Dispersion Effects in the Falkner-Skan Problem and in the Kinetic Theory

Galaev, Oleg; Prozorova, Evelina

doi:10.4236/jamp.2017.52045

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…An important component of research is the choice of model. Previous works have shown 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 effect [1]- [6]. When the action of the distributed moment is taken into account, the system of equations is supplemented by the moment conservation law.…”

Section: Introductionmentioning

confidence: 99%

The Law of Conservation of Momentum and the Contribution of No Potential Forces to the Equations for Continuum Mechanics and Kinetics

Prozorova¹

2022

JAMP

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The most common systems are open non-stationary systems. From the previously formulated equations and some experiments, the connection between the gradients of physical quantities and the moment of momentum (force) is traced. The article investigates this trace. The use of the Hamiltonian formalism and the dependence of the force only on the distance between particles limit the study. In the collision integral, for example, for a rarefied gas, the Lennard-Jones potential is often used, which is not of the type considered. The foregoing forces us to turn to the study of the influence of forces of a more general form on the equations of mechanics. Hamilton's formalism traces the behavior of closed systems. The general form of boundary conditions and forces changes the theory proposed in the works by N.N. Bogolyubov. The results of the reformulation are discussed. Even in classical theory, after taking moments, we arrive at Boltzmann's theory at no symmetric stress tensor. The symmetric tensor is obtained after the assumption of a small effect of no symmetry and from the condition of the balance of forces. The requirement of simultaneous fulfillment of the laws of conservation of forces and moments of forces leads to the existence of two solutions. To take into account the moment, in addition to the conditions for the equilibrium of forces, the law of equilibrium of the moments of forces is required in the calculations. From it, the degree of no symmetry of the stress tensor is determined. The work illustrates the contribution of the distributed moment of force to the problems of continuum mechanics and the kinetic theory. Examples of the solution to the problem of fluid mechanics, the theory of elasticity and kinetic theory are given. A correspondence is established between the terms of the Liouville equation with more general and traditional forces. Pre-How to cite this paper: Prozorova, E. (2022) The Law of Conservation of Momentum and the Contribution of No Potential Forces to the Equations for Conti-

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Section: Introductionmentioning

confidence: 99%

The Law of Conservation of Momentum and the Contribution of No Potential Forces to the Equations for Continuum Mechanics and Kinetics

Prozorova¹

2022

JAMP

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“…We have laws that are not symmetric relatively time and space. It should be noted that for the kinetic theory (the Boltzmann equation) the law of conservation of angular momentum does not hold [6][7][8][9][10]. Analysis of the recording of the Lagrangian function for the collective interaction of the particles with the change of the inertia center of the moving particles and the effect influence angular momentum are made in more early work.…”

Section: Introductionmentioning

confidence: 99%

“…So all this questions require study. In works [6][7][8][9][10] these questions were solved partly, but their properties were discussed not full. In work [11] the self-diffusion and thermo-diffusion were obtained from phenomenologically consideration.…”

Section: Introductionmentioning

confidence: 99%

Some Paradoxes of Mathematical Theory of Continues Mechanics

Prozorova¹

2018

AJAM

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The classic theory of continuum mechanics does not preserve the continuity of the environment due to the use of the conditions of equilibrium of forces and the symmetry of the stress tensor. We used many unreasonable mathematical approximations when by the Boltzmann equation is solved to describe the equations of continuum mechanics. The paper presents an analysis of mathematical approximations underlying description in different environments, and new models, to avoid the resulting misunderstandings. For rarefied gas the self-diffusion and thermo-diffusion which were foretold by S. V. Vallander are obtained from kinetic theory.

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Effect of Mathematical Models on Experimental Data for the Gas and Liquids

Prozorova¹

2016

JMEA

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Dispersion Effects in the Falkner-Skan Problem and in the Kinetic Theory

Cited by 4 publications

References 11 publications

The Law of Conservation of Momentum and the Contribution of No Potential Forces to the Equations for Continuum Mechanics and Kinetics

The Law of Conservation of Momentum and the Contribution of No Potential Forces to the Equations for Continuum Mechanics and Kinetics

Some Paradoxes of Mathematical Theory of Continues Mechanics

Effect of Mathematical Models on Experimental Data for the Gas and Liquids

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