Influence of the Moment in Mathematical Models for Open Systems

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Influence of the Moment in Mathematical Models for Open Systems. / Prozorova, Evelina.

In: WSEAS Transactions on Applied and Theoretical Mechanics, Vol. 16, 28, 2021, p. 250-260.

Research output: Contribution to journal › Article › peer-review

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Prozorova, Evelina. / Influence of the Moment in Mathematical Models for Open Systems. In: WSEAS Transactions on Applied and Theoretical Mechanics. 2021 ; Vol. 16. pp. 250-260.

BibTeX

@article{ef4a1382e9934cdc82db9c5e3cbf41f9,

title = "Influence of the Moment in Mathematical Models for Open Systems",

abstract = "Article is proposed, built taking into account the influence of the angular momentum (force) in mathematical models of open mechanics. The speeds of various processes at the time of writing the equations were relatively small compared to modern ones. Theories have generally been developed for closed systems. As a result, in continuum mechanics, the theory developed for potential flows was expanded on flows with significant gradients of physical parameters without taking into account the combined action of force and moment. The paper substantiates the vector definition of pressure and the no symmetry of the stress tensor based on consideration of potential flows and on the basis of kinetic theory. It is proved that for structureless particles the symmetry condition for the stress tensor is one of the possible conditions for closing the system of equations. The influence of the moment is also traced in the formation of fluctuations in a liquid and in a plasma in the study of Brownian motion, Landau damping, and in the formation of nanostructures. The nature of some effects in nanostructures is discussed. The action of the moment leads to three-dimensional effects even for initially flat structures. It is confirmed that the action of the moment of force is the main source of the collective effects observed in nature. Examples of solving problems of the theory of elasticity are given.",

keywords = "Angular momentum, Boltzmann equations, Conservation laws, Landau equations, Langevin, No symmetrical stress tensor, Open systems",

author = "Evelina Prozorova",

year = "2021",

doi = "10.37394/232011.2021.16.28",

language = "English",

volume = "16",

pages = "250--260",

journal = "WSEAS Transactions on Applied and Theoretical Mechanics",

issn = "1991-8747",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Influence of the Moment in Mathematical Models for Open Systems

AU - Prozorova, Evelina

PY - 2021

Y1 - 2021

N2 - Article is proposed, built taking into account the influence of the angular momentum (force) in mathematical models of open mechanics. The speeds of various processes at the time of writing the equations were relatively small compared to modern ones. Theories have generally been developed for closed systems. As a result, in continuum mechanics, the theory developed for potential flows was expanded on flows with significant gradients of physical parameters without taking into account the combined action of force and moment. The paper substantiates the vector definition of pressure and the no symmetry of the stress tensor based on consideration of potential flows and on the basis of kinetic theory. It is proved that for structureless particles the symmetry condition for the stress tensor is one of the possible conditions for closing the system of equations. The influence of the moment is also traced in the formation of fluctuations in a liquid and in a plasma in the study of Brownian motion, Landau damping, and in the formation of nanostructures. The nature of some effects in nanostructures is discussed. The action of the moment leads to three-dimensional effects even for initially flat structures. It is confirmed that the action of the moment of force is the main source of the collective effects observed in nature. Examples of solving problems of the theory of elasticity are given.

AB - Article is proposed, built taking into account the influence of the angular momentum (force) in mathematical models of open mechanics. The speeds of various processes at the time of writing the equations were relatively small compared to modern ones. Theories have generally been developed for closed systems. As a result, in continuum mechanics, the theory developed for potential flows was expanded on flows with significant gradients of physical parameters without taking into account the combined action of force and moment. The paper substantiates the vector definition of pressure and the no symmetry of the stress tensor based on consideration of potential flows and on the basis of kinetic theory. It is proved that for structureless particles the symmetry condition for the stress tensor is one of the possible conditions for closing the system of equations. The influence of the moment is also traced in the formation of fluctuations in a liquid and in a plasma in the study of Brownian motion, Landau damping, and in the formation of nanostructures. The nature of some effects in nanostructures is discussed. The action of the moment leads to three-dimensional effects even for initially flat structures. It is confirmed that the action of the moment of force is the main source of the collective effects observed in nature. Examples of solving problems of the theory of elasticity are given.

KW - Angular momentum

KW - Boltzmann equations

KW - Conservation laws

KW - Landau equations

KW - Langevin

KW - No symmetrical stress tensor

KW - Open systems

UR - http://www.scopus.com/inward/record.url?scp=85122129374&partnerID=8YFLogxK

U2 - 10.37394/232011.2021.16.28

DO - 10.37394/232011.2021.16.28

M3 - Article

AN - SCOPUS:85122129374

VL - 16

SP - 250

EP - 260

JO - WSEAS Transactions on Applied and Theoretical Mechanics

JF - WSEAS Transactions on Applied and Theoretical Mechanics

SN - 1991-8747

M1 - 28

ER -

ID: 96618104