Is random close packing of spheres well defined?
نویسندگان
چکیده
Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally random jammed state, which can be made precise.
منابع مشابه
Universality of Random Close Packing ?
In 1611 Kepler proposed that the densest packing of spheres could be achieved by stacking close-packed planes of spheres. In such a packing, the spheres occupy π/ √ 18 ≈74.05% of space. The Kepler conjecture was (almost certainly) proved in 1998 by Thomas Hales. When we pour a large number of equal-sized spheres in a container and shake them down, we do not obtain the Kepler packing. Rather a d...
متن کاملViewpoint The tetrahedral dice are cast . . . and pack densely
Tetrahedra are special among the platonic solids. They are the simplest polyhedra and the ones most unlike spheres. Surprisingly, much of our knowledge about the packing properties of tetrahedra is very recent: the past year has witnessed a sudden proliferation of novel, and often surprising, findings. Using Monte Carlo simulations, Haji-Akbari et al.[1] found that, upon compression, systems of...
متن کاملThe simplest model of jamming
The packing fraction ρ of a collection of hard spheres in three dimension cannot exceed a maximum of about 0.74. In that limit, the spheres are arranged in a close-packed crystalline lattice (such as the HCP lattice). If, however, a loose collection of hard spheres is compactified, starting from some random initial condition, then the maximum packing fraction ρc that can be achieved by compacti...
متن کاملPushing the glass transition towards random close packing using self-propelled hard spheres.
Although the concept of random close packing with an almost universal packing fraction of approximately 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest packing is that states with packing fractions beyond the glass transition at approximately 0.58 are inherently non-equilibrium systems, where the dy...
متن کاملMean nearest-neighbor distance in random packings of hard D-dimensional spheres.
We derive the first nontrivial rigorous bounds on the mean distance between nearest neighbors l in ergodic, isotropic packings of hard D-dimensional spheres that depend on the packing fraction and nearest-neighbor distribution function. Several interesting implications of these bounds for equilibrium as well as nonequilibrium ensembles are explored. For an equilibrium ensemble, we find accurate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review letters
دوره 84 10 شماره
صفحات -
تاریخ انتشار 2000