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Hard sphere packings within cylinders  [PDF]
Lin Fu,William Steinhardt,Hao Zhao,Joshua E. S. Socolar,Patrick Charbonneau
Physics , 2015,
Abstract: The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement, however, grows increasingly complex with the cylinder diameter, $D$. Little is thus known about the densest achievable packings for $D>2.873\sigma$. In this work, we extend the identification of the packings up to $D=4.00\sigma$ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond $D\approx2.85\sigma$, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.
Circles, Spheres and Drops Packings  [PDF]
Tomaso Aste
Physics , 1997, DOI: 10.1103/PhysRevE.53.2571
Abstract: 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: $N(R) \propto R^{-\alpha}$. We obtained an approximate expression which relates the exponent $\alpha$ to the average coordination number and to the packing strategy. In the case of disordered packings (where the circles have random sizes and positions) we found the upper bound $\alpha_{Max} = 2$. The results obtained for circles-packing was extended to packing of spheres and hyper-spheres in spaces of arbitrary dimension D. We found that the size distribution of dense packed polydisperse $D$-spheres, follows -as in the two dimensional case- a power law, where the exponent $\alpha$ depends on the packing strategy. In particular, in the case of disordered packing, we obtained the upper bound $\alpha_{Max}=D$. Circle-covering generated by computer simulations, gives size distributions that are in agreement with these analytical predictions. Tin drops generated by vapour deposition on a hot substrate form breath figures where the drop-size distributions are power laws with exponent $\alpha \simeq 2$. We pointed out the similarity between these structures and the circle-packings. Despite the complicated mechanism of formation of these structures, we showed that it is possible to describe the drops arrangements, the size distribution and the evolution at constant coverage, in term of maximum packing of circles regulated by coalescence.
SPATIAL STATISTICS FOR SIMULATED PACKINGS OF SPHERES
Alexander Bezrukov,Dietrich Stoyan,Monika Bargie?
Image Analysis and Stereology , 2001, DOI: 10.5566/ias.v20.p203-206
Abstract: This paper reports on spatial-statistical analyses for simulated random packings of spheres with random diameters. The simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm. The sphere diameters are taken as constant or following a bimodal or lognormal distribution. Standard characteristics of spatial statistics are used to describe these packings statistically, namely volume fraction, pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretic union of all spheres. Furthermore, the coordination numbers are analysed.
Loose packings of frictional spheres  [PDF]
Greg R. Farrell,K. Michael Martini,Narayanan Menon
Physics , 2010, DOI: 10.1039/C0SM00038H
Abstract: We have produced loose packings of cohesionless, frictional spheres by sequential deposition of highly-spherical, monodisperse particles through a fluid. By varying the properties of the fluid and the particles, we have identified the Stokes number (St) - rather than the buoyancy of the particles in the fluid - as the parameter controlling the approach to the loose packing limit. The loose packing limit is attained at a threshold value of St at which the kinetic energy of a particle impinging on the packing is fully dissipated by the fluid. Thus, for cohesionless particles, the dynamics of the deposition process, rather than the stability of the static packing, defines the random loose packing limit. We have made direct measurements of the interparticle friction in the fluid, and present an experimental measurement of the loose packing volume fraction, \phi_{RLP}, as a function of the friction coefficient \mu_s.
Holographic characterization of imperfect colloidal spheres  [PDF]
Mark Hannel,Christine Middleton,David G. Grier
Physics , 2015, DOI: 10.1063/1.4932948
Abstract: We demonstrate precise measurements of the size and refractive index of individual dimpled colloidal spheres using holographic characterization techniques developed for ideal spheres.
Upper bounds for packings of spheres of several radii  [PDF]
David de Laat,Fernando Mario de Oliveira Filho,Frank Vallentin
Mathematics , 2012, DOI: 10.1017/fms.2014.24
Abstract: We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds for packings of spherical caps and of convex bodies through the use of semidefinite programming. We perform explicit computations, obtaining new bounds for packings of spherical caps of two different sizes and for binary sphere packings. We also slightly improve bounds for the classical problem of packing identical spheres.
Tetrahedral colloidal clusters from random parking of bidisperse spheres  [PDF]
Nicholas B. Schade,Miranda C. Holmes-Cerfon,Elizabeth R. Chen,Dina Aronzon,Jesse W. Collins,Jonathan A. Fan,Federico Capasso,Vinothan N. Manoharan
Physics , 2012, DOI: 10.1103/PhysRevLett.110.148303
Abstract: Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to -- or "park" on -- smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA sequences, and we vary the ratio $\alpha$ of large to small sphere radii. Once bound, the large spheres cannot rearrange, and thus the clusters do not form dense or symmetric packings. Nevertheless, this stochastic aggregation process yields a remarkably narrow distribution of clusters with nearly 90% tetrahedra at $\alpha=2.45$. The high yield of tetrahedra, which reaches 100% in simulations at $\alpha=2.41$, arises not simply because of packing constraints, but also because of the existence of a long-time lower bound that we call the "minimum parking" number. We derive this lower bound from solutions to the classic mathematical problem of spherical covering, and we show that there is a critical size ratio $\alpha_c=(1+\sqrt{2})\approx 2.41$, close to the observed point of maximum yield, where the lower bound equals the upper bound set by packing constraints. The emergence of a critical value in a random aggregation process offers a robust method to assemble uniform clusters for a variety of applications, including metamaterials.
Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres  [PDF]
Remi Dreyfus,Ye Xu,Tim Still,Lawrence A. Hough,A. G. Yodh,Salvatore Torquato
Physics , 2014, DOI: 10.1103/PhysRevE.91.012302
Abstract: Hyperuniformity characterizes a state of matter for which density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the detrimental effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize free volume. In addition, simulations show that hyperuniformity can be ascertained more accurately in direct space than in reciprocal space as a result of finite sample-size. Finally, experimental colloidal packings of soft polymeric spheres are shown to be hyperuniform.
Bridges in three-dimensional granular packings: experiments and simulations  [PDF]
Yixin Cao,Bandan Chakrabortty,G. C. Barker,Anita Mehta,Yujie Wang
Physics , 2011, DOI: 10.1209/0295-5075/102/24004
Abstract: In this letter, we present the first experimental study of bridge structures in three-dimensional dry granular packings. When bridges are small, they are predominantly 'linear', and have an exponential size distribution. Larger, predominantly 'complex' bridges, are confirmed to follow a power-law size distribution. Our experiments, which use X-ray tomography, are in good agreement with the simulations presented here, for the distribution of sizes, end-to-end lengths, base extensions and orientations of predominantly linear bridges. Quantitative differences between the present experiment and earlier simulations suggest that packing fraction is an important determinant of bridge structure.
Confined packings of frictionless spheres and polyhedra  [PDF]
Jean-Fran?ois Camenen,Yannick Descantes,Patrick Richard
Physics , 2013, DOI: 10.1063/1.4811932
Abstract: By means of numerical simulations, we study the influence of confinement on three-dimensional random close packed (RCP) granular materials subject to gravity. The effects of grain shape (spherical or polyhedral) and polydispersity on this dependence are investigated. In agreement with a simple geometrical model, the solid fraction is found to decrease linearly for increasing confinement no matter the grain shape. This decrease remains valid for bidisperse sphere packings although the gradient seems to reduce significantly when the proportion of small particles reaches 40% by volume. The aforementioned model is extended to capture the effect of the confinement on the coordination number.
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