A Toy Model of Chemical Reaction Networks - TBI - UniversitÃ¤t Wien

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6 CHAPTER 1. INTRODUCTION and symmetries are ignored. It nevertheless leads to excellent qualitative predictions of thermodynamic properties [61]. The graph representation of the molecule is now combined with a simple energy calculation. This suffices to fulfill the requirements of the laws of mass and energy conservation. It is then straightforward to represent reactions by graph rewritings (see ch. 2 and 4). The graph rewriting rules correponds to the reaction mechanism as understood by chemists. The Cannizarro reaction [16], for example, takes place between two aldehydes and produces an acid and an alcohol by disproportionation. The graph rewriting rule is analogous and adds a solvent proton node and a hydride node to one aldehyde graph to form an alcohol graph. The second aldehyde graph looses the former hydride node and gains a hydroxyl group (formed by two nodes), thus yielding the acid. The advantage of this reaction representation is that it represents the reaction itself also by graphs, and thus does not have the inherent limitations of e.g. string representations. It is also, of course, more flexible and simpler than a hard-coded implementation of reactions as complicated reactions might be very time-consuming to encode one per one.
Chapter 2 Artificial Chemistries In this section we very briefly survey artificial chemistry models. Tab. 2.1 compares different CRN models based on their implementation of the three components molecules, reactions and networks [26]. The models can also be categorized according to abstraction level and intended application. Very abstract models simulate artificial chemistries in which string or logical elements interact, like in the λ-calculus. There networks are built in a bottom-up approach to be studied phenomenologically. On the other hand, models for practical applications tend to be top-down. They concentrate on describing interactions and try to predict, for example, the time or space evolution of concentrations. Some approaches are further described in the following. 2.1 The λ-calculus The λ-calculus is a proof theory of constructive logic. This area of logic studies proofs using the interaction of logical elements called λ terms. Every λ term may be applied to another λ term to generate further λ terms, i.e. the deductions. Thus λ terms can be interpreted as objects as well as functions. The λ-calculus studies those functions and their applicative behavior, and indeed was founded to develop a general theory of functions, providing a foundation for logic and parts of mathematics [20]. In the related field of computer science, Turing [112] showed that the λ-calculus is strong enough to describe all mechanically computable functions. Ref. [109] reviews models based on the λ-calculus. In analogy to λ terms, molecules in chemistry can be viewed both as undergoing and fueling a reaction, i.e. reactants and reagents. This analogy was exploited in the base model of [40]. We will describe now features of this model. It consists of a well-stirred flow reactor of interacting functions 7
Page 1 and 2: A Toy Model of Chemical Reaction Ne
Page 3: i Dank an alle, die zum Gelingen di
Page 7: v Zusammenfassung Chemische Reaktio
Page 10 and 11: viii CONTENTS B GRW 61 C Organic re
Page 12 and 13: 2 CHAPTER 1. INTRODUCTION ▽ △
Page 14 and 15: 4 CHAPTER 1. INTRODUCTION ¡ ¡ ¡
Page 18 and 19: 8 CHAPTER 2. ARTIFICIAL CHEMISTRIES
Page 20 and 21: 10 CHAPTER 2. ARTIFICIAL CHEMISTRIE
Page 22: 12 CHAPTER 2. ARTIFICIAL CHEMISTRIE
Page 25 and 26: 3.1. EXTENDED HÜCKEL THEORY 15 is
Page 27 and 28: 3.2. FURTHER APPROXIMATIONS 17 K. F
Page 29 and 30: 3.2. FURTHER APPROXIMATIONS 19 Figu
Page 31 and 32: 3.2. FURTHER APPROXIMATIONS 21 are
Page 33 and 34: 3.3. CHEMICAL STRUCTURE REPRESENTAT
Page 35 and 36: 3.3. CHEMICAL STRUCTURE REPRESENTAT
Page 37 and 38: 3.4. WAVE FUNCTION ANALYSIS 27 Derw
Page 39 and 40: Table 3.6: Overlap matrix for prope
Page 41 and 42: 3.5. PERFORMANCE 31 3.5 Performance
Page 43 and 44: 3.6. FRONTIER MOLECULAR ORBITAL THE
Page 45 and 46: Chapter 4 Chemical reactions A mole
Page 47 and 48: 4.1. GRAPH REWRITING 37 Graphical t
Page 49 and 50: 4.1. GRAPH REWRITING 39 C C C C C C
Page 51 and 52: 4.2. GRAPH REWRITE ENGINE 41 O O O
Page 53 and 54: Chapter 5 Reaction networks 5.1 Net
Page 55 and 56: 5.3. NETWORK PROPERTIES 45 O 3 NO 3
Page 57 and 58: 5.3. NETWORK PROPERTIES 47 (see ch.
Page 59 and 60: Chapter 6 Computational results Whe
Page 61 and 62: O O O O O O O O O O O O O O O O O O
Page 63 and 64: 6.3. GRAPH-THEORETIC PROPERTIES 53
Page 65 and 66: Chapter 7 Conclusion and Outlook Th
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Using the rules of mass action kine
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Appendix A Parameters The energy ca
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Appendix B GRW GRW is implemented i
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Appendix C Organic reactions Fromht
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Bibliography [1] R. Albert and A.-L
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BIBLIOGRAPHY 67 [25] O. Diels and K
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BIBLIOGRAPHY 69 [50] J. Gasteiger a
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BIBLIOGRAPHY 71 [76] W. Langenbeck.
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BIBLIOGRAPHY 73 [102] S. Schuster,
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BIBLIOGRAPHY 75 [126] R. Woodward a
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The Wooing of Archibald Modern tren
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