Continuum percolation of congruent overlapping spherocylinders

Abstract

Continuum percolation of randomly orientated congruent overlapping spherocylinders (composed of cylinder of height H with semispheres of diameter D at the ends) with aspect ratio α=H/D in [0,∞) is studied. The percolation threshold ϕ_{c}, percolation transition width Δ, and correlation-length critical exponent ν for spherocylinders with α in [0, 200] are determined with a high degree of accuracy via extensive finite-size scaling analysis. A generalized excluded-volume approximation for percolation threshold with an exponent explicitly depending on both aspect ratio and excluded volume for arbitrary α values in [0,∞) is proposed and shown to yield accurate predictions of ϕ_{c} for an extremely wide range of α in [0, 2000] based on available numerical and experimental data. We find ϕ_{c} is a universal monotonic decreasing function of α and is independent of the effective particle size. Our study has implications in percolation theory for nonspherical particles and composite material design.

Permeability During Magma Expansion and Compaction

“…It is apparent that equation is inadequate at fitting samples that have undergone only small degrees of compaction, some of which show an increase in permeability. It is in principle feasible to improve the fit by adding another term to equation to account for increases in vesicle connectivity, for example, due to capillary forces (e.g., Kennedy et al, ), or due to bubble elongation, which has been shown to increase permeability and reduce the percolation threshold (e.g., Blower, ; Garboczi et al, ; Xu et al, ; Yi & Sastry, ). At present we lack a sound theoretical foundation to derive such an additional term and we therefore refrain from speculating based on empirical considerations.…”

Quantum work by a single photon

“…Our results are relevant not only to the field of light-matter interaction at the single-photon level [3][4][5][6][7][8][9][10][11][12][13][14][15], but also to quantum thermodynamics and quantum autonomous machines [16][17][18][19][20][21][22][23][24][25][26][27]. The quantum nature of the electromagnetic pulse here presents features of a quantized piston in an autonomous machine.…”

Approaching the Limit of Electromechanical Performance in Mixed-Phase Nanocomposites

“…26 The claim of universality though does come with some contention as values of t have been reported to decrease with aspect ratio of nanofiller. 27,28 Conversely, there are also uncertainties associated with these reports as values of t ~ 2 have also been observed in nanocomposites with large 3 and small 29 aspect ratio fillers. Thus, for simplicity, the model here will assume t to be constant with aspect ratio.…”