ﻻ يوجد ملخص باللغة العربية
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes n terms of the ratio $B/A$, where $A$ is volume coefficient and $B$ is surface-area coefficient associated with the local number variance $sigma^2(R)$ for a spherical window of radius $R$. To complement the known direct-space representation of the coefficient $B$ in terms of the total correlation function $h({bf r})$, we derive its corresponding Fourier representation in terms of the structure factor $S({bf k})$, which is especially useful when scattering information is available experimentally or theoretically. We show that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio $B/A$, the hyperuniformity index $H$ and the direct-correlation function length scale $xi_c$, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. We analyze equilibrium hard rods and sticky hard-sphere systems in arbitrary space dimension $d$ as a function of density. We also examine low-temperature excited states of many-particle systems interacting with stealthy long-ranged pair interactions as the temperature tends to zero. The capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally- or computationally-generated samples that are necessarily of finite size.
We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles wit
We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore si
Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs. We describe the structural relaxation of a tagged molecule as a coupled process of cage-scale dynamics and collective molecula
The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in
The enhancement of mobility at the surface of an amorphous alloy is studied using a combination of molecular dynamic simulations and normal mode analysis of the non-uniform distribution of Debye-Waller factors. The increased mobility at the surface i