Abstract
This book is about chemical reaction networks and the differential equations they induce. As such, it is primarily a work of mathematics. This opening chapter, however, contains no equations, nor does it contain any mathematical symbols. Instead, it contains several observations that, when taken together, tell us something about reaction network behavior viewed broadly.
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Notes
- 1.
We have in mind here a well-stirred mixture, maintained at constant temperature and volume, with instantaneous species concentrations independent of spatial position.
- 2.
I am referring here to the Mathematics Subject Classification 2000. Strangely, there is a chemistry subcategory under biology and other natural sciences, but it has the same rank there as the subcategory genetics and population dynamics. Mathematical Reviews does indeed abstract articles about the differential equations of chemistry, but—again strangely—these are often classified under the major applied mathematics category classical thermodynamics, heat transfer.
- 3.
Economics became a serious mathematical subject much earlier. As an example, Paul Samuelson’s Foundations of Economic Analysis was published in 1948. In its mathematical sophistication, the Samuelson book surpasses much of what is written about chemical reactors even today.
- 4.
It is interesting, however, to recall a 1955 chemical engineering paper by Bilous and Amundson [22], which was seminal in its consideration of stability questions. It too focused primarily on simple nonisothermal reactors and set in motion a burgeoning research effort about them, lasting decades and spanning many universities. Little noticed, though, was a section of the paper in which the authors examined a four-species, three-reaction isothermal system. They found it to be stable for all parameter values. Nevertheless, Bilous and Amundson understood that the stability question was one worth asking.
- 5.
The same is true of catalysis on metal surfaces, but it is in biochemistry that richer, more exotic behavior seems evolutionarily purposeful.
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Feinberg, M. (2019). Anticipating the Big Picture: Some Clues. In: Foundations of Chemical Reaction Network Theory. Applied Mathematical Sciences, vol 202. Springer, Cham. https://doi.org/10.1007/978-3-030-03858-8_1
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