  Particle transports in carriers with even-odd alternating dispersions
(introduced in Part I) are investigated. For the third-order dispersion as in
Korteweg-de-Vries (KdV), such alternating dispersion has the effects of not
only regularizing the velocity from forming shock singularity (thus the
attenuation of particle clustering strength) but also symmetrizing the
oscillations (thus the corresponding skewness of the particle densities), among
others, as demonstrated numerically. The analogy of such dispersion effects and
consequences (on particle transports in particular) with those of helicity in
Burgers turbulence, addressed in the context of astrophysics and cosmology, is
made for illumination and promoting models. Both dispersion and helicity
regularize the respective systems, and both are shown to be transferred by the
drag to the flows of the respective inertial particles carried by the latter
and to similarly affect the particle clustering. A reward from studying
particle transports is the understanding of the (asymptotic) $k^0$-scaling
(equipartition among the wavenumbers, $k$s), before large-$k$ exponential
decay, of the power spectrum of KdV solitons [resulting in the more general
statement (valid beyond the KdV soliton and Burgers shock) that "a
(one-dimensional) soliton is the derivative of a classical shock, just like the
Dirac delta is the derivative of a step function"], motivated by the
explanation of the the same scaling law of the particle densities as the
apparent approximation of the Dirac deltas; while, the "shocliton" from the
even-odd alternating dispersion in aKdV appears to be, indeed, $shock \oplus
soliton$, accordingly the decomposition of the averaged odd-mode spectrum, from
sinusoidal initial field, into a $k^{-2}$ part for the shock and a
$k^0$-scaling part for the solitonic pulses, only the latter being contained in
the averaged even-mode spectrum.
