining the diffusion path from a known initial concentration of the components. This approximation will allow for designing new materials without a time-consuming numerical simulation of the full system of equations. It is shown that the difference in intrinsic diffusion coefficients determines the up-hill diffusion.
Rocznik
Strony
1--8
Opis fizyczny
Bibliogr. 29 poz., rys., tab., wykr.
Twórcy
autor
  • Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
autor
  • Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
autor
  • Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
  • Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
  • Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
Bibliografia
  • [1] R.A. ADAMS: Sobolev spaces. Academic Press, New York 1975.
  • [2] V. Arnold: Mathematical methods of classic mechanics. Springer, New York 1986.
  • [3] V. ARNOLD and B.A. KHESIN: Topological methods in hydrodynamics. Springer, New York 1998.
  • [4] V. BARBU: Nonlinear semi groups and differential equations in Banach spaces. Springer Netherlands, Noordhoff, 1976.
  • [5] M.S. BERGER: Nonlinearity and functional analysis. Academic Press, New York 1977.
  • [6] A. BENSOUSSAN, J.L. LIONS, G. PAPANIKOLAOU: Asymptotoc analysis for periodic structures. Elsevier, North Holland 1978.
  • [7] H. BREZIS: Functional analysis, Sobolev spaces and partial differential equations. Springer, New York 2011.
  • [8] F.E. BROWDER: Nonlinear operators and nonlinear equation in Banach spaces. American Mathematical Society 1976.
  • [9] C. CERCIGNANI: The Boltzmann equations and its applications. Springer, New York 1988.
  • [10] L. HORMANDER: The analysis of linear partial differential operators, vol. 1-4. Springer, Berlin 1983.
  • [11] L. HORMANDER: Fourier integral operators. I. Acta Math., 127(1971), 79-189.
  • [12] P.D. LAX: Functional analysis. Wiley - Interscience, New York 2002.
  • [13] P.L. LIONS: Mathematical topics in fluid mechanics, Vol 1. Incompressible models, Clarendon Press, Oxford 2006.
  • [14] P.L. LIONS: Mathematical topics in fluid mechanics, Vol 2. Compressible models, Clarendon Press, Oxford 2006.
  • [15] P.L. LIONS: Generalization solutions of Hamilton Jacobi equations, Longman Harlow, Essex 1982.
  • [16] C. VILLANI: Topic in optimal transportation. American Mathematical Society 2003.
  • [17] T. TAO: An epsilon of room I: real analysis. American Mathematical Society 2010.
  • [18] C. FOIAS, et al.: Navier-Stokes equation and turbulence. Cambridge University Press, Cambridge 2001.
  • [19] V. GIRAULT, P.A. RAVIART: Finite element method for NavierStokes equations. Springer, Berlin 1986.
  • [20] R. TEMAM: Navier-Stokes equations. Theory and numerical analysis. Elsevier, North-Holland 1985.
  • [21] G. TOSCANI, C. VILLANI: Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell Gas. J. Stat. Phys., 94(1999), 619-637.
  • [22] D. ZWILLINGER: Handbook of differential equations. Academic Press, New York 1984.
  • [23] L.S. DARKEN: Trans. AIME, 174(1948), 184.
  • [24] M. DANIELEWSKI, B. WIERZBA, K. TKACZ-SMIECH: Diffus. Found., 1(2014), 31.
  • [25] B. WIERZBA: Physica A, 454(2016), 110-116.
  • [26] A.A. KODENTSOV, et al.: J Alloys Compd., 320(2001), 207.
  • [27] J.S. KIRKALDY, L.S. BROWN: Can. Metal. Q., 2(1963), 89.
  • [28] L.C. EVANS: Convergence methods for nonlinear partial differential equations. American Mathematical Society, 1990.
  • [29] K. HOLLY, M. DANIELEWSKI: Phys. Rev. B: Condens. Matter Mater. Phys., 50(1994), 13336.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0a75f919-f508-4502-97b3-daa68520d443
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