Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics science. For equal spheres, it has only recently been proved that face-centered cubic lattice highest possible packing fraction phi=pi/18 approximately 0.74. It is also well known certain random (amorphous) jammed packings have phi 0.64. Here, we show experimentally with new simulation algorithm ellipsoids randomly pack more densely-up to phi= 0.68 0.71 for...

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using collision-driven packing generation algorithm, we obtain the first estimates for fractions maximally random (MRJ) states space dimensions d=4, 5, 6 to be phi(MRJ) approximately 0.46, 0.31, 0.20, respectively. To good approximation, MRJ density obeys scaling form phi(MRJ)=c1/2(d)+(c2d)/2d, where c1=-2.72 c2=2.56, which appears consistent with high-dimensional asymptotic...

In this Letter, we report on the densest-known packings of congruent ellipsoids. The family new consists crystal arrangements spheroids with a wide range aspect ratios, and density phi always surpassing that densest Bravais lattice packing approximately equal to 0.7405. A remarkable maximum 0.7707 is achieved for maximal ratios larger than sqrt[3], when each ellipsoid has 14 touching neighbors. Our results are directly relevant understanding equilibrium behavior systems hard ellipsoids, and,...

Continuing on recent computational and experimental work jammed packings of hard ellipsoids [Donev et al., Science 303, 990 (2004)] we consider jamming in smooth strictly convex nonspherical particles. We explain why an isocounting conjecture, which states that for large disordered the average contact number per particle is twice degrees freedom $(\overline{Z}=2{d}_{f})$, does not apply to develop first- second-order conditions demonstrate particles can be even though they are...

Composite materials are ideally suited to achieve multifunctionality since the best features of different can be combined form a new material that has broad spectrum desired properties. Nature's ultimate multifunctional composites biological materials. There presently no simple examples rigorously demonstrate effect competing property demands on composite microstructures. To illustrate fascinating types microstructures arise in optimization, we maximize simultaneous transport heat and...

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25:1:0.8 approach the densest crystal packing (fcc) of spheres, with a fraction 74%. We demonstrate such dense packings are realizable. introduce novel way determining density finite sample minimizes surface effects. have fabricated and show that, in sphere, radial phi(r) be obtained from V(h), volume added fluid to fill sphere height h. also obtain magnetic...

We computationally study jammed disordered hard-sphere packings as large a million particles. show that the are saturated and hyperuniform, i.e., local density fluctuations grow only logarithmically augmented surface area rather than volume of window. The structure factor shows an unusual nonanalytic linear dependence near origin, S(k) approximately |k|. In addition to exponentially damped oscillations seen in liquids, this implies weak power-law tail total correlation function, h(r) -r(-4),...

Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure granular media, liquids, living cells, glasses, random media. The nature “jammed” hard-particle is current subject keen interest. Elsewhere, we introduced rigorous efficient linear-programming algorithms assess whether hard-sphere packing locally, collectively, or strictly jammed, defined by Torquato Stillinger [J. Phys. Chem. B 105, 11849...

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The relies on formulation Ewald summation the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that real-space and wave-space contributions to tensor are independently symmetric positive-definite all possible particle configurations. drawn from superposition two independent samples: (far-field or long-ranged) contribution, computed using techniques fluctuating...

We develop a rigid multiblob method for numerically solving the mobility problem suspensions of passive and active particles complex shape in Stokes flow unconfined, partially confined, fully confined geometries.As number existing methods, we discretize bodies using collection minimally-resolved spherical blobs constrained to move as body, arrive at potentially large linear system equations unknown Lagrange multipliers rigid-body motions.Here block-diagonal preconditioner this show that...

We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization the fluid equations based on standard staggered-grid approach. Fluid-body interaction handled using Peskin's IB method; however, unlike existing approaches to such problems, we do not rely penalty fractional-step formulations. Instead, use unsplit scheme ensures no-slip...

Previous Monte Carlo investigations by Wojciechowski et al. have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase fourfold symmetry for squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and nonperiodic degenerate solid hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study system rectangles aspect ratio two, i.e., hard-square (or dominos), demonstrate that it exhibits with both these properties. The liquid shows...

We present an optimization method to design three-dimensional composite microstructures with multifunctional characteristics. To illustrate the fascinating types of that can arise in optimization, we apply our methodology study simultaneous transport heat and electricity three-dimensional, two-phase composites. assume phase 1 has a high thermal conductivity but low electrical 2 conductivity. The objective functions consist different combinations dimensionless effective conductivities. When...

We introduce numerical methods for simulating the diffusive motion of rigid bodies arbitrary shape immersed in a viscous fluid. parameterize orientation using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. construct system overdamped Langevin equations quaternion representation that accounts hydrodynamic effects, preserves unit-norm constraint on quaternion, is time reversible with respect Gibbs-Boltzmann distribution at equilibrium. two...

To overcome the reversible nature of low-Reynolds-number flow, a variety biomimetic microrobotic propulsion schemes and devices capable rapid transport have been developed. However, these approaches typically optimized for specific function or environment do not flexibility that many real organisms exhibit to thrive in complex microenvironments. Here, inspired by adaptable microbes using combination experiment simulation, we demonstrate one-dimensional colloidal chains can fold into...

Recent studies of random packing ellipsoids show a cusplike increase in the density as aspect ratio deviates from 1 (spheres) followed by maximum and then strong decrease at higher ratio. We introduce simple one-dimensional model, "Paris" parking problem with ellipses randomly oriented along curb, many same features. Our results suggest that cusp approaching terminal (jammed) state, relaxing parameter constraint (orientation or size particle) packing, excluded volume effects. also discuss...

We study the thermodynamics of a binary hard-disk mixture in which ratio disk diameters is kappa=1.4. use recently developed molecular dynamics algorithm to calculate free-volume entropy glassy configurations and obtain configurational (degeneracy) supercompressed liquid as function density. find that glasses near kinetic glass transition very close mixing entropy, suggesting degeneracy zero only for phase-separated crystal. explicitly construct an exponential number jammed packings with...

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles arbitrary shape suspended in a fluctuating fluid. Our method adds motion to the multiblob [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at cost comparable deterministic simulations. demonstrate that we can efficiently generate and random displacements using preconditioned Krylov iterative methods, if kernel compute action Rotne-Prager-Yamakawa (RPY) mobility...

We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension colloidal rollers sedimented above wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev and P. Chaikin, Nature Physics, 2016, doi:10.1038/nphys3970]. present stochastic Adams-Bashforth integrator the equations dynamics, which has same cost as but is more accurate than widely-used Euler-Maruyama scheme, uses random...