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Particle transports in carriers with even-odd alternating dispersions(introduced in Part I) are investigated. For the third-order dispersion as inKorteweg-de-Vries (KdV), such alternating dispersion has the effects of notonly regularizing the velocity from forming shock singularity (thus theattenuation of particle clustering strength) but also symmetrizing theoscillations (thus the corresponding skewness of the particle densities), amongothers, as demonstrated numerically. The analogy of such dispersion effects andconsequences (on particle transports in particular) with those of helicity inBurgers turbulence, addressed in the context of astrophysics and cosmology, ismade for illumination and promoting models. Both dispersion and helicityregularize the respective systems, and both are shown to be transferred by thedrag to the flows of the respective inertial particles carried by the latterand to similarly affect the particle clustering. A reward from studyingparticle transports is the understanding of the (asymptotic) $k^0$-scaling(equipartition among the wavenumbers, $k$s), before large-$k$ exponentialdecay, of the power spectrum of KdV solitons [resulting in the more generalstatement (valid beyond the KdV soliton and Burgers shock) that "a(one-dimensional) soliton is the derivative of a classical shock, just like theDirac delta is the derivative of a step function"], motivated by theexplanation of the the same scaling law of the particle densities as theapparent approximation of the Dirac deltas; while, the "shocliton" from theeven-odd alternating dispersion in aKdV appears to be, indeed, $shock \oplussoliton$, accordingly the decomposition of the averaged odd-mode spectrum, fromsinusoidal 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 inthe averaged even-mode spectrum.

Even-odd alternative dispersions and beyond. Part II. Noninertial and inertial particles, and, astrophysical chirality analogy