457 research outputs found

    Elasticity of highly cross-linked random networks

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    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

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    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 Ï•=4000/4671=0.856347...\phi= 4000/4671 = 0.856347.... 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

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    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 η\eta lower than the glass close packing fraction ηJ\eta_{J} 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

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    Superfluid-insulator transition in an ultracold Fermi gas in the external disorder potential of the amplitude V0V_0 is studied as a function of the concentration of the gas nn and magnetic field BB in the presence of the Feshbach resonance. We find the zero temperature phase diagrams in the plane (B,nB,n) at a given V0V_0 and in the plane (V0,n)(V_0, n) at a given BB. 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

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    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

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    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

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    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

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    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

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    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

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    We performed detailed conductivity and tunneling mesurements on the amorphous, magnetically doped material α\alpha-Gdx_xSi1−x_{1-x} (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 N(E)N(E), 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. N(E)∼EcN(E) \sim E^c, c≲2c \lesssim 2, towards metallic behavior, with EdE^d, 0.5<d<10.5 \lt d \lt 1 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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