Related papers: Analytical Construction of A Dense Packing of Trun…
The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures…
The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures…
We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal…
Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically…
Dense packings have served as useful models of the structure of liquid, glassy and crystal states of matter, granular media, heterogeneous materials, and biological systems. Probing the symmetries and other mathematical properties of the…
We formulate the problem of generating dense packings of nonoverlapping, non-tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the Adaptive Shrinking Cell…
We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both…
Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are…
We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856347... Like the recently discovered packings of Kallus et al. [arXiv:0910.5226] and Torquato-Jiao [arXiv:0912.4210], our packing is crystalline…
The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
We construct a dense packing of regular tetrahedra, with packing density $D > >.7786157$.
All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of {\phi} = {\pi}/\sqrt18 ~ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction. For…
Since antiquity, the packing of convex shapes has been of great interest to many scientists and mathematicians. Recently, particular interest has been given to packings of three-dimensional tetrahedra. Dense packings of both crystalline and…
Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle…
We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids, and certain smoothly-shaped convex nonspherical particles [Torquato and Jiao, Phys. Rev. E 81, 041310 (2010)]. Here we…
In \cite{Sz17-2} we considered hyperball packings in $3$-dimensional hyperbolic space. We developed a decomposition algorithm that for each saturated hyperball packing provides a decomposition of $\HYP$ into truncated tetrahedra. In order…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…
A new tetrahedral structure model was developed and the geometrical structure of jammed disordered packings of monodisperse spheres with different friction coefficients was systematically characterized. An intrinsic structure feature is…
Symbolic and graphical tools, such as Mathematica, enable precise visualization and analysis of void spaces in sphere packings. In the cubic close packing (CCP, or face-centred cubic packing; FCC) arrangement these voids can be partitioned…