328 research outputs found
Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter
Local structure characterization with the bond-orientational order parameters
q4, q6, ... introduced by Steinhardt et al. has become a standard tool in
condensed matter physics, with applications including glass, jamming, melting
or crystallization transitions and cluster formation. Here we discuss two
fundamental flaws in the definition of these parameters that significantly
affect their interpretation for studies of disordered systems, and offer a
remedy. First, the definition of the bond-orientational order parameters
considers the geometrical arrangement of a set of neighboring spheres NN(p)
around a given central particle p; we show that procedure to select the spheres
constituting the neighborhood NN(p) can have greater influence on both the
numerical values and qualitative trend of ql than a change of the physical
parameters, such as packing fraction. Second, the discrete nature of
neighborhood implies that NN(p) is not a continuous function of the particle
coordinates; this discontinuity, inherited by ql, leads to a lack of robustness
of the ql as structure metrics. Both issues can be avoided by a morphometric
approach leading to the robust Minkowski structure metrics ql'. These ql' are
of a similar mathematical form as the conventional bond-orientational order
parameters and are mathematically equivalent to the recently introduced
Minkowski tensors [Europhys. Lett. 90, 34001 (2010); Phys. Rev. E. 85, 030301
(2012)]
Jammed Spheres: Minkowski Tensors Reveal Onset of Local Crystallinity
The local structure of disordered jammed packings of monodisperse spheres
without friction, generated by the Lubachevsky-Stillinger algorithm, is studied
for packing fractions above and below 64%. The structural similarity of the
particle environments to fcc or hcp crystalline packings (local crystallinity)
is quantified by order metrics based on rank-four Minkowski tensors. We find a
critical packing fraction \phi_c \approx 0.649, distinctly higher than
previously reported values for the contested random close packing limit. At
\phi_c, the probability of finding local crystalline configurations first
becomes finite and, for larger packing fractions, increases by several orders
of magnitude. This provides quantitative evidence of an abrupt onset of local
crystallinity at \phi_c. We demonstrate that the identification of local
crystallinity by the frequently used local bond-orientational order metric q_6
produces false positives, and thus conceals the abrupt onset of local
crystallinity. Since the critical packing fraction is significantly above
results from mean-field analysis of the mechanical contacts for frictionless
spheres, it is suggested that dynamic arrest due to isostaticity and the
alleged geometric phase transition in the Edwards framework may be disconnected
phenomena
Local Anisotropy of Fluids using Minkowski Tensors
Statistics of the free volume available to individual particles have
previously been studied for simple and complex fluids, granular matter,
amorphous solids, and structural glasses. Minkowski tensors provide a set of
shape measures that are based on strong mathematical theorems and easily
computed for polygonal and polyhedral bodies such as free volume cells (Voronoi
cells). They characterize the local structure beyond the two-point correlation
function and are suitable to define indices of
local anisotropy. Here, we analyze the statistics of Minkowski tensors for
configurations of simple liquid models, including the ideal gas (Poisson point
process), the hard disks and hard spheres ensemble, and the Lennard-Jones
fluid. We show that Minkowski tensors provide a robust characterization of
local anisotropy, which ranges from for vapor
phases to for ordered solids. We find that for fluids,
local anisotropy decreases monotonously with increasing free volume and
randomness of particle positions. Furthermore, the local anisotropy indices
are sensitive to structural transitions in these simple
fluids, as has been previously shown in granular systems for the transition
from loose to jammed bead packs
Minkowski Tensors of Anisotropic Spatial Structure
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
Gel-Electrophoresis and Diffusion of Ring-Shaped DNA
A model for the motion of ring-shaped DNA in a gel is introduced and studied
by numerical simulations and a mean-field approximation. The ring motion is
mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion
around the gel obstructions. This constitutes an extension of previous
reptation tube treatments. It is shown that tension is essential for describing
the dynamics in the presence of hernias. It is included in the model as long
range interactions over stretched DNA regions. The mobility of ring-shaped DNA
is found to saturate much as in the well-studied case of linear DNA.
Experiments in polymer gels, however, show that the mobility drops
exponentially with the DNA ring size. This is commonly attributed to
dangling-ends in the gel that can impale the ring. The predictions of the
present model are expected to apply to artificial 2D obstacle arrays (W.D.
Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In
the zero-field case an exact solution of the model steady-state is obtained,
and quantities such as the average ring size are calculated. An approximate
treatment of the ring dynamics is given, and the diffusion coefficient is
derived. The model is also discussed in the context of spontaneous symmetry
breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres
Worldwide Relationships in the Fern Genus Pteridium (Bracken) Based on Nuclear Genome Markers
PREMISE: Spore-bearing plants are capable of dispersing very long distances. However, it is not known if gene flow can prevent genetic divergence in widely distributed taxa. Here we address this issue, and examine systematic relationships at a global geographic scale for the fern genus Pteridium.
METHODS: We sampled plants from 100 localities worldwide, and generated nucleotide data from four nuclear genes and two plastid regions. We also examined 2801 single nucleotide polymorphisms detected by a restriction site-associated DNA approach.
RESULTS: We found evidence for two distinct diploid species and two allotetraploids between them. The “northern” species (Pteridium aquilinum) has distinct groups at the continental scale (Europe, Asia, Africa, and North America). The northern European subspecies pinetorum appears to involve admixture among all of these. A sample from the Hawaiian Islands contained elements of both North American and Asian P. aquilinum. The “southern” species, P. esculentum, shows little genetic differentiation between South American and Australian samples. Components of African genotypes are detected on all continents.
CONCLUSIONS: We find evidence of distinct continental-scale genetic differentiation in Pteridium. However, on top of this is a clear signal of recent hybridization. Thus, spore-bearing plants are clearly capable of extensive long-distance gene flow; yet appear to have differentiated genetically at the continental scale. Either gene flow in the past was at a reduced level, or vicariance is possible even in the face of long-distance gene flow
Cell shape analysis of random tessellations based on Minkowski tensors
To which degree are shape indices of individual cells of a tessellation
characteristic for the stochastic process that generates them? Within the
context of stochastic geometry and the physics of disordered materials, this
corresponds to the question of relationships between different stochastic
models. In the context of image analysis of synthetic and biological materials,
this question is central to the problem of inferring information about
formation processes from spatial measurements of resulting random structures.
We address this question by a theory-based simulation study of shape indices
derived from Minkowski tensors for a variety of tessellation models. We focus
on the relationship between two indices: an isoperimetric ratio of the
empirical averages of cell volume and area and the cell elongation quantified
by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for
these quantities, as well as for distributions thereof and for correlations of
cell shape and volume, are presented for Voronoi mosaics of the Poisson point
process, determinantal and permanental point processes, and Gibbs hard-core and
random sequential absorption processes as well as for Laguerre tessellations of
polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data
are complemented by mechanically stable crystalline sphere and disordered
ellipsoid packings and area-minimising foam models. We find that shape indices
of individual cells are not sufficient to unambiguously identify the generating
process even amongst this limited set of processes. However, we identify
significant differences of the shape indices between many of these tessellation
models. Given a realization of a tessellation, these shape indices can narrow
the choice of possible generating processes, providing a powerful tool which
can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense
Criptógamos do Parque Estadual das Fontes do Ipiranga, São Paulo, SP: Pteridophyta: 21. Tectariaceae
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