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Existence of metastable solutions for a thermodynamically consistent Becker–Döring model

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we prove the existence of metastable solutions to a general thermodynamically consistent mass-conserving Becker–Döring model which incorporates an inert substance. We make use of the methods for the standard model discussed by Penrose in 1989. We include an efficient numerical algorithm for approximating the thermodynamically consistent models.
Wydawca
Rocznik
Strony
91--124
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
autor
  • Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
Bibliografia
  • [1] J. M. Ball, J. Carr and O. Penrose, The Becker-Döring cluster equations: Basic properties and asymptotic behavior of solutions, Commun. Math. Phys. 104 (1986), 657-692.
  • [2] R. Becker and W. Döring, Kinetische Behandlung der Keimbildung in übersättigten Dämpfen, Ann. Phys. (5) 24 (1935), 719-752.
  • [3] J. J. Burton, Nucleation theory, in: Statistical Mechanics, Part A: Equilibrium Techniques, Plenum Press, New York (1977), 195-234.
  • [4] J. Carr, D. B. Duncan and C. H Walshaw, Numerical approximation of a metastable system, IMA J. Numer. Anal. 15 (1995), 505-521.
  • [5] K. Dekker and J. G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, Elsevier, Amsterdam, 1984.
  • [6] W. Dreyer and F. Duderstadt, On the Becker-Döring theory of nucleation of liquid droplets in solids, J. Stat. Phys. 123 (2006), 55-87.
  • [7] D. B. Duncan and R. M. Dunwell, Metastability in the classical truncated Becker-Döring equations, Proc. Edinb. Math. Soc. (2) 45 (2002), 701-716.
  • [8] D. B. Duncan and A. R. Soheili, Approximating the Becker-Döring equations, App. Num. Math. 37 (2001), 1-29.
  • [9] E. Hairer and G. Wanner, Solving Differential Equations II. Stiff and Differential-Algebraic Problems, Springer, Berlin, 1991.
  • [10] M. Herrmann, M. Naldzhieva and B. Niethammer, On a thermodynamically consistent modification of the Becker-Döring equations, Physica D 222 (2006), 116-130.
  • [11] M. Kreer, Classical Becker-Döring cluster equations: Rigorous results on metastability and long-time behaviour, Ann. Physik 505 (1993), 398-417.
  • [12] P. Laurençot and S. Mischler, From the Becker-Döring to the Lifschitz-Slyozov-Wagner equations, J. Stat. Phys. 106 (2002), 957-991.
  • [13] O. Penrose, Metastable states for the Becker-Döring cluster equations, Commun. Math. Phys. 124 (1989), 515-541.
  • [14] O. Penrose and J. L. Lebowitz, Towards a rigorous molecular theory of metastability, in: Fluctuation Phenomena, 2nd ed., North-Holland, Amsterdam (1987), 323-375.
  • [15] L. F. Shampine, Numerical Solution of Ordinary Differential Equations, Chapman and Hall, New York, 1994.
  • [16] L. F Shampine, I. Gladwell and S. Thompson, Solving ODEs with Matlab, Cambridge University Press, 2003.
  • [17] L. F Shampine and M. W. Reichelt, The Matlab ODE suite, SIAM J. Sci. Comput. 18 (1997), 1-22.
  • [18] V. Ssemaganda, The dynamics of the Becker-Döring model of nucleation, Ph.D. thesis, Otto-von-Guericke Universität Magdeburg, Department of Mathematics, 2011.
  • [19] V. Ssemaganda, K. Holstein and G. Warnecke, Uniqueness of steady-state solutions for thermodynamically consistent Becker-Döring models, J. Math. Phys. 52 (2011), 1-28.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-21a0ec02-53d4-4156-a700-9a4bb60bd925
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