279,138 research outputs found
A calculable and quasi-practical gas
A new kinetic approach is developed and a quasi-practical gas is defined to
which the new approach can be applied. One of the advantages of this new
approach over the standard one is direct calculability in terms of today's
computational means.Comment: 12 pages, 6 figures, late
Paradoxical aspects of the kinetic equations
Two paradoxical aspects of the prevailing kinetic equations are presented.
One is related to the usual understanding of distribution function and the
other to the usual understanding of the phase space. With help of simple
counterexamples and direct analyses, involved paradoxes manifest themselves.Comment: 9 pages, Late
A path-integral approach to the collisional Boltzmann gas
Collisional effects are included in the path-integral formulation that was
proposed in one of our previous paper for the collisionless Boltzmann gas. In
calculating the number of molecules entering a six-dimensional phase volume
element due to collisions, both the colliding molecules and the scattered
molecules are allowed to have distributions; thus the calculation is done
smoothly and no singularities arise.Comment: 18 pages, 11 figure
Boltzmann's H-theorem and time irreversibility
It is shown that the justification of the Boltzman H-theorem needs more than
just the assumption of molecular chaos and the picture of time irreversibility
related to it should be reinvestigated.Comment: 7 pages, 3 figures, changes in languag
Mathematical investigation of the Boltzmann collisional operator
Problems associated with the Boltzmann collisional operator are unveiled and
discussed. By careful investigation it is shown that collective effects of
molecular collisions in the six-dimensional position and velocity space are
more sophisticated than they appear to be.Comment: 5 pages, 1 figure
Nonexistence of time reversibility in statistical physics
Contrary to the customary thought prevailing for long, the time reversibility
associated with beam-to-beam collisions does not really exist. Related facts
and consequences are presented. The discussion, though involving simple
mathematics and physics only, is well-related to the foundation of statistical
theory.Comment: 10 pages, 5 figures, late
A counterexample against the Vlasov equation
A simple counterexample against the Vlasov equation is put forward, in which
a magnetized plasma is perturbed by an electromagnetic standing wave.Comment: 5 pages, 1 figur
Counterexamples of Boltzmann's equation
To test kinetic theories, simple and practical setups are proposed. It turns
out that these setups cannot be treated by Boltzmann's equation. An alternative
method, called the path-integral approach, is then employed and a number of
ready-for-verification results are obtained.Comment: 17 pages, 6 figures, theoretical analyses have been moved to
appendixe
A new uncertainty principle
By examining two counterexamples to the existing theory, it is shown, with
mathematical rigor, that as far as scattered particles are concerned the true
distribution function is in principle not determinable (indeterminacy principle
or uncertainty principle) while the average distribution function over each
predetermined finite velocity solid-angle element can be calculated.Comment: 12 pages, 7 figure
A path-integral approach to the collisionless Boltzmann gas
On contrary to the customary thought, the well-known ``lemma'' that the
distribution function of a collisionless Boltzmann gas keeps invariant along a
molecule's path represents not the strength but the weakness of the standard
theory. One of its consequences states that the velocity distribution at any
point is a condensed ``image'' of all, complex and even discontinuous,
structures of the entire spatial space. Admitting the inability to describe the
entire space with a microscopic quantity, this paper introduces a new type of
distribution function, called the solid-angle-average distribution function.
With help of the new distribution function, the dynamical behavior of
collisionless Boltzmann gas is formulated in terms of a set of integrals
defined by molecular paths. In the new formalism, not only that the
difficulties associated with the standard theory are surmounted but also that
some of practical gases become calculable in terms of today's computer.Comment: 18 pages, 8 figure
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