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We extend the results from the first part of this series of two papers byexamining hyperuniformity in heterogeneous media composed of impenetrableanisotropic inclusions. Specifically, we consider maximally random jammedpackings of hard ellipses and superdisks and show that these systems bothpossess vanishing infinite-wavelength local-volume-fraction fluctuations andquasi-long-range pair correlations. Our results suggest a strong generalizationof a conjecture by Torquato and Stillinger [Phys. Rev. E. 68, 041113 (2003)],namely that all strictly jammed saturated packings of hard particles, includingthose with size- and shape-distributions, are hyperuniform with signaturequasi-long-range correlations. We show that our arguments concerning theconstrained distribution of the void space in MRJ packings directly extend tohard ellipse and superdisk packings, thereby providing a direct structuralexplanation for the appearance of hyperuniformity and quasi-long-rangecorrelations in these systems. Additionally, we examine general heterogeneousmedia with anisotropic inclusions and show for the first time that one candecorate a periodic point pattern to obtain a hard-particle system that is nothyperuniform with respect to local-volume-fraction fluctuations. This apparentdiscrepancy can also be rationalized by appealing to the irregular distributionof the void space arising from the anisotropic shapes of the particles. Ourwork suggests the intriguing possibility that the MRJ states of hard particlesshare certain universal features independent of the local properties of thepackings, including the packing fraction and average contact number perparticle.

physical review. e, statistical, nonlinear and soft matter physics

Hyperuniformity, quasi-long-range correlations, and void-space  constraints in maximally random jammed particle packings. II. Anisotropy in  particle shape