Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThree simple scenarios for high-dimensional sphere packings
123
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: (A) crystallization is impeded and the glass phase constitutes the densest packing, (B) crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible, or (C) crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings in dimension $d=3$-$10$ using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close-packing tend to support scenario C. We additionally confirm that the crystal equation of state is dominated by the free volume expansion and that a meaningful polynomial correction can be formulated.
rate research
Read More
In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here, we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.
We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional $Ltimes L times L$ cubic lattice using the graphics processing unit (GPU). By the combination of Metropolis single-spin flip, over-relaxation and parallel-tempering methods, we simulate systems up to L=160. Performing the finite-size scaling analysis, we obtain estimates of the critical exponents for the three-dimensional XY universality class: $alpha=-0.01293(48)$ and $ u=0.67098(16)$. Our estimate for the correlation-length exponent $ u$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $ u_{rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment.
A modified three-dimensional mean spherical model with a L-layer film geometry under Neumann-Neumann boundary conditions is considered. Two spherical fields are present in the model: a surface one fixes the mean square value of the spins at the boundaries at some $rho > 0$, and a bulk one imposes the standard spherical constraint (the mean square value of the spins in the bulk equals one). The surface susceptibility $chi_{1,1}$ has been evaluated exactly. For $rho =1$ we find that $chi_{1,1}$ is finite at the bulk critical temperature $T_c$, in contrast with the recently derived value $gamma_{1,1}=1$ in the case of just one global spherical constraint. The result $gamma_{1,1}=1$ is recovered only if $rho =rho_c= 2-(12 K_c)^{-1}$, where $K_c$ is the dimensionless critical coupling. When $rho > rho_c$, $chi_{1,1}$ diverges exponentially as $Tto T_c^{+}$. An effective hamiltonian which leads to an exactly solvable model with $gamma_{1,1}=2$, the value for the $nto infty $ limit of the corresponding O(n) model, is proposed too.
Understanding granular materials aging poses a substantial challenge: Grain contacts form networks with complex topologies, and granular flow is far from equilibrium. In this letter, we experimentally measure a three-dimensional granular systems reversibility and aging under cyclic compression. We image the grains using a refractive-index-matched fluid, then analyze the images using the artificial intelligence of variational autoencoders. These techniques allow us to track all the grains translations and three-dimensional rotations with accuracy sufficient to infer contact-point sliding and rolling. Our observations reveal unique roles played by three-dimensional rotations in granular flow, aging, and energy dissipation. First, we find that granular rotations dominate the bulk dynamics, penetrating more deeply into the granular material than translations do. Second, sliding and rolling do not exhibit aging across the experiment, unlike translations. Third, aging appears not to minimize energy dissipation, according to our experimental measurements of rotations, combined with soft-sphere simulations. The experimental tools, analytical techniques, and observations that we introduce expose all the degrees of freedom of the far-from-equilibrium dynamics of granular flow.
We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
