The weakest stability theory for stochastic momentum equation: revealing the sizes in biological and abiological particles

The world is filled with various scales of particles from subatomic to astronomical stars (nebulosity), while each type of particle will be flexible and deform time-dependently. Some previous researches based on stochastic momentum equation including immersed mass effect and quasi-stability principle, which is the weakest stability principle, lead to clarification of the various size ratios of biological particles and those appearing in breaking up of abiological particles having lifetime, while especially revealing the bi-modal frequency distribution around about 2:3 close to golden–silver ratio and 1:1 of Yamato ratio for particle pair sizes (Naitoh in Artif Life Robot 18:133–143, 2013; Kobayashi and Naitoh in J Adv Simul Sci Eng 6(1):80–93, 2019). It should also be stressed that traditional theories stated by Bohr with energy conservation law cannot predict the bi-modal distribution of about 2:3 and 1:1. In this report, the size ratios seen in the stabler particles having longer lifetime than that of unstable particles like super-heavy elements having very short lifetime, i.e., description of size ratios seen in stabler atoms like Ne, Ar, Kr, Xe, and Rn in periodic table, are revealed by considering the frequency distribution of the quasi-stable ratios based on a new “mostly neutral” stability principle between the weakest stability (quasi-stability) proposed by the authors and the neutral stability known well in fluid dynamics.