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# Chemical and Biochemical Systems

Chapter

## Abstract

Basically, we may distinguish between two different kinds of chemical processes:

- 1)
Several chemical reactants are put together at a certain instant, and we are then studying the processes going on. In customary thermodynamics, one usually compares only the reactants and the final products and observes in which direction a process goes. This is not the topic we want to treat in this book. We rather consider the following situation, which may serve as a model for biochemical reactants.

- 2)Several reactants are continuously fed into a reactor where new chemicals are continuously produced. The products are then removed in such a way that we have steady state conditions. These processes can be maintained only under conditions far from thermal equilibrium. A number of interesting questions arise which will have a bearing on theories of formation of structures in biological systems and on theories of evolution. The questions we want to focus our attention on are especially the following:
- 1)
Under which conditions can we get certain products in large well-controlled concentrations?

- 2)
Can chemical reactions produce spatial or temporal or spatio-temporal patterns?

- 1)

## Keywords

Transition Rate Master Equation Malonic Acid Detailed Balance Soft Mode
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## References

- In this chapter we particularly consider the occurrence of spatial or temporal structures in chemical reactions. Concentration oscillation were reported as early as 1921 by C. H. Bray: J. Am. Chem. Soc.
**43**, 1262 (1921)CrossRefGoogle Scholar - A different reaction showing oscillations was studied by B. P. Belousov: Sb. ref. radats. med. Moscow (1959)Google Scholar
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**B 237**, 37 (1952)ADSGoogle Scholar - Models of chemical reactions showing spatial and temporal structures were treated in numerous publications by Prigogine and his coworkers. See P. Glansdorff and I. Prigogine 1.c. on page 307 with many references, and G. Nicolis, I. Prigogine:
*Self-organization in Non-equilibrium Systems*(Wiley, New York 1977)Google Scholar - A review of the statistical aspects of chemical reactions can be found in D. Mc Quarry:
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## Deterministic Processes, Without Diffusion, One Variable 9.3 Reaction and Diffusion Equations

- We essentially follow F. Schlögl: Z. Phys.
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## Reaction-Diffusion Model with Two or Three Variables: the Brusselator and the Oregonator

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**37**, 589 (1975)CrossRefGoogle Scholar - The Belousov-Zhabotinsky reaction is described in the already cited articles by Belousov and Zhabotinsky. The “Oregonator” model reaction was formulated and treated by R. J. Field, E. Korös, R. M. Noyes: J. Am. Chem. Soc.
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## Stochastic Model for a Chemical Reaction Without Diffusion. Birth and Death Processes. One Variable

- A first treatment of this model is due to V. J. McNeil, D. F. Walls: J. Stat. Phys.
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## Stochastic Model for a Chemical Reaction with Diffusion. One Variable

- The master equation with diffusion is derived by H. Haken: Z. Phys.
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**52**, 1481 (1974)ADSCrossRefGoogle Scholar - M. Malek-Mansour, G. Nicolis: preprint Febr. 1975Google Scholar

## Stochastic Treatment of the Brusselator Close to Its Soft Mode Instability

- We essentially follow H. Haken: Z. Phys.
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## Chemical Networks

- Related to this chapter are G. F. Oster, A. S. Perelson: Chem. Reaction Dynamics. Arch. Rat. Mech. Anal.
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## Copyright information

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