690 research outputs found
Elastic properties of mono- and polydisperse two-dimensional crystals of hard--core repulsive Yukawa particles
Monte Carlo simulations of mono-- and polydisperse two--dimensional crystals
are reported. The particles in the studied system, interacting through
hard--core repulsive Yukawa potential, form a solid phase of hexagonal lattice.
The elastic properties of crystalline Yukawa systems are determined in the
ensemble with variable shape of the periodic box. Effects of the Debye
screening length (), contact value of the potential (),
and the size polydispersity of particles on elastic properties of the system
are studied. The simulations show that the polydispersity of particles strongly
influences the elastic properties of the studied system, especially on the
shear modulus. It is also found that the elastic moduli increase with density
and their growth rate depends on the screening length. Shorter screening length
leads to faster increase of elastic moduli with density and decrease of the
Poisson's ratio. In contrast to its three-dimensional version, the studied
system is non-auxetic, i.e. shows positive Poisson's ratio
Elastic properties of cubic crystals: Every's versus Blackman's diagram
Blackman's diagram of two dimensionless ratios of elastic constants is
frequently used to correlate elastic properties of cubic crystals with
interatomic bondings. Every's diagram of a different set of two dimensionless
variables was used by us for classification of various properties of such
crystals. We compare these two ways of characterization of elastic properties
of cubic materials and consider the description of various groups of materials,
e.g. simple metals, oxides, and alkali halides. With exception of intermediate
valent compounds, the correlation coefficients for Every's diagrams of various
groups of materials are greater than for Blackaman's diagrams, revealing the
existence of a linear relationship between two dimensionless Every's variables.
Alignment of elements and compounds along lines of constant Poisson's ratio
, ( arbitrary perpendicular to ) is
observed. Division of the stability region in Blackman's diagram into region of
complete auxetics, auxetics and non-auxetics is introduced. Correlations of a
scaling and an acoustic anisotropy parameter are considered.Comment: 8 pages, 9 figures, presented on The Ninth International School on
Theoretical Physics "Symmetry and Structural Properties of Condensed Matter",
5 - 12 September 2007, Myczkowce, Polan
Tetratic Order in the Phase Behavior of a Hard-Rectangle System
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found
two unusual phases in two-dimensional systems of anisotropic hard particles: a
tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science
and Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase for
hard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, we
study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers
(or dominos), and demonstrate that it exhibits a solid phase with both of these
unusual properties. The solid shows tetratic, but not nematic, order, and it is
nonperiodic having the structure of a random tiling of the square lattice with
dominos. We obtain similar results with both a classical Monte Carlo method
using true rectangles and a novel molecular dynamics algorithm employing
rectangles with rounded corners. It is remarkable that such simple convex
two-dimensional shapes can produce such rich phase behavior. Although we have
not performed exact free-energy calculations, we expect that the random domino
tiling is thermodynamically stabilized by its degeneracy entropy, well-known to
be per particle from previous studies of the dimer problem on the
square lattice. Our observations are consistent with a KTHNY two-stage phase
transition scenario with two continuous phase transitions, the first from
isotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio
Elasticity of the Sm[1-x]Y[x]S alloy Based on Ultrasonic Measurements
The elastic moduli, sound velocities, Gruneisen parameter, Poisson's ratios and brittleness-plasticity criterion ratios are studied for the Sm[1-x]Y[x]S alloys. Their dependence on the concentration of alloy components including a valence transition from semiconductors into the metal phase is presented. Auxeticity (negative Poisson's ratio) is found for some concentrations
Demixing and orientational ordering in mixtures of rectangular particles
Using scaled-particle theory for binary mixtures of two-dimensional hard
particles with rotational freedom, we analyse the stability of nematic phases
and the demixing phase behaviour of a variety of mixtures, focussing on cases
where at least one of the components consists of hard rectangles or hard
squares. A pure fluid of hard rectangles may exhibit, aside from the usual
uniaxial nematic phase, an additional (tetratic) oriented phase, possessing two
directors, which is the analogue of the biaxial or cubatic phases in three-
dimensional fluids. There is computer simulation evidence that the tetratic
phase might be stable with respect to phases with spatial order for rectangles
with low aspect ratios. As hard rectangles are mixed with other particles not
possessing stable tetratic order by themselves, the tetratic phase is
destabilised, via a first- or second-order phase transition, to uniaxial
nematic or isotropic phases; for hard rectangles of low aspect ratio tetratic
order persists in a relatively large range of volume fractions. The order of
these transitions depends on the particle geometry, dimensions and
thermodynamic conditions of the mixture. The second component of the mixture
has been chosen to be hard discs or disco-rectangles, the geometry of which is
different from that of rectangles, leading to packing frustration and demixing
behaviour, or simply rectangles of different aspect ratio. These mixtures may
be good candidates for observing thermodynamically stable tetratic phases in
monolayers of hard particles. Finally, demixing between fluid
(isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixtures
of hard squares of different sizes when the size ratio is sufficiently large.Comment: 27 pages, 9 figure
Conformal lattice of magnetic bubble domains in garnet film
We report experimental observations of magnetic bubble domain arrays with no
apparent translational symmetry. Additionally the results of comparative
numerical studies are discussed. Our goal is to present experimental evidence
for natural occurence of conformal structures.Comment: 7 pages, 2 figures, LaTeX2e, accepted as paper E090 at JEMS'01 (Joint
European Magnetic Symposia, formerly EMMA + MRM), August 28th to September
1st, 2001, Grenoble, Franc
Spectral asymmetry for bag boundary conditions
We give an expression, in terms of boundary spectral functions, for the
spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its
domain is determined by local boundary conditions, and the manifold is of
product type. As an application, we explicitly evaluate the asymmetry in the
case of a finite-length cylinder, and check that the outcome is consistent with
our general result. Finally, we study the asymmetry in a disk, which is a
non-product case, and propose an interpretation.Comment: Some minor changes. To appear in Journal of Physics A: Mathematical
and Genera
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
Optimal Packings of Superballs
Dense hard-particle packings are intimately related to the structure of
low-temperature phases of matter and are useful models of heterogeneous
materials and granular media. Most studies of the densest packings in three
dimensions have considered spherical shapes, and it is only more recently that
nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs
(whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a
versatile family of convex particles (p >= 0.5) with both cubic- and
octahedral-like shapes as well as concave particles (0 < p < 0.5) with
octahedral-like shapes. In this paper, we provide analytical constructions for
the densest known superball packings for all convex and concave cases. The
candidate maximally dense packings are certain families of Bravais lattice
packings. The maximal packing density as a function of p is nonanalytic at the
sphere-point (p = 1) and increases dramatically as p moves away from unity. The
packing characteristics determined by the broken rotational symmetry of
superballs are similar to but richer than their two-dimensional "superdisk"
counterparts, and are distinctly different from that of ellipsoid packings. Our
candidate optimal superball packings provide a starting point to quantify the
equilibrium phase behavior of superball systems, which should deepen our
understanding of the statistical thermodynamics of nonspherical-particle
systems.Comment: 28 pages, 16 figure
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