457 research outputs found
Elasticity of highly cross-linked random networks
Starting from a microscopic model of randomly cross-linked particles with
quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary
cross-link densities. Considering pure shear deformations, S takes the form of
the elastic energy of an isotropic amorphous solid state, from which the shear
modulus can be identified. It is found to be an universal quantity, not
depending on any microscopic length-scales of the model.Comment: 6 pages, 5 figure
Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra
The determination of the densest packings of regular tetrahedra (one of the
five Platonic solids) is attracting great attention as evidenced by the rapid
pace at which packing records are being broken and the fascinating packing
structures that have emerged. Here we provide the most general analytical
formulation to date to construct dense periodic packings of tetrahedra with
four particles per fundamental cell. This analysis results in six-parameter
family of dense tetrahedron packings that includes as special cases recently
discovered "dimer" packings of tetrahedra, including the densest known packings
with density . This study strongly suggests that
the latter set of packings are the densest among all packings with a
four-particle basis. Whether they are the densest packings of tetrahedra among
all packings is an open question, but we offer remarks about this issue.
Moreover, we describe a procedure that provides estimates of upper bounds on
the maximal density of tetrahedron packings, which could aid in assessing the
packing efficiency of candidate dense packings.Comment: It contains 25 pages, 5 figures
Free-energy functional for freezing transitions: Hard sphere systems freezing into crystalline and amorphous structures
A free-energy functional that contains both the symmetry conserved and
symmetry broken parts of the direct pair correlation function has been used to
investigate the freezing of a system of hard spheres into crystalline and
amorphous structures. The freezing parameters for fluid-crystal transition have
been found to be in very good agreement with the results found from
simulations. We considered amorphous structures found from the molecular
dynamics simulations at packing fractions lower than the glass close
packing fraction and investigated their stability compared to that
of a homogeneous fluid. The existence of free-energy minimum corresponding to a
density distribution of overlapping Gaussians centered around an amorphous
lattice depicts the deeply supercooled state with a heterogeneous density
profile
Superfluid-insulator transition and BCS-BEC crossover in dirty ultracold Fermi gas
Superfluid-insulator transition in an ultracold Fermi gas in the external
disorder potential of the amplitude is studied as a function of the
concentration of the gas and magnetic field in the presence of the
Feshbach resonance. We find the zero temperature phase diagrams in the plane
() at a given and in the plane at a given . Our
results for BEC side of the diagram are also valid for the superfluid-insulator
transition in a Bose gas.Comment: Reference added, typos correcte
Density of States for a Specified Correlation Function and the Energy Landscape
The degeneracy of two-phase disordered microstructures consistent with a
specified correlation function is analyzed by mapping it to a ground-state
degeneracy. We determine for the first time the associated density of states
via a Monte Carlo algorithm. Our results are described in terms of the
roughness of the energy landscape, defined on a hypercubic configuration space.
The use of a Hamming distance in this space enables us to define a roughness
metric, which is calculated from the correlation function alone and related
quantitatively to the structural degeneracy. This relation is validated for a
wide variety of disordered systems.Comment: Accepted for publication in Physical Review Letter
Electronic and phononic properties of cinnabar: ab initio calculations and some experimental results
We report ab initio calculations of the electronic band structure, the
corresponding optical spectra, and the phonon dispersion relations of trigonal
alpha-HgS (cinnabar). The calculated dielectric functions are compared with
unpublished optical measurements by Zallen and coworkers. The phonon dispersion
relations are used to calculate the temperature and isotopic mass dependence of
the specific heat which has been compared with experimental data obtained on
samples with the natural isotope abundances of the elements Hg and S (natural
minerals and vapor phase grown samples) and on samples prepared from isotope
enriched elements by vapor phase transport. Comparison of the calculated
vibrational frequencies with Raman and ir data is also presented. Contrary to
the case of cubic beta-HgS (metacinnabar), the spin-orbit splitting of the top
valence bands at the Gamma-point of the Brillouin zone (Delta_0) is positive,
because of a smaller admixture of 5d core electrons of Hg. Calculations of the
lattice parameters, and the pressure dependence of Delta_0 and the
corresponding direct gap E_0~2eV are also presented. The lowest absorption edge
is confirmed to be indirect.Comment: 13 pages, 15 figure
Topologically disordered systems at the glass transition
The thermodynamic approach to the viscosity and fragility of amorphous oxides was used to determine the topological characteristics of the disordered network-forming systems. Instead of the disordered system of atoms we considered the congruent disordered system of interconnecting bonds. The Gibbs free energy of network-breaking defects (configurons) was found based on available viscosity data. Amorphous silica and germania were used as reference disordered systems for which we found an excellent agreement of calculated and measured glass transition temperatures. We reveal that the Hausdorff dimension of the system of bonds changes from Euclidian three-dimensional below to fractal 2.55 ± 0.05-dimensional geometry above the glass transition temperature
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
Dense Packings of Superdisks and the Role of Symmetry
We construct the densest known two-dimensional packings of superdisks in the
plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both
convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and
concave-shaped particles (0 < p < 0.5). The packings of the convex cases with p
1 generated by a recently developed event-driven molecular dynamics (MD)
simulation algorithm [Donev, Torquato and Stillinger, J. Comput. Phys. 202
(2005) 737] suggest exact constructions of the densest known packings. We find
that the packing density (covering fraction of the particles) increases
dramatically as the particle shape moves away from the "circular-disk" point (p
= 1). In particular, we find that the maximal packing densities of superdisks
for certain p 6 = 1 are achieved by one of the two families of Bravais lattice
packings, which provides additional numerical evidence for Minkowski's
conjecture concerning the critical determinant of the region occupied by a
superdisk. Moreover, our analysis on the generated packings reveals that the
broken rotational symmetry of superdisks influences the packing characteristics
in a non-trivial way. We also propose an analytical method to construct dense
packings of concave superdisks based on our observations of the structural
properties of packings of convex superdisks.Comment: 15 pages, 8 figure
Variation of the density of states in amorphous GdSi at the metal-insulator transition
We performed detailed conductivity and tunneling mesurements on the
amorphous, magnetically doped material -GdSi (GdSi), which
can be driven through the metal-insulator transition by the application of an
external magnetic field. Conductivity increases linearly with field near the
transition and slightly slower on the metallic side. The tunneling conductance,
proportional to the density of states , undergoes a gradual change with
increasing field, from insulating, showing a soft gap at low bias, with a
slightly weaker than parabolic energy dependence, i.e. , , towards metallic behavior, with , energy
dependence. The density of states at the Fermi level appears to be zero at low
fields, as in an insulator, while the sample shows already small, but
metal-like conductivity. We suggest a possible explanation to the observed
effect.Comment: 6 pages, 6 figure
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