Free Access
Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015
Dynamics of Chemical Reaction Networks
Page(s) 16 - 46
Published online 27 August 2015
  1. V.P. Belavkin, V.N. Kolokoltsov. On general kinetic equation for many particle systems with interaction, fragmentation and coagulation. Proc. Royal Society London A, 459 (2003), issue 2031, 727–748. [CrossRef] [Google Scholar]
  2. G.E. Briggs, J.B.S. Haldane. A note on the kinetics of enzyme action. Biochem. J., 19 (1925), 338–339. [PubMed] [Google Scholar]
  3. L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, 66 (1872), 275–370. [Google Scholar]
  4. L. Boltzmann. Neuer Beweis zweier Sätze über das Wärmegleichgewicht unter mehratomigen Gasmolekülen. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, 95 (2) (1887), 153–164. [Google Scholar]
  5. C. Cercignani, M. Lampis. On the H-theorem for polyatomic gases. J. Stat. Phys., 26 (4) (1981) 795–801. [CrossRef] [Google Scholar]
  6. J.A. Christiansen. The elucidation of reaction mechanisms by the method of intermediates in quasi-stationary concentrations. Adv. Catal. , 5 (1953), 311–353. [Google Scholar]
  7. R. Clausius. Über vershiedene für die Anwendungen bequeme Formen der Hauptgleichungen der Wärmetheorie. Poggendorffs Annalen der Physic und Chemie, 125 (1865), 353–400. [CrossRef] [Google Scholar]
  8. I. Csiszár. Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. Magyar. Tud. Akad. Mat. Kutató Int. Közl., 8 (1963), 85–108. [Google Scholar]
  9. H. Eyring. The activated complex in chemical reactions. The Journal of Chemical Physics, 3(2) (1935), 107–115. [Google Scholar]
  10. H. Eyring. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. The Journal of chemical physics, 4(4) (1936), 283–291. [CrossRef] [Google Scholar]
  11. M. Feinberg. Complex balancing in general kinetic systems. Arch. Rat. Mechan. Anal., 49 (1972), 187–194. [Google Scholar]
  12. D.T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Computational Physics, 22 (4) (1976), 403–434. [Google Scholar]
  13. A.N. Gorban. Equilibrium encircling. Equations of Chemical Kinetics and Their Thermodynamic Analysis. Nauka: Novosibirsk, 1984. [Google Scholar]
  14. A.N. Gorban. Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes. Results in Physics 4 (2014), 142–147. [CrossRef] [Google Scholar]
  15. A.N. Gorban. Local equivalence of reversible and general Markov kinetics. Physica A, 392 (2013), 1111–1121; arXiv:1205.2052 [physics.chem-ph]. [CrossRef] [Google Scholar]
  16. A.N. Gorban, P.A. Gorban, G. Judge. Entropy: The Markov ordering approach. Entropy, 12 (5) (2010), 1145–1193; arXiv:1003.1377 []. [CrossRef] [MathSciNet] [Google Scholar]
  17. A.N. Gorban, V.I. Bykov, G.S. Yablonski. Essays on chemical relaxation, Nauka, Novosibirsk, 1986. [In Russian]. [Google Scholar]
  18. A.N. Gorban, I.V. Karlin. Invariant Manifolds for Physical and Chemical Kinetics (Lecture Notes in Physics). Springer: Berlin, Germary, 2005. [Google Scholar]
  19. A.N. Gorban, I. Karlin. Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations. Bulletin of the American Mathematical Society, 51(2) (2014), 186–246. [Google Scholar]
  20. A.N. Gorban, E.M. Mirkes, G.S. Yablonsky. Thermodynamics in the limit of irreversible reactions. Physica A, 392 (2013) 1318–1335. [CrossRef] [Google Scholar]
  21. A.N. Gorban, H.P. Sargsyan, H.A. Wahab. Quasichemical Models of Multicomponent Nonlinear Diffusion. Mathematical Modelling of Natural Phenomena, 6 (05) (2011), 184–262. [CrossRef] [Google Scholar]
  22. A.N. Gorban, M. Shahzad. The Michaelis–Menten–Stueckelberg Theorem. Entropy, 13 (2011) 966–1019; arXiv:1008.3296 [CrossRef] [MathSciNet] [Google Scholar]
  23. A.N. Gorban, G.S. Yablonskii. Extended detailed balance for systems with irreversible reactions. Chem. Eng. Sci., 66 (2011) 5388–5399; arXiv:1101.5280 [cond-mat.stat-mech]. [CrossRef] [Google Scholar]
  24. D. Grigoriev, P.D. Milman. Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2, Advances in Mathematics, 231 (6) (2012), 3389–3428. [CrossRef] [MathSciNet] [Google Scholar]
  25. F. Horn, R. Jackson. General mass action kinetics. Arch. Ration. Mech. Anal., 47 (1972), 81–116. [CrossRef] [Google Scholar]
  26. K.M. Hangos. Engineering model reduction and entropy-based Lyapunov functions in chemical reaction kinetics. Entropy, 12 (2010), 772–797. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Kac. Foundations of kinetic theory. In: Neyman, J., ed. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3., University of California Press, Berkeley, California, 171–197. [Google Scholar]
  28. V.N. Kolokoltsov. Nonlinear Markov processes and kinetic equations. Cambridge Tracks in Mathematics 182, Cambridge Univ. Press, 2010. [Google Scholar]
  29. V.N. Kolokoltsov. On Extensions of Mollified Boltzmann and Smoluchovski Equations to Particle Systems with a κ-nary Interaction. Russian Journal of Mathematical Physics, 10 (3) (2003), 268–295. [MathSciNet] [Google Scholar]
  30. V.N. Kolokoltsov. Hydrodynamic limit of coagulation-fragmentation type models of κ-nary interacting particles. J. Stat. Phys., 115 (5-6) (2004), 1621–1653. [CrossRef] [Google Scholar]
  31. V.N. Kolokoltsov. On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Advanced Studies in Contemporary Math, 12 (1) (2006), 9–38. [Google Scholar]
  32. V.N. Kolokoltsov. Kinetic equations for the pure jump models of κ-nary interacting particle systems. Markov Processes and Related Fields, 12 (2006), 95–138. [MathSciNet] [Google Scholar]
  33. V.N. Kolokoltsov. Nonlinear Markov Semigroups and Interacting Lévy Type Processes. J. Stat. Phys., 126 (3) (2007), 585–642. [CrossRef] [Google Scholar]
  34. M.D. Korzukhin. Oscillatory processes in biological and chemical systems, Nauka, Moscow, 1967. [in Russian] [Google Scholar]
  35. K. Kowalski. Universal formats for nonlinear dynamical systems. Chemical Physics Letters, 209 (1-2) (1993), 167–170 [CrossRef] [Google Scholar]
  36. G.N. Lewis. A new principle of equilibrium. Proceedings of the National Academy of Sciences, 11 (1925), 179–183. [CrossRef] [PubMed] [Google Scholar]
  37. J.C. Maxwell. On the dynamical theory of gases. Philosophical Transactions of the Royal Society of London, 157 (1867), 49–88. [Google Scholar]
  38. L. Michaelis, M. Menten, Die Kinetik der Intervintwirkung. Biochem. Z., 49 (1913), 333–369. [Google Scholar]
  39. T. Morimoto, Markov processes and the H-theorem. J. Phys. Soc. Jpn., 12 (1963), 328–331. [CrossRef] [Google Scholar]
  40. K.J. Laidler, A. Tweedale. The current status of Eyring’s rate theory. In Advances in Chemical Physics: Chemical Dynamics: Papers in Honor of Henry Eyring, J.O. Hirschfelder, D. Henderson, Eds. John Wiley & Sons, Inc., Hoboken, NJ, USA, 2007; Volume 21. [Google Scholar]
  41. H.-A. Lorentz. Über das Gleichgewicht der lebendigen Kraft unter Gasmolekülen. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, 95 (2) (1887), 115–152. [Google Scholar]
  42. I. Prigogine, R. Balescu. Irreversible processes in gases II. The equations of evolution. Physica, 25 (1959), 302–323 [CrossRef] [MathSciNet] [Google Scholar]
  43. A. Rényi. On measures of entropy and information. In Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability 1960. University of California Press, Berkeley, CA, USA, 1961; Volume 1; pp. 547–561. [Google Scholar]
  44. L.A. Segel, M. Slemrod. The quasi-steady-state assumption: A case study in perturbation. SIAM Rev., 31 (1989), 446–477. [CrossRef] [MathSciNet] [Google Scholar]
  45. E.C.G. Stueckelberg. Théorème H et unitarité de S. Helv. Phys. Acta, 25 (1952), 577–580. [MathSciNet] [Google Scholar]
  46. A.I. Volpert, S.I. Khudyaev. Analysis in classes of discontinuous functions and equations of mathematical physics. Nijoff, Dordrecht, The Netherlands, 1985. [Google Scholar]
  47. G. Yaari, A. Nowak, K. Rakocy, S. Solomon. Microscopic study reveals the singular origins of growth. Eur. Phys. J. B, 62 (2008), 505–513. DOI: 10.1140/epjb/e2008-00189-6 [CrossRef] [EDP Sciences] [Google Scholar]
  48. G.S. Yablonskii, V.I. Bykov, A.N. Gorban, V.I. Elokhin. Kinetic Models of Catalytic Reactions. Elsevier, Amsterdam, The Netherlands, 1991. [Google Scholar]

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