Symbolic algebra in the analysis of dynamic chemical-kinetic systems

Mathematical and Computer Modelling

Volumn 30, Issue 5-6, 1999, Pages 33-47

  Jemmer P ^a,b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Bacterial populations; Chemical process kinetics; Plasma modelling; Reaction advection diffusion; Symbolic algebra

Indexed keywords

EID: 0033199529     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(99)00146-6     Document Type: Article

References (55)

1. P. J̈emmer, Plasma Diagnostics in Chemical Vapour Deposition, A dissertation submitted to the University of Cambridge, in partial fulfilment of the requirements for the Certificate of Postgraduate Study, University of Cambridge, (1993).
2. J.M. Kay and R.M. Nedderman, Fluid Mechanics and Transfer Processes, Cambridge University Press, Cambridge, (1985).
3. M.J. Pilling and P.W. Seakins, Reaction Kinetics, Oxford Science Publications, Oxford University Press, New York, (1985).
4. P. J̈emmer, Symbolic algebra in the analysis of chemical-kinetic systems, Journal of Computational Chemistry 18 (15), 1903-1917, (1997).
5. D.A. Barry, K. Bajracharya and C.T. Miller, Alternative split-operator approach for solving chemical-reaction groundwater transport models, Advances in Water Resources 19 (5), 261-275, (1996).
6. T.M. Johnson and D.J. Depaolo, Reaction-transport models for radiocarbon in groundwater - The effects of longitudinal dispersion and the use of Sr isotope ratios to correct for water-rock interaction, Water Resources Research 32 (7), 2203-2212, (1996).
7. W. Nadler and D.L. Stein, Reaction-diffusion description of biological transport process in general dimension, J. Chem. Phys. 104 (5), 1918-1936, (1996).
8. S.E.A.T.M. Vanderzee, Reaction-kinetics and transport in soil-compatibility and differences between some simple models, Transport in Porous Media 6 (5/6), 703-737, (1991).
9. A. Bermudez, J. Durany, M. Posse and C. Vazquez, An upwind method for solving transport-diffusion-reaction systems, International Journal for Numerical Methods in Engineering 28 (9), 2021-2039, (1989).
10. L.K. Bieniasz and B. Speiser, Use of sensitivity analysis methods in the modelling of electrochemical transients, Part 1. Gaining more insight into the behaviour of kinetic models, Journal of Electroanalytical Chemistry 441 (1/2), 271-285, (1998).
11. L.K. Bieniasz, O. Osterby and D. Britz, Numerical stability of the Saulyev finite-difference algorithms for electrochemical kinetic simulations - Matrix stability analysis for an example problem involving mixed boundary-conditions, Computers and Chemistry 19 (4), 357-370, (1995).
12. L.K. Bieniasz, O. Osterby and D. Britz, Numerical stability of finite-difference algorithms for electrochemical kinetic simulations - Matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods, extended to the 3-point and 4-point gradient approximation at the electrodes, Computers and Chemistry 19 (4), 351-355, (1995).
13. L.K. Bieniasz, O. Osterby and D. Britz, Numerical stability of finite-difference algorithms for electrochemical kinetic simulations - Matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods and typical problems involving mixed boundary-conditions, Computers and Chemistry 19 (2), 121-136, (1995).
14. L.K. Bieniasz and D. Britz, Effieciency of electrochemical kinetic simulations by orthogonal collocation and finite-difference methods - A comparison, Acta Chemica Scandinavica 47 (8), 757-767, (1993).
15. L.K. Bieniasz and D. Britz, Electrochemical kinetic simulations of mixed diffusion homogeneous reaction problems by the Saulyev finite-difference algorithms, Analytica Chimica Acta 278 (1), 59-70, (1993).
16. L.K. Bieniasz, The von neumann stability of finite-difference algorithms for the electrochemical kinetic simulation of diffusion coupled with homogeneous reactions, Journal of Electroanalytical Chemistry 345 (1/2), 13-25, (1993).
17. 2 in water up to 200-degrees-C, Journal of the Chemical Society - Faraday Transactions 88 (17), 2465-2470, (1992).
18. A. Rojnuckarin, C.A. Floudas, H. Rabitz and R.A. Yetter, Optimal-control of a plug-flow reactor with a complex-reaction mechanism, Journal of Physical Chemistry 97 (45), 11689-11695, (1993).
19. D. Swiatlawojcik and G.V. Buxton, Modelling of radiation spur processes in water at temperatures up to 300-degrees-C, Journal of Physical Chemistry 99 (29), 11464-11471, (1995).
20. 2H (HFC-125) studied by FTIR spectroscopy: Product yields and kinetic modelling, Journal of the Chemical Society - Faraday Transactions 93 (6), 2693-2699, (1997).
21. P.m. Martineau and P.B. Davies, PECVD - A technique for new technologies, Chemistry in Britain 25, 1018-1020, (1989).
22. P.b. Davies and P.M. Martineau, Infrared diode-laser diagnostics of methane plasmas produced in a deposition reactor, Applied Physics Letters 57 (3), 237-239, (1990).
23. P.b. Davies and P.M. Martineau, Diagnostics and modeling of silane and methane plasma CVD processes, Advanced Materials 4 (11), 729-736, (1992).
24. P.b. Davies and P.M. Martineau, Infrared laser diagnostics in methane chemical-vapour-deposition plasmas, Journal of Applied Physics 71 (12), 6125-6135, (1992).
25. 2 chemical vapor deposition reactor studied by infrared diode laser spectroscopy, Journal of Vacuum Science and Technology A - Vacuum Surfaces and Films 14 (5), 2970-2972, (1996).
26. L.K. Bieniasz, A reaction complier for electrochemical kinetics, Computers and Chemistry 20 (4), 403-418, (1996).
27. L.K. Bieniasz, Automatic derivation of the governing equations that describe a transient electrochemical experiment, given a reaction-mechanism of arbitrary complexity. 2. Governing equations in one-dimensional geometry, Journal of Electroanalytical Chemistry 406 (1/2), 45-52, (1996).
28. L.K. Bieniasz, Automatic derivation of the governing equations that describe a transient electrochemical experiment, given a reaction-mechanism of arbitrary complexity. 1. Problem parameters and initial conditions, Journal of Electroanalytical Chemistry 406 (1/2), 33-43, (1996).
29. L.K. Bieniasz, A method-oriented approach to the formulation of algorithms for electrochemical kinetic simulations. 2. Extensions to kinetic problems characterized by the simultaneous presence of bulk and interfacial species, Journal of Electroanalytical Chemistry 404 (1/2), 195-208, (1996).
30. L.K. Bieniasz, A method-oriented approach to the formulation of algorithms for electrochemical kinetic simulations, Journal of Electroanalytical Chemistry 340 (1/2), 19-34, (1992).
31. L.K. Bieniasz, ELSIM - Problem-solving environment for electrochemical kinetic simulations, Version 3.0 - Solution of governing equations associated with interfacial species, independent of spatial coordinates or in one-dimensional geometry, Computers and Chemistry 21 (1), 1-12, (1997).
32. L.K. Bieniasz, ELSIM - A PC program for electrochemical kinetic simulations, Version 2.0 - Solution of the sets of kinetic partial-differential equations in one-dimensional geometry, using finite-difference and orthogonal collocation methods, Computers and Chemistry 17 (2), 355-368, (1993).
33. L.K. Bieniasz, ELSIM - A user-friendly PC program for electrochemical kinetic simulations, Version 1.0 - Solution of integral-equations for linear cyclic voltammetry, Computers and Chemistry 16 (1), 11-14, (1992).
34. G.d. Byrne and A.C. Hindmarsh, Stiff ODE solvers: A review of current and coming attractions, Journal of Computational Physics 70 (1), 1-62, (1987).
35. L.R. Petzold, Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations, SIAM Journal of Scientific and Statistical Computing 4, 136-148, (1983).
36. P. Sun, D.p. Chock and S.L. Winkler, Implicit-explicit hybrid solver, Journal of Computational Physics 115, 515, (1994).
37. D. Schwalbe, H. Kooljman and R. Taylor, Solving stiff differential equations and differential algebraic systems with Maple V, Mapletech 3 (2), 47-53, (1996).
38. C.J. Aro, CHEMSODE: A stiff ODE solver for the equations of chemical kinetics, Computer Physics Communications 97 (3), 304-314, (1996).
39. C.J. Aro, A stiff ODE preconditioner based on Newton linearization, Applied Numerical Mathematics 21 (4), 335-352, (1996).
40. P. J̈emmer, K. Kratz and N. Read, Symbolic algebra in the analysis of bacterial populations, Mathl. Comput. Modelling 30 (1/2), 169-178, (1999).
41. F.C. Stults, R.w. Moulton and J.L. McCarthy, Formaldehyde-sodium-paraphenol-sulphonatye condensation, Chemical Engineering Progress Symposium 4, 38-50, (1952).
42. S.M. Walas, Reaction kinetics for chemical engineers, in Butterworths Reprint Series in Chemical Engineering, Butterworths, London, UK, (1989).
43. P.W. Atkins, Physical Chemistry, Fifth Edition, Oxford University Press, New York, (1994).
44. J.R. Doyle, Chemical kinetics in low pressure acetylene radio frequency glow discharges, Journal of Applied Physics 82 (10), 4763-4471, (1997).
45. M. Shiratani, J. Jolly, H. Videlot and J. Perrin, Mass spectroscopic investigations of a hydrocarbon arcjet plasma operating under diamond deposition conditions, Applied Physics Letters 68 (26), 3710-3712, (1996).
46. 4 RF discharge studied by time-resolved threshold ionization mass spectrometry, Japanese Journal of Applied Physics Part 1 - Regular Papers, Short Notes and Review Papers 36 (7B), 4752-4755, (1997).
47. D.J. Dagel, C.m. Mallouris and J.R. Doyle, Radical and film growth kinetics in methane radio-frequency glow discharges, Journal of Applied Physics 79 (11), 8735-8747, (1996).
48. 2, Diamond and Related Materials 4 (7), 1000-1008, (1995).
49. 4/Ar systems, Plasma Chemistry and Plasma Processing 11 (4), 473-488, (1991).
50. 2 plasma, Journal of the American Chemical Society 108 (19), 5780-5783, (1986).
51. S.j. Harris and A.M. Weiner, Methyl radical and H-atom concentrations during diamond growth, Journal of Applied Physics 67 (10), 6520-6526, (1990).
52. M. Frenklach and K.E. Spear, Growth-mechanism of vapour-deposited diamond, Journal of Materials Research 3 (1), 133-140, (1988).
53. D. Huang, M. Frenklach and M. Maroncelli, Energetics of acetylene-addition mechanism of diamond growth, Journal of Physical Chemistry 92 (22), 6379-6381, (1988).
54. M. Frenklach, The role of hydrogen in vapour-deposition of diamond, Journal of Applied Physics 65 (12), 5142-5149, (1989).
55. P. J̈emmer, Mathematical Modelling and Interpretation of Reactive Plasma Chemistry, unpublished work.