Research Gallery
1. Metallic Glasses
1.1 Delaunay triangulation and the associated non-affine displacement fields
We simulate two-dimensional binary Lennard-Jones systems as simple models of metallic glasses and subject the systems to athermal, quasistatic simple shear (AQS). We develop a novel methodology for characterizing the non-affine deformation based on Delaunay triangulation. We demonstrated that local pure shear strains of triangular elements, which give rise to mostly quadrupolar displacement fields, are activated during both the quasi-elastic growth of stress versus strain and during the abrupt stress drops. Our results provide fundamental insights for understanding the atomic-scale defects that control mechanical response in amorphous solids. [Jin et al., Soft Matter 17, 8612 (2021)]
2. Granular Materials
2.1 Homogeneous crystallization in cyclically sheared frictionless grains
When water is cooled sufficiently slow, the randomly positioned molecules rearrange and ice crystallites emerge and grow. Crystallites have also been observed to form and grow in periodically sheared granular matter. Comparing crystallization achieved by adding energy through shearing versus removing energy by cooling should help clarify the general phenomenon. The computer simulations identify the minimal ingredients necessary for granular crystallization; in particular, gravity and friction are not necessary. Further, the results shed light on so-called random close packing (RCP) of granular materials, where the volume occupied by the grains reached 62%-66% of the container volume. Our results reveal that, under sufficiently small amplitude of cyclic shear, granular matter remains disordered below 64.6% volume fraction, while crystallites emerge and grow when the volume fraction is increased above this value. [ Jin et al., PRL 125, 258003 (2020) ]
2.2 Hypostatic jammed packings of frictionless nonspherical particles
We perform computational studies of static packings of a variety of nonspherical particles including circulo- lines, circulo-polygons, ellipses, asymmetric dimers, dumbbells, and others to determine which shapes form packings with fewer contacts than degrees of freedom (hypostatic packings) and which have equal numbers of contacts and degrees of freedom (isostatic packings), and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naive constraint counting. We show that the packing fraction and coordination number at jamming onset obey a masterlike form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity. [ VanderWerf et al., PRE 97, 012909 (2018) ]
3. Self-assembly (Modeling Structures from Shapes)
3.1 Crystal structures of spheroids in cylindrical confinement
The question “how densely a given solid object can fill a container” is easy to address but difficult to answer. The densest packing of identical spheres in 3D space has only been proven recently, yet very little is known about anisotropic shapes. Here we extend the particle shape to the spheroid, which is a common, and relatively simple, widely-used model for anisotropic particles. By varying the shape anisotropy of spheroids and also the cylinder-to-spheroid size ratio, a variety of densest possible crystalline structures have been discovered, including achiral structures with specific orientations of particles and chiral helical structures with rotating orientations of particles. Hence, this work reveals insight into the interplay between the particle shape (anisotropy) and packing environment on packing structures. [ Jin et al., PRL 124, 248002 (2020) (Editors' Suggestion) ]
3.2 Maps of densest-packed structures of ellipses in strip confinement
We report a novel class of confinement-induced, orientationally ordered columnar crystals as obtained from the densest possible packings of identical hard ellipses within an infinitely long parallel strip. We found that any densest-packed structure of identical ellipses in strip confinement is an affine transformation of a particular densest-packed structure of circular disks. Based on this general result, we have developed an analytic theory that describes all such densest-packed structures of ellipses in a unified framework, where we classify such structures into three types (X, Y, M) and give a full account of all possible structural transitions from one type to another. Our theory provides a unified explanation of how this novel class of crystals emerge as candidates of densest-packed structures, and it offers new possibilities of developing novel low-dimensional crystalline materials with specific orientational ordering. [ Jin et al., PRR 3, 013053 (2021) ]
3.3 Square-triangular crystalline packings of ellipsoids
The densest packing of congruent hard ellipsoids, which is intimately related to the high-density phase of many condensed matter systems, is still an open problem. We discover an unusual family of dense crystalline packings of self-dual ellipsoids, containing 24 particles with a quasi-square-triangular (SQ-TR) tiling arrangement in the fundamental cell. The associated packing density exceeds that of the densest known crystal of ellipsoids for a certain aspect ratio range. We show that the SQ-TR phase is thermodynamically stable at high densities over the aforementioned aspect ratio range and report a phase diagram for self-dual ellipsoids. The discovery of the SQ-TR crystal suggests organizing principles for nonspherical particles and self-assembly of colloidal systems. [ Jin et al., PRE 95, 033003 (2017) ]
