相关论文: Optimal Packing Behavior of some 2-block Patterns
Four packings of hyperbolic 3-space are known to yield the optimal packing density of $0.85328\dots$. They are realized in the regular tetrahedral and cubic Coxeter honeycombs with Schl\"afli symbols $\{3,3,6 \}$ and $\{4,3,6\}$. These…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
In previous work a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an…
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 study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…
We study the optimal packing of hard spheres in an infinitely long cylinder, using simulated annealing, and compare our results with the analogous problem of packing disks on the unrolled surface of a cylinder. The densest structures are…
In this letter, we used a combination of DEM and the multi-sphere method to investigate the random packing dynamics of $\Sigma_{2v}(2\pi/3)$-triplets. These triplets consist of three overlapping primary spheres, forming a bent structure…
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…
A toy model of particles packings is presented, which consists in arranging hexagons on a triangular lattice according to local stability rules. The number of stable packings is analytically computed and found to grow exponentially with the…
Photonic lanterns rely on a close packed arrangement of single mode fibers, which are tapered and fused into one multi-mode core. Topologically optimal circle packing arrangements have been well studied. Using this, we fabricate PLs with 19…
We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment and investigate the formation of particle clusters. In the presence of a hard-core interaction, cluster sizes exhibit an algebraically…
We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters.…
Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is `optimal' in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction $\phi_{\rm…
Sphere packings in high dimensions interest mathematicians and physicists and have direct applications in communications theory. Remarkably, no one has been able to provide exponential improvement on a 100-year-old lower bound on the…
We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{{\rm {\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing…
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such…
We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
In this paper we study the horoball packings related to the hyperbolic 24 cell in the extended hyperbolic space $\overline{\mathbf{H}}^4$ where we allow {\it horoballs in different types} centered at the various vertices of the 24 cell. We…
We adapt a construction of Klee (1981) to find a packing of unit balls in $\ell_p$ ($1\leq p<\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value…