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A macroscopic theory for predicting catastrophic phenomena in both biological and mechanical chemical reactions

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Abstract

A possibility for predicting the time-dependent pattern of sickness of human beings, i.e., biological catastrophe, has been shown by proposal of a nonlinear ordinary differential equation, describing temporal features of six macroscopic molecular groups chemically interacting in living beings, (Naitoh in Jpn J Ind Appl Math 28:15–26, 2011; Naitoh and Inoue in J Artif Life Robot 18:127–132, 2013). Logically, we also find that, six is minimum and essential as the number of macroscopic molecular groups for describing living systems. Then, along with the number theory applied for the differential equation, we derive critical mathematical conditions for predicting the premonition just before sickness (discrepancy from a healthy condition), which agree with an important knowledge revealed by the linear analysis proposed by Chen (Dynamical network biomarkers for identifying early-warning signals of complex diseases, Beppu, Oita Japan, 2015). In the present report, we first show that computational several time-histories of sickness obtained by solving the nonlinear differential equation with various parameters describing polymorphism agree well with actual time-dependent patterns of sickness for human beings, which is further evidence of usefulness of the nonlinear differential equation and its critical mathematical conditions. Thus, to examine the boundary between biological and abiological chemical reaction systems, which is related to the origin of living systems, we next check whether or not the nonlinear equation can also predict such abiological catastrophic phenomenon as misfire in artifacts including mechanical combustion engines.

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Acknowledgements

This article is part of the outcome of research performed under a Waseda university Grant for special research project (2015, 2016).

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Authors and Affiliations

  1. Faculty of Science and Engineering, Waseda University, Shinjuku, Japan

    Remi Konagaya, Tsubasa Takizawa & Ken Naitoh

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  1. Remi Konagaya
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  2. Tsubasa Takizawa
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  3. Ken Naitoh
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Correspondence to Remi Konagaya.

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Appendices

Appendix A: Influence of random noise on lifespan

In this report, a small amount of numerical errors was used instead of stochastic disturbance entering from the outside of the human being, which results in good agreements between computations and actual data of medical history of illness.

To go further, stochastic differential equations including random noise, which are shown in our previous reports [15, 22, 23], can also be used after discretizing in time by numerical methods having higher-order of accuracy. Then, terms of random noise in the equations can be calculated using random number generators in computers. Magnitude of the random noises should be evaluated basically by actual noise data, which should be measured from actual patients and obtained many times per year, over a certain period of time. Other theoretical evaluation may also be included, which comes from statistical vagueness (statistical indeterminacy) related to relatively smaller number of molecules in molecular group than that for continuum mechanics (deterministic model) [20, 24, 25].

Appendix B: New engine tested on combustion instability

Figure 10 demonstrates two prototype engines developed originally by us. Results in Fig. 8a–c are obtained for the engine shown in the lower part of Fig. 10.

Fig. 10
figure 10

New type of combustion engines leading to high thermal efficiency due to relatively silent high-compression and nearly complete air-insulation. (Upper: for aircrafts and rockets, Lower: for automobiles and power generation on the ground)

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Appendix C: The origin of information

Abiological molecules such as those in hydrocarbons including fossil fuels are relatively short; whereas, genes in DNA and RNA are long with various arrays of nitrogenous bases of A, T, G, and C. This variety leads to information. Then, the origin of variety will come from two different sizes of purines (A and G) and pyrimidines (A and T), because abiological fuels such as hydrogen and methanol are only one type of molecule size. Our previous model based on statistic fluid dynamics and mathematical principle of quasi-stability shows a possibility for explaining the inevitability of two sizes of purines and pyrimidines [14, 20].

In living systems, information must generate function related to complex three-dimensional structure. Our previous reports show some possibilities of explanation on relation between information, structure, and function [14, 20, 26].

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Konagaya, R., Takizawa, T. & Naitoh, K. A macroscopic theory for predicting catastrophic phenomena in both biological and mechanical chemical reactions. Artif Life Robotics 25, 178–188 (2020). https://doi.org/10.1007/s10015-020-00595-6

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