17,206 research outputs found
Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
Hyperuniform many-particle distributions possess a local number variance that
grows more slowly than the volume of an observation window, implying that the
local density is effectively homogeneous beyond a few characteristic length
scales. Previous work on maximally random strictly jammed sphere packings in
three dimensions has shown that these systems are hyperuniform and possess
unusual quasi-long-range pair correlations, resulting in anomalous logarithmic
growth in the number variance. However, recent work on maximally random jammed
sphere packings with a size distribution has suggested that such
quasi-long-range correlations and hyperuniformity are not universal among
jammed hard-particle systems. In this paper we show that such systems are
indeed hyperuniform with signature quasi-long-range correlations by
characterizing the more general local-volume-fraction fluctuations. We argue
that the regularity of the void space induced by the constraints of saturation
and strict jamming overcomes the local inhomogeneity of the disk centers to
induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic
behavior in the spectral density, resulting in quasi-long-range spatial
correlations. A numerical and analytical analysis of the pore-size distribution
for a binary MRJ system in addition to a local characterization of the
n-particle loops governing the void space surrounding the inclusions is
presented in support of our argument. This paper is the first part of a series
of two papers considering the relationships among hyperuniformity, jamming, and
regularity of the void space in hard-particle packings.Comment: 40 pages, 15 figure
Simulation studies of a phenomenological model for elongated virus capsid formation
We study a phenomenological model in which the simulated packing of hard,
attractive spheres on a prolate spheroid surface with convexity constraints
produces structures identical to those of prolate virus capsid structures. Our
simulation approach combines the traditional Monte Carlo method with a modified
method of random sampling on an ellipsoidal surface and a convex hull searching
algorithm. Using this approach we identify the minimum physical requirements
for non-icosahedral, elongated virus capsids, such as two aberrant flock house
virus (FHV) particles and the prolate prohead of bacteriophage , and
discuss the implication of our simulation results in the context of recent
experimental findings. Our predicted structures may also be experimentally
realized by evaporation-driven assembly of colloidal spheres
Fractal free energy landscapes in structural glasses
Glasses are amorphous solids whose constituent particles are caged by their
neighbors and thus cannot flow. This sluggishness is often ascribed to the free
energy landscape containing multiple minima (basins) separated by high
barriers. Here we show, using theory and numerical simulation, that the
landscape is much rougher than is classically assumed. Deep in the glass, it
undergoes a "roughness transition" to fractal basins. This brings about
isostaticity at jamming and marginality of glassy states near jamming. Critical
exponents for the basin width, the weak force distribution, and the spatial
spread of quasi-contacts at jamming can be analytically determined. Their value
is found to be compatible with numerical observations. This advance therefore
incorporates the jamming transition of granular materials into the framework of
glass theory. Because temperature and pressure control which features of the
landscape are experienced, glass mechanics and transport are expected to
reflect the features of the topology we discuss here. Hitherto mysterious
properties of low-temperature glasses could be explained by this approach.Comment: 13 pages, 4 figures. This version was initially submitted to Nature
Communications in December 2013. The (much improved) final version is
available on the Nature Communications website (see DOI below). A detailed
version of this work is available on arXiv:1310.254
Self Assembled Clusters of Spheres Related to Spherical Codes
We consider the thermodynamically driven self-assembly of spheres onto the
surface of a central sphere. This assembly process forms self-limiting, or
terminal, anisotropic clusters (N-clusters) with well defined structures. We
use Brownian dynamics to model the assembly of N-clusters varying in size from
two to twelve outer spheres, and free energy calculations to predict the
expected cluster sizes and shapes as a function of temperature and inner
particle diameter. We show that the arrangements of outer spheres at finite
temperatures are related to spherical codes, an ideal mathematical sequence of
points corresponding to densest possible sphere packings. We demonstrate that
temperature and the ratio of the diameters of the inner and outer spheres
dictate cluster morphology and dynamics. We find that some N-clusters exhibit
collective particle rearrangements, and these collective modes are unique to a
given cluster size N. We present a surprising result for the equilibrium
structure of a 5-cluster, which prefers an asymmetric square pyramid
arrangement over a more symmetric arrangement. Our results suggest a promising
way to assemble anisotropic building blocks from constituent colloidal spheres.Comment: 15 pages, 10 figure
Stable Frank-Kasper phases of self-assembled, soft matter spheres
Single molecular species can self-assemble into Frank Kasper (FK) phases,
finite approximants of dodecagonal quasicrystals, defying intuitive notions
that thermodynamic ground states are maximally symmetric. FK phases are
speculated to emerge as the minimal-distortional packings of space-filling
spherical domains, but a precise quantitation of this distortion and how it
affects assembly thermodynamics remains ambiguous. We use two complementary
approaches to demonstrate that the principles driving FK lattice formation in
diblock copolymers emerge directly from the strong-stretching theory of
spherical domains, in which minimal inter-block area competes with minimal
stretching of space-filling chains. The relative stability of FK lattices is
studied first using a diblock foam model with unconstrained particle volumes
and shapes, which correctly predicts not only the equilibrium {\sigma} lattice,
but also the unequal volumes of the equilibrium domains. We then provide a
molecular interpretation for these results via self-consistent field theory,
illuminating how molecular stiffness regulates the coupling between
intra-domain chain configurations and the asymmetry of local packing. These
findings shed new light on the role of volume exchange on the formation of
distinct FK phases in copolymers, and suggest a paradigm for formation of FK
phases in soft matter systems in which unequal domain volumes are selected by
the thermodynamic competition between distinct measures of shape asymmetry.Comment: 40 pages, 22 figure
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