We provide suucient conditions for packing two hypergraphs. The emphasis is on the asymptotic case when one of the hypergraphs has a bounded degree and the other is dense. As an application, we give an alternative proof for the bipartite case of the recently developed Blow-up Lemma 12].

We consider the problem of constructing dense lattices of Rn with a given non trivial automorphism group. We exhibit a family of such lattices of density at least cn2−n, which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions n, we exhibit a finite set of lattices that come with an automorphism group of size n, and a co...

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London) 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space R(d). W...

We studied the geometrical and topological rules underlying the dispositions and the size distribution of non– overlapping, polydisperse circle–packings. We found that the size distribution of circles that densely cover a plane follows the power law: N(R) ∝ R. We obtained an approximate expression which relates the exponent α to the average coordination number and to the packing strategy. In th...

This paper reports on the structural studies of 3–phenyl propyl and 9–benzyloxynonanyl self–assembled monolayers (SAMs) on Si(100). Surface compositional analysis of both SAMs reveal they are robust and do not undergo oxidation over extended periods. Scanning tunneling microscopy reveals that both SAMs exhibit dense layers which is attributed to the π−π stacking between the phenyl rings. The C9...

The spatially resolved diffusive dynamic cross correlations of a pair of colloids in dense quasi-two-dimensional monolayers of identical particles are studied experimentally and theoretically at early times where motion is Fickian. In very dense systems where strong oscillatory equilibrium packing correlations are present, we find an exponential decay of the dynamic cross correlations on small ...

The dense packing observed in protein interiors appears to be crucial for stabilizing the native structure--even subtle internal substitutions are usually destabilizing. Thus, steric complementarity of core residues is thought to be an important criterion for "inverse folding" predictive methods, which judge whether a newly determined sequence is consistent with any known folds. A major problem...

Dense packings of nonoverlapping bodies in three-dimensional Euclidean space R(3) are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing behavior of congruent ring tori in R(3), which are multiply connected nonconvex bodies of genus 1, as well as horn and spindle tori. Specifically, we analytic...

This paper investigates the validity of azimuthal averaging 3D temperature fields in analysis lateral heat transfer dense particle packings. is conducted by synthetic generation packing surrogates spheres, cylinders and Raschig rings with tube-to-pellet diameter ratio, 3 < N 6, using an in-house Rigid Body Dynamics algorithm, followed detailed discrete pellet CFD simulations from wall to bed fo...