Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity, Z(k), to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of Z(k) as k tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, σ 2 (R), in the number of points contained in an interval of length 2R. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope 1/τ fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, Z(k) ∼ k 4 ; for all others, Z(k) ∼ k 2 . This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.

Defects, and in particular topological defects, are architectural motifs that play a crucial role in natural materials. Here we provide a systematic strategy to introduce such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials, and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects by experiments and simulations, and leverage this to design complex metamaterials in which we can steer deformations and stresses towards parts of the system. Our work presents a new avenue to systematically include spatial complexity, frustration, and topology in mechanical metamaterials.arXiv:1903.07919v1 [cond-mat.soft]

The phase diagram of Yukawa particles confined between two parallel hard walls is calculated at zero-temperature beyond the bilayer regime by lattice-sum-minimization. Tuning the screening, a rich phase behavior is found in the regime bounded by stable two-triangular layers and 3-square layers. In this regime, alternating prism phases with square and triangular basis, structures derived from a hcp bulk lattice, and a structure with two outer layers and two inner staggered rectangular layers, reminiscent of a Belgian waffle iron, are stable. These structures are verifiable in experiments on charged colloidal suspensions and dusty plasma sheets.

We show that hard spheres confined between two parallel hard plates pack denser with periodic adaptive prismatic structures which are composed of alternating prisms of spheres. The internal structure of the prisms adapts to the slit height which results in close packings for a range of plate separations, just above the distance where three intersecting square layers fit exactly between the plates. The adaptive prism phases are also observed in real-space experiments on confined sterically stabilized colloids and in Monte Carlo simulations at finite pressure.PACS numbers: 82.70. Dd, 05.20.Jj, 68.65.Ac How to pack the largest number of hard objects in a given volume is a classic optimization problem in pure geometry [1]. The close-packed structures obtained from such optimizations are also pivotal in understanding the basic physical mechanisms behind freezing [2,3] and glass formation [4]. Moreover, close-packed structures are highly relevant to numerous applications ranging from packaging macroscopic bodies and granulates [5] to the self-assembly of colloidal [6] and biological [7,8] soft matter. For the case of hard spheres, Kepler conjectured that the highest-packing density should be that of a periodic face-centered-cubic (fcc) lattice composed of stacked hexagonal layers; it took until 2005 for a strict mathematical proof [9]. More recent studies on close packing concern either non-spherical hard objects [10] such as ellipsoids [11,12], convex polyhedra [13,14] (in particular tetrahedra [15]), and irregular non-convex bodies [16] or hard spheres confined in hard containers [17][18][19] or other complex environments.If hard spheres of diameter σ are confined between two hard parallel plates of distance H, as schematically illustrated in Fig. 1, the close-packed volume fraction φ and its associated structure depend on the ratio H/σ. Typically, the complexity of the observed phases increases tremendously on confining the system. Parallel slices from the fcc bulk crystal are only close-packed for certain values of H/σ: A stack of n hexagonal (square) layers aligned with the walls, denoted by n△ (n ), is bestpacked at the plate separation H n△ (H n ) where the layers exactly fit between the walls. Clearly, for the minimal plate distance H ≡ H 1△ = σ, packing by a hexagonal monolayer is optimal. Increasing H/σ up to H 2△ , a buckled monolayer [20] and then a rhombic bilayer [21] become close-packed. However, for H 2△ < H < H 4△ , the close-packed structures are much more complex and still debated. Both, prism phases with alternating parallel prism-like arrays composed of hexagonal and square base [22,23] and morphologies derived from the hexagonalclose-packed (hcp) structure [24,25] were proposed as possible candidates.For confined hard spheres, the knowledge and control over the close-packed configuration is of central relevance for at least two reasons: First, the hard sphere system away from close-packing is of fundamental interest as a quasi-two-dimensional statistical mechanics model. At low densities, a ha...

We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that match perfectly the reference. The site averaged LOM and its standard deviation define two scalar order parameters, S and δS, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that S, δS and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling.