179 research outputs found
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
Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
Systems of particles interacting with "stealthy" pair potentials have been
shown to possess infinitely degenerate disordered hyperuniform classical ground
states with novel physical properties. Previous attempts to sample the
infinitely degenerate ground states used energy minimization techniques,
introducing algorithmic dependence that is artificial in nature. Recently, an
ensemble theory of stealthy hyperuniform ground states was formulated to
predict the structure and thermodynamics that was shown to be in excellent
agreement with corresponding computer simulation results in the canonical
ensemble (in the zero-temperature limit). In this paper, we provide details and
justifications of the simulation procedure, which involves performing molecular
dynamics simulations at sufficiently low temperatures and minimizing the energy
of the snapshots for both the high-density disordered regime, where the theory
applies, as well as lower densities. We also use numerical simulations to
extend our study to the lower-density regime. We report results for the pair
correlation functions, structure factors, and Voronoi cell statistics. In the
high-density regime, we verify the theoretical ansatz that stealthy disordered
ground states behave like "pseudo" disordered equilibrium hard-sphere systems
in Fourier space. These results show that as the density decreases from the
high-density limit, the disordered ground states in the canonical ensemble are
characterized by an increasing degree of short-range order and eventually the
system undergoes a phase transition to crystalline ground states. We also
provide numerical evidence suggesting that different forms of stealthy pair
potentials produce the same ground-state ensemble in the zero-temperature
limit. Our techniques may be applied to sample this limit of the canonical
ensemble of other potentials with highly degenerate ground states
Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases
Stealthy potentials, a family of long-range isotropic pair potentials,
produce infinitely degenerate disordered ground states at high densities and
crystalline ground states at low densities in d-dimensional Euclidean space
R^d. In the previous paper in this series, we numerically studied the
entropically favored ground states in the canonical ensemble in the
zero-temperature limit across the first three Euclidean space dimensions. In
this paper, we investigate using both numerical and theoretical techniques
metastable stacked-slider phases, which are part of the ground-state manifold
of stealthy potentials at densities in which crystal ground states are favored
entropically. Our numerical results enable us to devise analytical models of
this phase in two, three, and higher dimensions. Utilizing this model, we
estimated the size of the feasible region in configuration space of the
stacked-slider phase, finding it to be smaller than that of crystal structures
in the infinite-system-size limit, which is consistent with our recent previous
work. In two dimensions, we also determine exact expressions for the pair
correlation function and structure factor of the analytical model of
stacked-slider phases and analyze the connectedness of the ground-state
manifold of stealthy potentials in this density regime. We demonstrate that
stacked-slider phases are distinguishable states of matter; they are
nonperiodic, statistically anisotropic structures that possess long-range
orientational order but have zero shear modulus. We outline some possible
future avenues of research to elucidate our understanding of this unusual phase
of matter
Negative thermal expansion in single-component systems with isotropic interactions
We have devised an isotropic interaction potential that gives rise to
negative thermal expansion (NTE) behavior in equilibrium many-particle systems
in both two and three dimensions over a wide temperature and pressure range
(including zero pressure). An optimization procedure is used in order to find a
potential that yields a strong NTE effect. A key feature of the potential that
gives rise to this behavior is the softened interior of its basin of
attraction. Although such anomalous behavior is well known in material systems
with directional interactions (e.g., zirconium tungstate), to our knowledge
this is the first time that NTE behavior has been established to occur in
single-component many-particle systems for isotropic interactions. Using
constant-pressure Monte Carlo simulations, we show that as the temperature is
increased, the system exhibits negative, zero and then positive thermal
expansion before melting (for both two- and three-dimensional systems). The
behavior is explicitly compared to that of a Lennard-Jones system, which
exhibits typical expansion upon heating for all temperatures and pressures.Comment: 21 pages, 13 figure
Scaled Particle Theory for Hard Sphere Pairs. II. Numerical Analysis
We use the extension of scaled particle theory (ESPT) presented in the
accompanying paper [Stillinger et al. J. Chem. Phys. xxx, xxx (2007)] to
calculate numerically pair correlation function of the hard sphere fluid over
the density range . Comparison with computer
simulation results reveals that the new theory is able to capture accurately
the fluid's structure across the entire density range examined. The pressure
predicted via the virial route is systematically lower than simulation results,
while that obtained using the compressibility route is lower than simulation
predictions for and higher than simulation predictions
for . Numerical predictions are also presented for the
surface tension and Tolman length of the hard sphere fluid
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