arXiv subjects

Aleksandar Donev

Publications and source records attributed to Aleksandar Donev.

39 records · Page 3Linked to original sources

arXiv2004

Superdense Crystal Packings of Ellipsoids

Particle packing problems have fascinated people since the dawn of civilization, and continue to intrigue mathematicians and scientists. Resurgent interest has been spurred by the recent proof of Kepler's conjecture: the face-centered cubic lattice provides the densest packing of equal spheres with a packing fraction $ϕ\approx0.7405$ \cite{Kepler_Hales}. Here we report on the densest known packings of congruent ellipsoids. The family of new packings are crystal (periodic) arrangements of nearly spherically-shaped ellipsoids, and always surpass the densest lattice packing. A remarkable maximum density of $ϕ\approx0.7707$ is achieved for both prolate and oblate ellipsoids with aspect ratios of $\sqrt{3}$ and $1/\sqrt{3}$, respectively, and each ellipsoid has 14 touching neighbors. Present results do not exclude the possibility that even denser crystal packings of ellipsoids could be found, and that a corresponding Kepler-like conjecture could be formulated for ellipsoids.

cond-mat.stat-mech↗

arXiv2002

A Linear Programming Algorithm to Test for Jamming in Hard-Sphere Packings

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B, 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze an equivalent contact network of the packing under applied displacements, but leave the design of such algorithms as a future task. In this work we present a rigorous and efficient algorithm to assess whether a hard-sphere packing is jammed according to the afformentioned categories. The algorithm is based on linear programming and is applicable to regular as well as random packings of finite size with hard-wall and periodic boundary conditions. If the packing is not jammed, the algorithm yields representative multi-particle unjamming motions. We have implemented this algorithm and applied it to ordered lattices as well as random packings of disks and spheres under periodic boundary conditions. Some representative results for ordered and disordered packings are given, but more applications are anticipated for the future. One important and interesting result is that the random packings that we tested were strictly jammed in three dimensions, but not in two dimensions. Numerous interactive visualization models are provided on the authors' webpage.

cond-mat.mtrl-sci↗

arXiv1998

Generalized von Smoluchowski model of reaction rates, with reacting particles and a mobile trap

We study diffusion-limited coalescence, A+A<-->A, in one dimension, in the presence of a diffusing trap. The system may be regarded as a generalization of von Smoluchowski's model for reaction rates, in that: (a) it includes reactions between the particles surrounding the trap, and (b) the trap is mobile -- both considerations which render the model more physically relevant. As seen from the trap's frame of reference, the motion of the particles is highly correlated, because of the motion of the trap. An exact description of the long -time asymptotic limit is found using the IPDF method, and exploiting a "shielding" property of reversible coalescence that was discovered recently. In the case where the trap also acts as a source -- giving birth to particles -- the shielding property breaks down, but we find an "equivalence principle": Trapping and diffusion of the trap may be compensated by an appropriate rate of birth, such that the steady state of the system is identical with the equilibrium state in the absence of a trap.

cond-mat.stat-mech↗