2,636 research outputs found
Controlling the Short-Range Order and Packing Densities of Many-Particle Systems
Questions surrounding the spatial disposition of particles in various
condensed-matter systems continue to pose many theoretical challenges. This
paper explores the geometric availability of amorphous many-particle
configurations that conform to a given pair correlation function g(r). Such a
study is required to observe the basic constraints of non-negativity for g(r)
as well as for its structure factor S(k). The hard sphere case receives special
attention, to help identify what qualitative features play significant roles in
determining upper limits to maximum amorphous packing densities. For that
purpose, a five-parameter test family of g's has been considered, which
incorporates the known features of core exclusion, contact pairs, and damped
oscillatory short-range order beyond contact. Numerical optimization over this
five-parameter set produces a maximum-packing value for the fraction of covered
volume, and about 5.8 for the mean contact number, both of which are within the
range of previous experimental and simulational packing results. However, the
corresponding maximum-density g(r) and S(k) display some unexpected
characteristics. A byproduct of our investigation is a lower bound on the
maximum density for random sphere packings in dimensions, which is sharper
than a well-known lower bound for regular lattice packings for d >= 3.Comment: Appeared in Journal of Physical Chemistry B, vol. 106, 8354 (2002).
Note Errata for the journal article concerning typographical errors in Eq.
(11) can be found at http://cherrypit.princeton.edu/papers.html However, the
current draft on Cond-Mat (posted on August 8, 2002) is correct
Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function
Dynamical signatures are known to precede jamming in hard-particle systems,
but static structural signatures have proven more elusive. The observation that
compressing hard-particle packings towards jamming causes growing
hyperuniformity has paved the way for the analysis of jamming as an "inverted
critical point" in which the direct correlation function diverges. We
establish quantitative relationships between various singularities in
and the total correlation function that provide a concrete means of
identifying features that must be expressed in if one hopes to reproduce
details in the pair correlation function accurately. We also analyze systems of
three-dimensional monodisperse hard-spheres of diameter as they approach
ordered and disordered jammed configurations. For the latter, we use the
Lubachevsky-Stillinger (LS) and Torquato-Jiao (TJ) packing algorithms, which
both generate disordered packings, but can show perceptible structural
differences. We identify a short-ranged scaling as and show that this, along with the developing delta function at
, is a consequence of the growing long-rangedness in . Near the
freezing density, we identify qualitative differences in the structure factor
as well as between TJ- and LS-generated configurations and link
them to differences in the protocols' packing dynamics. Configurations from
both algorithms have structure factors that approach zero in the low-wavenumber
limit as jamming is approached and are shown to exhibit a corresponding
power-law decay in for large as a consequence. Our work advances the
notion that static signatures are exhibited by hard-particle packings as they
approach jamming and underscores the utility of the direct correlation function
as a means of monitoring for an incipient rigid network
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