%0 Journal Article
%T Quantization of the Kinetic Energy of Deterministic Chaos
%A Victor A. Miroshnikov
%J American Journal of Computational Mathematics
%P 1-81
%@ 2161-1211
%D 2023
%I Scientific Research Publishing
%R 10.4236/ajcm.2023.131001
%X In previous
works, the theoretical and experimental deterministic scalar kin<span><span><span style=\"font-family:;\" \"=\"\">ematic structures,
the theoretical and experimental deterministic vector kin</span></span></span><span><span><span style=\"font-family:;\" \"=\"\">ematic structures,
the theoretical and experimental deterministic scalar dynamic structures, and the
theoretical and experimental deterministic vector dynamic structures have been developed
to compute the exact solution for deterministic chaos of the exponential pulsons
and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes
equations. To explore properties of the kinetic energy, rectangular, diagonal, and
triangular summations of a matrix of the kinetic energy and general terms of various
sums have been used in the current paper to develop quantization of the kinetic
energy of deterministic chaos. Nested structures of a cumulative energy pulson,
an energy pulson of propagation, an internal energy oscillon, a diagonal energy
oscillon, and an external energy oscillon have been established. In turn, the energy
pulsons and oscillons include group pulsons of propagation, internal group oscillons,
diagonal group oscillons, and external group oscillons. Sequentially, the group
pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons,
diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons
and oscillons are composed <span>of elementary pulsons
of propagation, internal elementary oscillons, diagonal elementary oscillons, and
external elementary oscillons. Topology, periodicity,</span> and integral properties
of the exponential pulsons and oscillons have been studied using the novel method
of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time.
Symbolic computations of the exact expansions have been performed using the experimental
and theoretical programming in Maple. Results of the symbolic computation</span></span></span><span><span><span style=\"font-family:;\" \"=\"\">s</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"> have been
justified by probe visualizations.</span></span></span>
%K The Navier-Stokes Equations
%K Quantization of Kinetic Energy
%K Deterministic Chaos
%K Elementary Pulson of Propagation
%K Internal Elementary Oscillon
%K Diagonal Elementary Oscillon
%K External Elementary Oscillon
%K Wave Pulson of Propagation
%K Internal Wave Oscillon
%K Diagonal Wave Oscillon
%K External Wave Oscillon
%K Group Pulson of Propagation
%K Internal Group Oscillon
%K Diagonal Group Oscillon
%K External Group Oscillon
%K Energy Pulson of Propagation
%K Internal Energy Oscillon
%K Diagonal Energy Oscillon
%K External Energy Oscillon
%K Cumulative Energy Pulson
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=122334