535 research outputs found
Stochastic reconstruction of sandstones
A simulated annealing algorithm is employed to generate a stochastic model
for a Berea and a Fontainebleau sandstone with prescribed two-point probability
function, lineal path function, and ``pore size'' distribution function,
respectively. We find that the temperature decrease of the annealing has to be
rather quick to yield isotropic and percolating configurations. A comparison of
simple morphological quantities indicates good agreement between the
reconstructions and the original sandstones. Also, the mean survival time of a
random walker in the pore space is reproduced with good accuracy. However, a
more detailed investigation by means of local porosity theory shows that there
may be significant differences of the geometrical connectivity between the
reconstructed and the experimental samples.Comment: 12 pages, 5 figure
Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
We have formulated the problem of generating periodic dense paritcle packings
as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation
[S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the
objective function and impenetrability constraints can be exactly linearized
for sphere packings with a size distribution in -dimensional Euclidean space
, it is most suitable and natural to solve the corresponding ASC
optimization problem using sequential linear programming (SLP) techniques. We
implement an SLP solution to produce robustly a wide spectrum of jammed sphere
packings in for and with a diversity of disorder
and densities up to the maximally densities. This deterministic algorithm can
produce a broad range of inherent structures besides the usual disordered ones
with very small computational cost by tuning the radius of the {\it influence
sphere}. In three dimensions, we show that it can produce with high probability
a variety of strictly jammed packings with a packing density anywhere in the
wide range . We also apply the algorithm to generate various
disordered packings as well as the maximally dense packings for
and 6. Compared to the LS procedure, our SLP protocol is able to ensure that
the final packings are truly jammed, produces disordered jammed packings with
anomalously low densities, and is appreciably more robust and computationally
faster at generating maximally dense packings, especially as the space
dimension increases.Comment: 34 pages, 6 figure
Geometrical Ambiguity of Pair Statistics. I. Point Configurations
Point configurations have been widely used as model systems in condensed
matter physics, materials science and biology. Statistical descriptors such as
the -body distribution function is usually employed to characterize
the point configurations, among which the most extensively used is the pair
distribution function . An intriguing inverse problem of practical
importance that has been receiving considerable attention is the degree to
which a point configuration can be reconstructed from the pair distribution
function of a target configuration. Although it is known that the pair-distance
information contained in is in general insufficient to uniquely determine
a point configuration, this concept does not seem to be widely appreciated and
general claims of uniqueness of the reconstructions using pair information have
been made based on numerical studies. In this paper, we introduce the idea of
the distance space, called the space. The pair distances of a
specific point configuration are then represented by a single point in the
space. We derive the conditions on the pair distances that can be
associated with a point configuration, which are equivalent to the
realizability conditions of the pair distribution function . Moreover, we
derive the conditions on the pair distances that can be assembled into distinct
configurations. These conditions define a bounded region in the
space. By explicitly constructing a variety of degenerate point configurations
using the space, we show that pair information is indeed
insufficient to uniquely determine the configuration in general. We also
discuss several important problems in statistical physics based on the
space.Comment: 28 pages, 8 figure
Nucleation-induced transition to collective motion in active systems
While the existence of polar ordered states in active systems is well
established, the dynamics of the self-assembly processes are still elusive. We
study a lattice gas model of self-propelled elongated particles interacting
through excluded volume and alignment interactions, which shows a phase
transition from an isotropic to a polar ordered state. By analyzing the
ordering process we find that the transition is driven by the formation of a
critical nucleation cluster and a subsequent coarsening process. Moreover, the
time to establish a polar ordered state shows a power-law divergence
Using Available Volume to Predict Fluid Diffusivity in Random Media
We propose a simple equation for predicting self-diffusivity of fluids
embedded in random matrices of identical, but dynamically frozen, particles
(i.e., quenched-annealed systems). The only nontrivial input is the volume
available to mobile particles, which also can be predicted for two common
matrix types that reflect equilibrium and non-equilibrium fluid structures. The
proposed equation can account for the large differences in mobility exhibited
by quenched-annealed systems with indistinguishable static pair correlations,
illustrating the key role that available volume plays in transport.Comment: to appear in Physical Review E (12 pages, 4 figures
Levantamento do consumo de água para processamento da cana-de-açúcar na região de abrangência do Pólo Centro-Sul, Piracicaba, SP.
Resumo: A região de Piracicaba é tradicional produtora de cana-de-açúcar e na safra 2012/13 apresentou 327 mil hectares de área plantada. Os benefícios ambientais gerados com a eliminação da queima da cana para fins de colheita, também repercutem na diminuição do consumo de água pelas usinas. Com a introdução do novo sistema de colheita não é mais necessário, via de regra, o uso da água para a lavagem da cana-de-açúcar. No levantamento realizado para o Protocolo Agroambiental, feito nas usinas signatárias e com atividade na região de abrangência do Pólo Centro ? Sul da APTA, foi possível constatar que as 14 usinas desta região consomem em média 1,97 mm de água por tonelada de cana-de-açúcar. Esse trabalho apresenta os dados de precipitação pluviométrica da estação climatológica da Unidade de Pesquisa e Desenvolvimento ? UPD (antiga estação experimental de Tietê) da Agência Paulista de Tecnologia dos Agronegócios ? APTA, no período de 2009 a 2014
Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
It is well known that one can map certain properties of random matrices,
fermionic gases, and zeros of the Riemann zeta function to a unique point
process on the real line. Here we analytically provide exact generalizations of
such a point process in d-dimensional Euclidean space for any d, which are
special cases of determinantal processes. In particular, we obtain the
n-particle correlation functions for any n, which completely specify the point
processes. We also demonstrate that spin-polarized fermionic systems have these
same n-particle correlation functions in each dimension. The point processes
for any d are shown to be hyperuniform. The latter result implies that the pair
correlation function tends to unity for large pair distances with a decay rate
that is controlled by the power law r^[-(d+1)]. We graphically display one- and
two-dimensional realizations of the point processes in order to vividly reveal
their "repulsive" nature. Indeed, we show that the point processes can be
characterized by an effective "hard-core" diameter that grows like the square
root of d. The nearest-neighbor distribution functions for these point
processes are also evaluated and rigorously bounded. Among other results, this
analysis reveals that the probability of finding a large spherical cavity of
radius r in dimension d behaves like a Poisson point process but in dimension
d+1 for large r and finite d. We also show that as d increases, the point
process behaves effectively like a sphere packing with a coverage fraction of
space that is no denser than 1/2^d.Comment: 40 pages, 11 figures, 1 table, iopart; corrected mislabeled section
numbers and minor typographical issues; minor text change
Novel Features Arising in the Maximally Random Jammed Packings of Superballs
Dense random packings of hard particles are useful models of granular media
and are closely related to the structure of nonequilibrium low-temperature
amorphous phases of matter. Most work has been done for random jammed packings
of spheres, and it is only recently that corresponding packings of nonspherical
particles (e.g., ellipsoids) have received attention. Here we report a study of
the maximally random jammed (MRJ) packings of binary superdisks and
monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1
with d = 2 and 3, respectively, where p is the deformation parameter with
values in the interval (0, infinity). We find that the MRJ densities of such
packings increase dramatically and nonanalytically as one moves away from the
circular-disk and sphere point. Moreover, the disordered packings are
hypostatic and the local arrangements of particles are necessarily nontrivially
correlated to achieve jamming. We term such correlated structures "nongeneric".
The degree of "nongenericity" of the packings is quantitatively characterized
by determining the fraction of local coordination structures in which the
central particles have fewer contacting neighbors than average. We also show
that such seemingly special packing configurations are counterintuitively not
rare. As the anisotropy of the particles increases, the fraction of rattlers
decreases while the minimal orientational order increases. These novel
characteristics result from the unique rotational symmetry breaking manner of
the particles.Comment: 20 pages, 8 figure
Estimates of the optimal density and kissing number of sphere packings in high dimensions
The problem of finding the asymptotic behavior of the maximal density of
sphere packings in high Euclidean dimensions is one of the most fascinating and
challenging problems in discrete geometry. One century ago, Minkowski obtained
a rigorous lower bound that is controlled asymptotically by , where
is the Euclidean space dimension. An indication of the difficulty of the
problem can be garnered from the fact that exponential improvement of
Minkowski's bound has proved to be elusive, even though existing upper bounds
suggest that such improvement should be possible. Using a
statistical-mechanical procedure to optimize the density associated with a
"test" pair correlation function and a conjecture concerning the existence of
disordered sphere packings [S. Torquato and F. H. Stillinger, Experimental
Math. {\bf 15}, 307 (2006)], the putative exponential improvement was found
with an asymptotic behavior controlled by . Using the same
methods, we investigate whether this exponential improvement can be further
improved by exploring other test pair correlation functions correponding to
disordered packings. We demonstrate that there are simpler test functions that
lead to the same asymptotic result. More importantly, we show that there is a
wide class of test functions that lead to precisely the same exponential
improvement and therefore the asymptotic form is much
more general than previously surmised.Comment: 23 pages, 4 figures, submitted to Phys. Rev.
Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
Heterogeneous materials abound in nature and man-made situations. Examples
include porous media, biological materials, and composite materials. Diverse
and interesting properties exhibited by these materials result from their
complex microstructures, which also make it difficult to model the materials.
In this first part of a series of two papers, we collect the known necessary
conditions on the standard two-point correlation function S2(r) and formulate a
new conjecture. In particular, we argue that given a complete two-point
correlation function space, S2(r) of any statistically homogeneous material can
be expressed through a map on a selected set of bases of the function space. We
provide new examples of realizable two-point correlation functions and suggest
a set of analytical basis functions. Moreover, we devise an efficient and
isotropy- preserving construction algorithm, namely, the Lattice-Point
algorithm to generate realizations of materials from their two- point
correlation functions based on the Yeong-Torquato technique. Subsequent
analysis can be performed on the generated images to obtain desired macroscopic
properties. These developments are integrated here into a general scheme that
enables one to model and categorize heterogeneous materials via two-point
correlation functions.Comment: 37 pages, 26 figure
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