Abstract
The dynamics of spatial reaction systems that consists of many molecular species can be difficult to understand. Here we introduce a method that allows to observe the dynamics of a diverse spatial reaction system at different spatial scales. Using chemical organization theory we define for a given spatial location its so called spatial organization, which is the organization generated by the molecular species present in the neighborhood of this location. The scale determines the size of that neighborhood. We show that at one scale, patterns become visible that can not be seen at a different scale. Furthermore, different scales tend to map to different parts of the lattice of organizations; at small scales spatial organizations tend to be small (lower part of the lattice of organizations) while at large scales spatial organizations tend to be large (upper part of the lattice of organizations). Finally we show how the right scale can be selected by comparing the spatial reactor with its well-stirred counterpart. The method is illustrated using an artificial chemistry.
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Lehmann, R.: Determination of dominant pathways in chemical reaction systems: An algorithm and its application to stratospheric chemistry. J. Atmos. Chem. 41, 297–314 (2002)
Puchalka, J., Kierzek, A.: Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J. 86(3), 1357–1372 (2004)
Moreac, G., Blurock, E., Mauss, F.: Automatic generation of a detailed mechanism for the oxidation of n-decane. Combust. Sci. Technol. 178(10-11), 2025–2038 (2006)
Dittrich, P., Speroni di Fenizio, P.: Chemical organization theory. Bull. Math. Biol. 69(4), 1199–1231 (2007)
Banzhaf, W.: Self-replicating sequences of binary numbers. Comput. Math. Appl. 26, 1–8 (1993)
Speroni di Fenizio, P., Dittrich, P., Ziegler, J., Banzhaf, W.: Towards a theory of organizations. In: German Workshop on Artificial Life (GWAL 2000), Bayreuth, 5.-7. April, 2000 (in print)
Eigen, M., Schuster, P.: The hypercycle: a principle of natural self-organisation, part A. Naturwissenschaften 64(11), 541–565 (1977)
Schuster, P., Sigmund, K.: Replicator dynamics. J. Theor. Biol. 100, 533–538 (1983)
Fontana, W., Buss, L.W.: ‘The arrival of the fittest’: Toward a theory of biological organization. Bull. Math. Biol. 56, 1–64 (1994)
Fontana, W.: Algorithmic chemistry. In: Langton, C.G., Taylor, C., Farmer, J.D., Rasmussen, S. (eds.) Proc. Artificial Life II, Redwood City, CA, pp. 159–210. Addison-Wesley, Reading (1992)
Lindgren, K., Eriksson, A., Eriksson, K.E.: Flows of information in spatially extended chemical dynamics. In: Pollack, J., Bedau, M., Husbands, P., Ikegami, T., Watson, R.A. (eds.) Proc. Artififical Life IX, pp. 456–460. MIT Press, Boston (2004)
Centler, F., Dittrich, P.: Chemical organizations in atmospheric photochemistries: a new method to analyze chemical reaction networks. Planet. Space Sci. 55(4), 413–428 (2007)
Matsumaru, N., Centler, F., Speroni di Fenizio, P., Dittrich, P.: Chemical organization theory applied to virus dynamics. it - Information Technology 48(3), 154–160 (2006)
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Speroni di Fenizio, P., Dittrich, P. (2007). Chemical Organizations at Different Spatial Scales. In: Almeida e Costa, F., Rocha, L.M., Costa, E., Harvey, I., Coutinho, A. (eds) Advances in Artificial Life. ECAL 2007. Lecture Notes in Computer Science(), vol 4648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74913-4_1
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DOI: https://doi.org/10.1007/978-3-540-74913-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74912-7
Online ISBN: 978-3-540-74913-4
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