9247a10b-41bf-4d12-9d46-b6171e5ac9a020211216083036655wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS2224-34291991-874710.37394/232011http://wseas.org/wseas/cms.action?id=40063420213420211610.37394/232011.2021.16https://wseas.org/wseas/cms.action?id=23298Influence of the Moment in Mathematical Models for Open SystemsEvelinaProzorovaMathematical-Mechanical Department St. Petersburg State University Av. 28 , Peterhof, 198504 RUSSIAArticle 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.121620211216202125026028https://wseas.com/journals/mechanics/2021/a565111-019(2021).pdf10.37394/232011.2021.16.28https://wseas.com/journals/mechanics/2021/a565111-019(2021).pdfV.I. Smirnov. Higher mathematics course. T.2. M .: Nauka, 1974 .. 655. L.G. Loytsyansky. Mechanics of liquid and gas. M .: Nauka. 1970. 904. Y.L. Klimontovich. Statistical theory of open systems. T. 1.2. Moscow: Lenand, 2019 E. A. Bulanov. Moment stresses in the mechanics of solid, bulk and liquid bodies. M .; University book. 2012.140. A.M. Katz. The theory of elasticity. St. Petersburg. 2002. N.G .Kolbasnikov. Theory of metal pressure treatment. Resistance to deformation and ductility. St. Petersburg: St. Petersburg State University Publishing House, 2000. 314. E.V. Prozorova. Mathematical modeling of the processes of mechanics with large gradients. St.Petersburg. St. Petersburg University. 2005. 339. E.V. Prozorova. The influence of dispersion in models of continuum mechanics. St.Petersburg. St. Petersburg University. 2013, 94. 10.1088/1742-6596/1334/1/012009Evelina Prozorova. Ostrogradsky-Gauss Theorem for Problems of Gas and Fluid. International Conference on Mathematical Models & Computational Techniques in Science & Engineering. 23–25 February 2019, London, UK. Mechanics. Journal of Physics: Conference Series Volume 1334. 2019. 012009 10.17654/hm017010001Evelina V. Prozorova. Influence of discrete model on derivatives in kinetic theory. JP Journal of Heat and Mass Transfer Volume 17, Number 1, 2019, Pages 1-19 ISSN: 0973-5763 10.1088/1742-6596/1250/1/012023E. V. Prozorova. Features of the rarefied gas description in terms of a distribution function. APhM2018. IOP Conf. Series: Journal of Physics: Conf. Series 1250 (2019) 012023. IOP Publishing. doi:10.1088/1742- 6596/1250/1/012023 10.37394/232011.2020.15.9Evelina Prozorova. The influence of the no symmetric stress tensor on the flow separation Wseas Transaction on Applied and Theoretical Mechanics. DOI: 10.37394/232011.2020.15.9 10.37394/232013.2020.15.2Evelina Prozorova. The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanic. Wseas transactions on flued mechanics DOI: 11.37394/232013.2020.15.2 10.37394/232011.2021.16.1Evelina Prozorova. Influence of the Angular Momentum in Problems Continuum Mechanics .Wseas transactions on applied and theoretical mechanics DOI:10.37394/232011.2021.16.1 10.46300/9104.2021.15.8Marek Barski, Adam Stawiarski, Pawe, J. Romanowicz, Bogdan Szybi?ski, Local Elasto– plastic Buckling of Isotropic Plates with Cutouts under Tension Loading Conditions, International journal of mechanics, Volume 15, 2021, pp. 69-87. 10.46300/9104.2021.15.21M. V. Klychnikova, Kyaw Ye Ko, Investigation of Mechanical Properties of LowDensity Polyethylene with Copper Nanoparticles, International journal of mechanics, Volume 15, 2021, pp. 181-188. 10.20948/prepr-2019-83Yu.A., Volkov, M.B. Markov Kinetic equations for a phonon gas. Keldysh Institute preprints. M.V. Keldysh. 2019. No. 83.15 p. doi: 10.20948 / prepr-2019-83 URL: http://library.keldysh.ru/preprint.asp?id=2019- 8391, N.6, 2021. A. C. Dmitriev. Introduction to nanothermal physics. 2nd edition, electronic. M .: Laboratory of knowledge. 2020 10.3367/ufne.2020.06.038795E. D. Eidelman. Thermoelectric effect and thermoelectric generator based on carbon nanostructures: achievements and prospects. Advances in physical sciences. Т. 191, N.6, 2021. S.V. Vallander. Equations of motion of a viscous gas. Reports of the Academy of Sciences of the USSR, 1951, v13. S.M. Belotserkovsky, M.I. Nisht. Wing and aircraft aerodynamics. Aeromechanics. M .: Science. 1976.9-24 V. V. Kozlov. Separation of the flow Novosibirsk State University. https://vihrestruktura.3dn.ru/publ/2-1-0-6. 10.1007/978-3-540-73376-8_7S. V. Alekseenko, P. A. Kuibin, V.L. Okulov, Introduction to the theory of concentrated vortices. Moscow-Izhevsk. Institute for Computer Research. 2005.504 p. R. Balescu. Equilibrium and nonequilibrium statistic mechanics. A WileyIntersciences Publication John Willey and Sons. New-yourk-London…1975. N.G. Van Kampen. Stochastic processes in physics and chemistry. North-Holland. 1984. 10.1016/b978-0-08-017783-0.50004-xA.I. Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko, K.N. Stepanov. Plasma electrodynamics. M.: Science, 1974 P. Silin. Introduction to the kinetic theory of gases. M .: Science. 1971. S. Ishimaru. Basic principles of plasma physics. M .: Atomizdat. 1975. A.A. Vlasov. Nonlocal statistical mechanics. M.: Science 1978. Peter M¨orters and Yuval Peres. Brownian .Notes on Brownian motion and related phenomena Deb Shankar Ray∗ Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700032,. (February 2, 2008) ol. 78 (1), p. 25-27. F. Goodman, G. Vachmann. Dynamics of gas scattering by a surface. M .: Mir, 1980. 423.