1,112 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
Classical many-particle systems with unique disordered ground states
Classical ground states (global energy-minimizing configurations) of
many-particle systems are typically unique crystalline structures, implying
zero enumeration entropy of distinct patterns (aside from trivial symmetry
operations). By contrast, the few previously known disordered classical ground
states of many-particle systems are all high-entropy (highly degenerate)
states. Here we show computationally that our recently-proposed "perfect-glass"
many-particle model [Sci. Rep., 6, 36963 (2016)] possesses disordered classical
ground states with a zero entropy: a highly counterintuitive situation. For all
of the system sizes, parameters, and space dimensions that we have numerically
investigated, the disordered ground states are unique such that they can always
be superposed onto each other or their mirror image. At low energies, the
density of states obtained from simulations matches those calculated from the
harmonic approximation near a single ground state, further confirming
ground-state uniqueness. Our discovery provides singular examples in which
entropy and disorder are at odds with one another. The zero-entropy ground
states provide a unique perspective on the celebrated Kauzmann-entropy crisis
in which the extrapolated entropy of a supercooled liquid drops below that of
the crystal. We expect that our disordered unique patterns to be of value in
fields beyond glass physics, including applications in cryptography as
pseudo-random functions with tunable computational complexity
Inverse Statistical Mechanics: Probing the Limitations of Isotropic Pair Potentials to Produce Ground-State Structural Extremes
Inverse statistical-mechanical methods have recently been employed to design
optimized short-ranged radial (isotropic) pair potentials that robustly produce
novel targeted classical ground-state many-particle configurations. The target
structures considered in those studies were low-coordinated crystals with a
high degree of symmetry. In this paper, we further test the fundamental
limitations of radial pair potentials by targeting crystal structures with
appreciably less symmetry, including those in which the particles have
different local structural environments. These challenging target
configurations demanded that we modify previous inverse optimization
techniques. Using this modified optimization technique, we have designed
short-ranged radial pair potentials that stabilize the two-dimensional kagome
crystal, the rectangular kagome crystal, and rectangular lattices, as well as
the three-dimensional structure of CaF crystal inhabited by a single
particle species. We verify our results by cooling liquid configurations to
absolute zero temperature via simulated annealing and ensuring that such states
have stable phonon spectra. Except for the rectangular kagome structure, all of
the target structures can be stabilized with monotonic repulsive potentials.
Our work demonstrates that single-component systems with short-ranged radial
pair potentials can counterintuitively self-assemble into crystal ground states
with low symmetry and different local structural environments. Finally, we
present general principles that offer guidance in determining whether certain
target structures can be achieved as ground states by radial pair potentials
Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
Disordered hyperuniform many-particle systems have attracted considerable
recent attention. One important class of such systems is the classical ground
states of "stealthy potentials." The degree of order of such ground states
depends on a tuning parameter. Previous studies have shown that these
ground-state point configurations can be counterintuitively disordered,
infinitely degenerate, and endowed with novel physical properties (e.g.,
negative thermal expansion behavior). In this paper, we focus on the disordered
regime in which there is no long-range order, and control the degree of
short-range order. We map these stealthy disordered hyperuniform point
configurations to two-phase media by circumscribing each point with a possibly
overlapping sphere of a common radius : the "particle" and "void" phases are
taken to be the space interior and exterior to the spheres, respectively. We
study certain transport properties of these systems, including the effective
diffusion coefficient of point particles diffusing in the void phase as well as
static and time-dependent characteristics associated with diffusion-controlled
reactions. Besides these effective transport properties, we also investigate
several related structural properties, including pore-size functions, quantizer
error, an order metric, and percolation threshold. We show that these
transport, geometrical and topological properties of our two-phase media
derived from decorated stealthy ground states are distinctly different from
those of equilibrium hard-sphere systems and spatially uncorrelated overlapping
spheres
Packing Hyperspheres in High-Dimensional Euclidean Spaces
We present the first study of disordered jammed hard-sphere packings in
four-, five- and six-dimensional Euclidean spaces. Using a collision-driven
packing generation algorithm, we obtain the first estimates for the packing
fractions of the maximally random jammed (MRJ) states for space dimensions
, 5 and 6 to be , 0.31 and 0.20, respectively. To
a good approximation, the MRJ density obeys the scaling form , where and , which appears to be
consistent with high-dimensional asymptotic limit, albeit with different
coefficients. Calculations of the pair correlation function and
structure factor for these states show that short-range ordering
appreciably decreases with increasing dimension, consistent with a recently
proposed ``decorrelation principle,'' which, among othe things, states that
unconstrained correlations diminish as the dimension increases and vanish
entirely in the limit . As in three dimensions (where ), the packings show no signs of crystallization, are isostatic,
and have a power-law divergence in at contact with power-law
exponent . Across dimensions, the cumulative number of neighbors
equals the kissing number of the conjectured densest packing close to where
has its first minimum. We obtain estimates for the freezing and
melting desnities for the equilibrium hard-sphere fluid-solid transition,
and , respectively, for , and
and , respectively, for .Comment: 28 pages, 9 figures. To appear in Physical Review
Non-Universality of Density and Disorder in Jammed Sphere Packings
We show for the first time that collectively jammed disordered packings of
three-dimensional monodisperse frictionless hard spheres can be produced and
tuned using a novel numerical protocol with packing density as low as
0.6. This is well below the value of 0.64 associated with the maximally random
jammed state and entirely unrelated to the ill-defined ``random loose packing''
state density. Specifically, collectively jammed packings are generated with a
very narrow distribution centered at any density over a wide density
range with variable disorder. Our results
support the view that there is no universal jamming point that is
distinguishable based on the packing density and frequency of occurence. Our
jammed packings are mapped onto a density-order-metric plane, which provides a
broader characterization of packings than density alone. Other packing
characteristics, such as the pair correlation function, average contact number
and fraction of rattlers are quantified and discussed.Comment: 19 pages, 4 figure
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