Yuanyuan Xu — Page 4

arXiv2019

Jamming transition in non-spherical particle systems: pentagons vs. disks

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 with static friction coefficient $μ\approx 1$. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, $Z_{nr}$ , reaches 3, and the dependence of $Z_{nr}$ on the packing fraction $ϕ$ changes again when $Z_{nr}$ reaches 4. (2) Though the packing fractions $ϕ_{c1}$ and $ϕ_{c2}$ at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of $ϕ_{c1}$ and $ϕ_{c2}$ for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs comparing to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.

cond-mat.soft↗

arXiv2018

Gaussian Approximation of the Distribution of Strongly Repelling Particles on the Unit Circle

In this paper, we consider a strongly-repelling model of $n$ ordered particles $\{e^{i θ_j}\}_{j=0}^{n-1}$ with the density $p({θ_0},\cdots, θ_{n-1})=\frac{1}{Z_n} \exp \left\{-\fracβ{2}\sum_{j \neq k} \sin^{-2} \left( \frac{θ_j-θ_k}{2}\right)\right\}$, $β>0$. Let $θ_j=\frac{2 πj}{n}+\frac{x_j}{n^2}+const$ such that $\sum_{j=0}^{n-1}x_j=0$. Define $ζ_n \left( \frac{2 πj}{n}\right) =\frac{x_j}{\sqrt{n}}$ and extend $ζ_n$ piecewise linearly to $[0, 2 π]$. We prove the functional convergence of $ζ_n(t)$ to $ζ(t)=\sqrt{\frac{2}β} \mathfrak{Re} \left( \sum_{k=1}^{\infty} \frac{1}{k} e^{ikt} Z_k \right)$, where $Z_k$ are i.i.d. complex standard Gaussian random variables.

math.PR↗