The random packing density of nearly spherical particles

Spheroid models to elaborate the broken symmetry and equivalent volume of molecules in crystalline phase

Dense packing of particles has provided powerful models to elaborate the important structural features of matter in various systems such as liquid, glassy, and crystalline phases. The simplest sphere packing models can represent and capture salient properties of the building blocks for covalent, metallic, and ionic crystals; it, however, becomes insufficient to reflect the broken symmetry of the commonly anisotropic molecules in molecular crystals. Here, we develop spheroid models with a minimal degree of anisotropy, which serve as a simple geometrical representation for a rich spectrum of molecules-including both isotropic and anisotropic, convex and concave ones-in crystalline phases. Our models are determined via an inverse packing approach: Given a molecular crystal, an optimal spheroid model is constructed using a contact diagram, which depicts the packing relationship between neighboring molecules within the crystal. The spheroid models are capable of accurately capturing the broken symmetry and characterizing the equivalent volume of molecules in the crystalline phases. Moreover, our model retrieves such molecular information from low-quality x-ray diffraction data with poorly resolved structures, and by using soft spheroids, it can also describe the packing behavior in cocrystals.

Machine learning approaches for the optimization of packing densities in granular matter

The fundamental question of how densely granular matter can pack and how this density depends on the shape of the constituent particles has been a longstanding scientific problem. Previous work has mainly focused on empirical approaches based on simulations or mean-field theory to investigate the effect of shape variation on the resulting packing densities, focusing on a small set of pre-defined shapes like dimers, ellipsoids, and spherocylinders. Here we discuss how machine learning methods can support the search for optimally dense packing shapes in a high-dimensional shape space. We apply dimensional reduction and regression techniques based on random forests and neural networks to find novel dense packing shapes by numerical optimization. Moreover, an investigation of the regression function in the dimensionally reduced shape representation allows us to identify directions in the packing density landscape that lead to a strongly non-monotonic variation of the packing density. The predictions obtained by machine learning are compared with packing simulations. Our approach can be more widely applied to optimize the properties of granular matter by varying the shape of its constituent particles.

Dense Disordered Jammed Packings of Hard Spherocylinders with a Low Aspect Ratio: A Characterization of Their Structure

This work numerically investigates dense disordered (maximally random) jammed packings of hard spherocylinders of cylinder length L and diameter D by focusing on L/D ∈ [0,2]. It is within this interval that one expects that the packing fraction of these dense disordered jammed packings ϕMRJ hsc attains a maximum. This work confirms the form of the graph ϕMRJ hsc versus L/D: here, comparably to certain previous investigations, it is found that the maximal ϕMRJ hsc = 0.721 ± 0.001 occurs at L/D = 0.45 ± 0.05. Furthermore, this work meticulously characterizes the structure of these dense disordered jammed packings via the special pair-correlation function of the interparticle distance scaled by the contact distance and the ensuing analysis of the statistics of the hard spherocylinders in contact: here, distinctly from all previous investigations, it is found that the dense disordered jammed packings of hard spherocylinders with 0.45 ≲ L/D ≤ 2 are isostatic.

Dense packings of geodesic hard ellipses on a sphere

Packing problems are abundant in nature and have been researched thoroughly both experimentally and in numerical models. In particular, packings of anisotropic, elliptical particles often emerge in models of liquid crystals, colloids, and granular and jammed matter. While most theoretical studies on anisotropic particles have thus far dealt with packings in Euclidean geometry, there are many experimental systems where anisotropically-shaped particles are confined to a curved surface, such as Pickering emulsions stabilized by ellipsoidal particles or protein adsorbates on lipid vesicles. Here, we study random close packing configurations in a two-dimensional model of spherical geodesic ellipses. We focus on the interplay between finite-size effects and curvature that is most prominent at smaller system sizes. We demonstrate that on a spherical surface, monodisperse ellipse packings are inherently disordered, with a non-monotonic dependence of both their packing fraction and the mean contact number on the ellipse aspect ratio, as has also been observed in packings of ellipsoids in both 2D and 3D flat space. We also point out some fundamental differences with previous Euclidean studies and discuss the effects of curvature on our results. Importantly, we show that the underlying spherical surface introduces frustration and results in disordered packing configurations even in systems of monodispersed particles, in contrast to the 2D Euclidean case of ellipse packing. This demonstrates that closed curved surfaces can be effective at introducing disorder in a system and could facilitate the study of monodispersed random packings.

Group size affects predation risk and foraging success in Pacific salmon at sea

Grouping is ubiquitous across animal taxa and environments. Safety in numbers is perhaps the most cited reason for grouping, yet this fundamental tenet of ecological theory has rarely been tested in wild populations. We analyzed a multidecadal dataset of Pacific salmon at sea and found that individuals in larger groups had lower predation risk; within groups of fish, size outliers (relatively small and large fish) had increased predation risk. For some species, grouping decreased foraging success, whereas for other species, grouping increased foraging success, indicating that safety competition trade-offs differed among species. These results indicate that survival and growth depend on group size; understanding the relationship between group size distributions and population size may be critical to unraveling ecology and population dynamics for marine fishes.

Structural universality in disordered packings with size and shape polydispersity

We numerically investigate disordered jammed packings with both size and shape polydispersity, using frictionless superellipsoidal particles. We implement the set Voronoi tessellation technique to evaluate the local specific volume, i.e., the ratio of cell volume over particle volume, for each individual particle. We focus on the average structural properties for different types of particles binned by their sizes and shapes. We generalize the basic observation that the larger particles are locally packed more densely than the smaller ones in a polydisperse-sized packing into systems with coupled particle shape dispersity. For this purpose, we define the normalized free volume vf to measure the local compactness of a particle and study its dependency on the normalized particle size A. The definition of vf relies on the calibrated monodisperse specific volume for a certain particle shape. For packings with shape dispersity, we apply the previously introduced concept of equivalent diameter for a non-spherical particle to define A properly. We consider three systems: (A) linear superposition states of mixed-shape packings, (B) merely polydisperse-sized packings, and (C) packings with coupled size and shape polydispersity. For (A), the packing is simply considered as a mixture of different subsystems corresponding to monodisperse packings for different shape components, leading to A = 1, and vf = 1 by definition. We propose a concise model to estimate the shape-dependent factor αc, which defines the equivalent diameter for a certain particle. For (B), vf collapses as a function of A, independent of specific particle shape and size polydispersity. Such structural universality is further validated by a mean-field approximation. For (C), we find that the master curve vf(A) is preserved when particles possess similar αc in a packing. Otherwise, the dispersity of αc among different particles causes the deviation from vf(A). These findings show that a polydisperse packing can be estimated as the combination of various building blocks, i.e., bin components, with a universal relation vf(A).

Decompaction of wet granular materials under freeze-thaw cycling

The packing fraction dynamics of a wet granular material submitted to freeze-thaw cycling is investigated experimentally. The dynamics is strongly influenced by the liquid volume fraction ω in the considered range of 0.03<ω<0.32. This range of liquid contents covers different regimes of wetness from the creation of the capillary network until the formation of large clusters and finally close to the saturated case. For the liquid contents ω≳0.15, the pile experiences a decompaction until a particular value of the packing fraction 0.56 corresponding to a random loose packing configuration for monosized spheres. Moreover, the decompaction starts after a cycling number that decreases exponentially with the liquid content. Finally, we show that the packing dynamics can be well modeled on the basis of a Landau potential with an asymmetric double-well structure. The onset of decompaction represents the tendency of the system to stay in a metastable state. After several cycles, the forces induced by the thermal cycling and local stochastic rearrangements of the grains can drive the system to overcome the energy barrier of the cohesive forces.

A Geometric-Structure Theory for Maximally Random Jammed Packings

Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density "random-close packing" polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.