## Abstract

In different areas of mechanics, highly non-equilibrium processes are accompanied by

self-organization of various type turbulent structures and localized inhomogeneities at intermediate

scale between macro and micro levels. In order to describe the self-organization of the new dynamic

structures on the mesoscale, a new problem formulation based on the results of non-equilibrium

statistical mechanics, control theory of adaptive systems, and theory of a special type nonlinear

operator sets is proposed. Determination of the turbulent structure parameters through constraints

imposed on the system in the form of nonlinear functionals is an inverse problem similar to problems

on spectra in quantum mechanics. Like in quantum mechanics, the bounded system in response

to impact forms a discrete spectrum of the turbulent structure sizes and lifetimes which goes into

continuous spectrum close-to-equilibrium. The proposed description of the structure evolution on the

intermediate scale level which is valid far from thermodynamic equilibrium bridges the gap between

macroscopic theories and quantum mechanics and affirms the unity of the physical laws of nature.

self-organization of various type turbulent structures and localized inhomogeneities at intermediate

scale between macro and micro levels. In order to describe the self-organization of the new dynamic

structures on the mesoscale, a new problem formulation based on the results of non-equilibrium

statistical mechanics, control theory of adaptive systems, and theory of a special type nonlinear

operator sets is proposed. Determination of the turbulent structure parameters through constraints

imposed on the system in the form of nonlinear functionals is an inverse problem similar to problems

on spectra in quantum mechanics. Like in quantum mechanics, the bounded system in response

to impact forms a discrete spectrum of the turbulent structure sizes and lifetimes which goes into

continuous spectrum close-to-equilibrium. The proposed description of the structure evolution on the

intermediate scale level which is valid far from thermodynamic equilibrium bridges the gap between

macroscopic theories and quantum mechanics and affirms the unity of the physical laws of nature.

Original language | English |
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Pages (from-to) | 562-575 |

Number of pages | 14 |

Journal | Particles |

Volume | 3 |

Issue number | 3 |

State | Published - 27 Jul 2020 |

## Scopus subject areas

- Physics and Astronomy(all)

## Keywords

- mesoscale, turbulent structure, wave packet, size spectrum, inverse problem, nonlinear functional