Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra

Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two first-order phase transitions as the density increases: first a liquid-solid transition and then a solid-solid transition. The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase at intermediate densities. At higher densities, we find that the CT phase undergoes another first-order phase transition to one associated with the densest-known crystal. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (about 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers

Structural characterization and statistical-mechanical model of epidermal patterns

In proliferating epithelia of mammalian skin, cells of irregular polygonal-like shapes pack into complex nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct and Fourier spaces of the cell centroids in the early stages of embryonic development show structural directional dependence, while in the late stages the patterns tend towards statistically isotropic states. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-ranged soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. Our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. We discuss ways in which our model might be extended so as to better understand morphogenesis (in particular the emergence of planar cell polarity), wound-healing, and disease progression processes in skin, and how it could be applied to the design of synthetic tissues

Comment on "Explicit Analytical Solution for Random Close Packing in d=2d=2 and d=3d=3"

In this short commentary we provide our comment on the article "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$" and its subsequent Erratum that are recently published in Physical Review Letters. In that Letter, the author presented an explicit analytical derivation of the volume fractions $\phi_{\rm RCP}$ for random close packings (RCP) in both $d=2$ and $d=3$. Here we first briefly show the key parts of the derivation in Ref.~\cite{Za22}, and then provide arguments on why we think the derivation of the analytical results is problematic and unjustified, and why the Erratum does not address or clarify the concerns raised previously by us

A Cellular Automaton Model for Tumor Dormancy: Emergence of a Proliferative Switch

Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a comprehensive understanding of cancer dormancy and the "switch" from a dormant to a proliferative state still needs to be strengthened from both a basic and clinical point of view. Computational modeling enables one to explore a variety of scenarios for possible but realistic microscopic dormancy mechanisms and their predicted outcomes. The aim of this paper is to devise such a predictive computational model of dormancy with an emergent "switch" behavior. Specifically, we generalize a previous cellular automaton (CA) model for proliferative growth of solid tumor that now incorporates a variety of cell-level tumor-host interactions and different mechanisms for tumor dormancy, for example the effects of the immune system. Our new CA rules induce a natural "competition" between the tumor and tumor suppression factors in the microenvironment. This competition either results in a "stalemate" for a period of time in which the tumor either eventually wins (spontaneously emerges) or is eradicated; or it leads to a situation in which the tumor is eradicated before such a "stalemate" could ever develop. We also predict that if the number of actively dividing cells within the proliferative rim of the tumor reaches a critical, yet low level, the dormant tumor has a high probability to resume rapid growth. Our findings may shed light on the fundamental understanding of cancer dormancy

Vibrational Properties of One-Dimensional Disordered Hyperuniform Atomic Chains

Disorder hyperuniformity (DHU) is a recently discovered exotic state of many-body systems that possess a hidden order in between that of a perfect crystal and a completely disordered system. Recently, this novel DHU state has been observed in a number of quantum materials including amorphous 2D graphene and silica, which are endowed with unexpected electronic transport properties. Here, we numerically investigate 1D atomic chain models, including perfect crystalline, disordered hyperuniform as well as randomly perturbed atom packing configurations to obtain a quantitative understanding of how the unique DHU disorder affects the vibrational properties of these low-dimensional materials. We find that the DHU chains possess lower cohesive energies compared to the randomly perturbed chains, implying their potential reliability in experiments. Our inverse partition ratio (IPR) calculations indicate that the DHU chains can support fully delocalized states just like perfect crystalline chains over a wide range of frequencies, i.e., $\omega \in (0, 100)$ cm$^{-1}$, suggesting superior phonon transport behaviors within these frequencies, which was traditionally considered impossible in disordered systems. Interestingly, we observe the emergence of a group of highly localized states associated with $\omega \sim 200$ cm$^{-1}$, which is characterized by a significant peak in the IPR and a peak in phonon density of states at the corresponding frequency, and is potentially useful for decoupling electron and phonon degrees of freedom. These unique properties of DHU chains have implications in the design and engineering of novel DHU quantum materials for thermal and phononic applications.Comment: 6 pages, 3 figure

Stone-Wales Defects Preserve Hyperuniformity in Amorphous Two-Dimensional Materials

Crystalline two-dimensional (2D) materials such as graphene possess unique physical properties absent in their bulk form, enabling many novel device applications. Yet, little is known about their amorphous counterparts, which can be obtained by introducing the Stone-Wales (SW) topological defects via proton radiation. Here we provide strong numerical evidence that SW defects preserve hyperuniformity in hexagonal 2D materials, a recently discovered new state of matter characterized by vanishing normalized infinite-wavelength density fluctuations, which implies that all amorphous states of these materials are hyperuniform. Specifically, the static structure factor S(k) of these materials possesses the scaling S(k) ~ k^{\alpha} for small wave number k, where 1<=\alpha(p)<=2 is monotonically decreasing as the SW defect concentration p increases, indicating a transition from type-I to type-II hyperuniformity at p ~= 0.12 induced by the saturation of the SW defects. This hyperuniformity transition marks a structural transition from perturbed lattice structures to truly amorphous structures, and underlies the onset of strong correlation among the SW defects as well as a transition between distinct electronic transport mechanisms associated with different hyperuniformity classes