TY - GEN

T1 - Analysis of the Influence of Boundary Conditions in Kinetic Problems

AU - Prozorova, E.

N1 - Conference code: 15

PY - 2023/1/1

Y1 - 2023/1/1

N2 - The object of the article is the analysis of mathematical models of the kinetic theory of rarefied gas and the influence of boundary conditions. The main equation of the theory is the Liouville equation. An attempt is made to trace the consequences of neglecting the boundary conditions in the equation. The problems that arise when using the Hamiltonian formalism under the action of forces of a more complex form than the classical ones are discussed; influence of the distributed torque on the Boltzmann equation and the equations of continuum mechanics. Boundary conditions significantly change the properties of systems in terms of reversibility and ergodicity. This work is a continuation of the previous ones, in which was made it possible to conclude that classical models do not include one of the most important laws—the law of conservation of angular momentum if the moment does not act as a given force. Mathematical analysis the equations of continuum mechanics of no symmetric stress tensor reveals for the plane case that for four unknowns we have three equations: two equations from the stress equilibrium condition and one equation from the moment equilibrium condition. Thus, we need to close the task with an additional condition. In the classical version, such a condition is the condition of symmetry of the stress tensor. Here a method for closing the problem for no symmetric tensor and examples are proposed. The connection between the accepted approximations of the kinetic theory and continuous medium models is traced. It is shown that the kinetic theory makes it possible to track the contribution of individual processes; in continuum mechanics structure are absent.

AB - The object of the article is the analysis of mathematical models of the kinetic theory of rarefied gas and the influence of boundary conditions. The main equation of the theory is the Liouville equation. An attempt is made to trace the consequences of neglecting the boundary conditions in the equation. The problems that arise when using the Hamiltonian formalism under the action of forces of a more complex form than the classical ones are discussed; influence of the distributed torque on the Boltzmann equation and the equations of continuum mechanics. Boundary conditions significantly change the properties of systems in terms of reversibility and ergodicity. This work is a continuation of the previous ones, in which was made it possible to conclude that classical models do not include one of the most important laws—the law of conservation of angular momentum if the moment does not act as a given force. Mathematical analysis the equations of continuum mechanics of no symmetric stress tensor reveals for the plane case that for four unknowns we have three equations: two equations from the stress equilibrium condition and one equation from the moment equilibrium condition. Thus, we need to close the task with an additional condition. In the classical version, such a condition is the condition of symmetry of the stress tensor. Here a method for closing the problem for no symmetric tensor and examples are proposed. The connection between the accepted approximations of the kinetic theory and continuous medium models is traced. It is shown that the kinetic theory makes it possible to track the contribution of individual processes; in continuum mechanics structure are absent.

KW - CHAOS

KW - CMSIM style

KW - Chaotic modeling

KW - Conference

UR - https://www.mendeley.com/catalogue/681a4782-53a4-3522-825e-4a1f79bcd622/

U2 - 10.1007/978-3-031-27082-6_20

DO - 10.1007/978-3-031-27082-6_20

M3 - Conference contribution

SN - 978-3-031-27081-9

T3 - Springer Proceedings in Complexity

SP - 239

EP - 253

BT - 15th Chaotic Modeling and Simulation International Conference

PB - Springer Nature

T2 - 15th Chaotic Modeling and Simulation International Conference

Y2 - 14 June 2022 through 17 June 2022

ER -