Real collective density variables C(k) [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor S(k), where k denotes the wave vector. Our...
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Real collective density variables C(k) [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor S(k), where k denotes the wave vector. Our objective is to prescribe C(k) and then to find many-particle configurations that correspond to such a target C(k) using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control S(k) in the neighborhood of ∣k∣=0. The optimization method employed generates multiparticle configurations for which S(k)∝∣k∣α, ∣k∣⩽K, and α=1, 2, 4, 6, 8, and 10. The case α=1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid He4, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground states are configurationally degenerate and disordered.
Maximally random jammed states of hard spheres are prototypical glasses. We study the small wavenumber k behavior of the structure factor S(k) of overcompressed million-sphere packings as a function of density up to t...
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Maximally random jammed states of hard spheres are prototypical glasses. We study the small wavenumber k behavior of the structure factor S(k) of overcompressed million-sphere packings as a function of density up to the jammed state. We find both a precursor to the glassy jammed state evident long before the jamming density is reached and two associated growing length scales, one extracted from the volume integral of the direct correlation function c(r) and the other from the small-k behavior of the structure factor S(k), that can diverge at the “critical” jammed state. We also define a nonequilibrium index X and use it to demonstrate that the packings studied are intrinsically nonequilibrium in nature well before the critical state is reached. The extension of the results reported in the present work to supercooled atomic-liquid models in which the atoms interact with both repulsive and attractive forces is also discussed.
The discovery of ferroelectricity in HfO2-based thin films opens up new opportunities for using this silicon-compatible ferroelectric to realize low-power logic circuits and high-density nonvolatile memories. The func...
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The discovery of ferroelectricity in HfO2-based thin films opens up new opportunities for using this silicon-compatible ferroelectric to realize low-power logic circuits and high-density nonvolatile memories. The functional performances of ferroelectrics are intimately related to their dynamic responses to external stimuli such as electric fields at finite temperatures. Molecular dynamics is an ideal technique for investigating dynamical processes on large length and time scales, though its applications to new materials are often hindered by the limited availability and accuracy of classical force fields. Here we present a deep neural network–based interatomic force field of HfO2 learned from ab initio data using a concurrent learning procedure. The model potential is able to predict structural properties such as elastic constants, equation of states, phonon dispersion relationships, and phase transition barriers of various hafnia polymorphs with accuracy comparable with density functional theory calculations. The validity of this model potential is further confirmed by the reproduction of experimental sequences of temperature-driven ferroelectric-paraelectric phase transitions of HfO2 with isobaric-isothermal ensemble molecular dynamics simulations. We suggest a general approach to extend the model potential of HfO2 to related material systems including dopants and defects.
By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts,...
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By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. The aforementioned correlation functions are special cases of the so-called canonical n-point correlation function Hn and generalize the ones that have been recently employed to advance our ability to reconstruct complex microstructures [Y. Jiao, F. H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. 106, 17634 (2009)]. The use of these generalized correlation functions is tantamount to dilating or eroding a reference phase of the target medium and incorporating the additional topological information of the modified media, thereby providing more accurate reconstructions of percolating, filamentary, and other topologically complex microstructures. We apply our methods to a multiply connected “donut” medium and a dilute distribution of “cracks” (a set of essentially zero measure), demonstrating improved accuracy in both cases with implications for higher-dimensional and biconnected two-phase systems. The high information content of the generalized two-point correlation functions suggests that it would be profitable to explore their use to characterize the structural and physical properties of not only random media, but also molecular systems, including structural glasses.
We study a continuum of photonic quasicrystal heterostructures derived from local isomorphism (LI) classes of pentagonal quasicrystal tilings. These tilings are obtained by direct projection from a five-dimensional hy...
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We study a continuum of photonic quasicrystal heterostructures derived from local isomorphism (LI) classes of pentagonal quasicrystal tilings. These tilings are obtained by direct projection from a five-dimensional hypercubic lattice. We demonstrate that, with the sole exception of the Penrose LI class, all other LI classes result in degenerate, effectively localized states, with precisely predictable and tunable properties (frequencies, frequency splittings, and densities). We show that localization and tunability are related to a mathematical property of the pattern known as “restorability,” i.e., whether the tiling can be uniquely specified given only a set of rules that fix all allowed clusters smaller than some bound.
作者：
Cinacchi, GiorgioTorquato, Salvatore
Instituto de Ciencias de Materiales "Nicolás Cabrera" Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco MadridE-28049 Spain Department of Chemistry
Department of Physics Institute for the Science and Technology of Materials Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States
Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is ‘optimal’ in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest pac...
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Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the do...
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The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the α−x plane of sphere radius ratio α and relative concentration x are at the Kepler lim...
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The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the α−x plane of sphere radius ratio α and relative concentration x are at the Kepler limit α=1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (α,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings.
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplish...
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