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The geometry of closed sets in the state of chemical transformation

A pedagogic review from first principles to first applications in an undergraduate thermal analysis laboratory for secondary schools

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Abstract

The history of technology provides many cases where simplified forms of man-made motion replace tangled forms of native motion. One of the reasons for these substitutions is the lack of approaches to the categorical recognition of information about the topology and the geometry of body in the state of transformation. As a consequence, there arises a barrier between chemistry and materials science. The aim of this paper is to direct a way to the solution of the problem, using a simple example of chemical bursting with the dimension of becoming D B = log 2/log 2 = 1 for the one-dimensional process and D B = log 7/log 2 ≈ 2.8074 for the three-dimensional process at all their scales.

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Acknowledgements

We are deeply grateful for the support of new combustion science at design stage from Russian State Committee of Science and Technology (Project “Konus”), Soros International Science Foundations (Grant N9K000), Russian Government (Grant N9K300), Russian Federal Program “Integration” (Projects: 2.1.-855, A0-113, and B0-115), and Russian Found of Basic Research (Grant 98-03-32593a). Authors are thankful to L.S. Bresler (Saint-Petersburg) for his help in the article preparation and Prof. J. Šesták (University of West Bohemia in Pilsen) for intriguing discussions about some problems of self-organization and thermal analysis of fractals. We would like also to express our keen appreciation to G. Wiese and K.A. Burkov for their mutual understanding which enabled to investigate in Leningrad State University the signs of discrete solvation in aqueous solutions by the use of precision dilatometer received as a gift from Freie Universität in West Berlin. Chemical materials science capable of distinguishing among consuming, combustion, and deflagration grew up on this ground owing to an introduction into random geometry from A.L. Efros [Physics and geometry of disorder. Moscow: Nauka; 1982 (in Russian)––Moscow: Mir; 1986 (in English)––Moscow: Mir; 1987 (in Spanish)––Tallinn: Valgus; 1987 (in Estonian)]. We remember it with thankfulness. This paper is dedicated to the memory of academician Yu. D. Tret’yakov, A.K. Gamazov, the teacher of the 42nd middle school in Tbilisi (GE-SU), and our parents, Victor & Emilia.

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The present article is based on the lecture presented at RTAC2013 conference in St. Petersburg on 23–28 September, 2013.

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Klyucharev, V.V., Klyuchareva, S.V. The geometry of closed sets in the state of chemical transformation. J Therm Anal Calorim 119, 1633–1651 (2015). https://doi.org/10.1007/s10973-014-4351-9

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