TITLE:
Influence of the Delay and Dispersion in Mechanics
AUTHORS:
Evelina V. Prozorova
KEYWORDS:
Angular Momentum Conservation Laws, Unbalanced Stress Tensor, The Boltzmann Equation, Chapman-Enskog Method
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.16,
October
30,
2014
ABSTRACT: The aim
of this work is to clarify the new mathematical model describing the mechanics
of continuous media and rarefied gas. The present study is associated with the
formulation of conservation laws as conditions of equilibrium of angular
momentums, while usually formulated in terms of balance of force. The equations
for gas are found from the modified Boltzmann equation and the phenomenological
theory. For a rigid body, the equations used the phenomenological theory, but
changed their interpretation. We elucidate the contribution of cross-effects in
the conservation laws of continuum mechanics, including the self-diffusion,
thermal diffusion, etc., which indicated S. Wallander. The paradox of Hilbert
in the solution of the Boltzmann equation by the Chapman-Enskog method was
resolved. Refined model of the boundary conditions for rarefied gas flows and
transient flow were near the moving surfaces. We establish conditions for the
existence of the A. N. Kolmogorov inertial range on the basis of the proposed
theory. Based on the theory, derivation of the Prandtl formula for boundary
layer was received. Delay in mechanics plays an important role on
commensurability of relaxation times and lateness. New accounting delay option
is proposed to consider the difference between the time derivative as a limit
and end values of the mean free path in a rarefied gas. The role of individual
time delay for each particle velocity and the average time is debated. The
Boltzmann equation is written with an additional term. This situation is
typical for discrete medium. The transition from discrete to continuous
environment is a key issue mechanics. Summary records of all effects lead to a
cumbersome system of equations and therefore require the selection of main
effects in a particular situation. The role of the time has similar problems in
quantum mechanics. Some examples are suggested.