Synchronization-controlled transport near an absorbing transition: Effective Enskog kinetic theory of a driven granular monolayer
Abstract
Synchronization with vibrating boundaries can qualitatively alter the dynamics of confined granular fluids and control the collision-induced transfer of energy to horizontal motion. We develop an Enskog kinetic theory for the active phase of a driven granular monolayer within the framework of the Δ-model, which accounts for the transfer of energy from the vertical to the horizontal degrees of freedom of grains. Synchronization effects are incorporated through a state-dependent effective collision rule governed by the interplay between the local collision frequency and a characteristic synchronization time. A viscous drag force is also included to account for energy dissipation arising from interactions with the confining plates. Within this framework, we characterize the homogeneous active state and use it as the reference state for a Chapman--Enskog expansion. The solution of the Enskog equation to Navier--Stokes order then yields explicit expressions for the shear and bulk viscosities, the thermal conductivity, the diffusive heat coefficient, and the first-order contribution to the cooling rate, consistently accounting for inelasticity, damping, finite-density effects, and synchronization. Event-driven molecular-dynamics simulations show that the theory accurately describes the steady temperature and shear and bulk viscosities over a broad region of the active phase. Close to the discontinuous synchronization-controlled absorbing transition, deviations are mainly attributed to the mean-field coarse-graining of the microscopic synchronization dynamics: fluctuations of the collision-dependent injection amplitude and correlations between synchronization and pre-collisional velocities become increasingly important. These results provide a kinetic description of synchronization-controlled transport and delineate its range of validity near the absorbing transition.
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BibTeX
@misc{mendez2026synchronizationcontrolled,
title = {{Synchronization-controlled transport near an absorbing transition: Effective Enskog kinetic theory of a driven granular monolayer}},
author = {David González Méndez and Rubén Gómez González and Raphaël Maire and Vicente Garzó and Ignacio Pagonabarraga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35270},
eprint = {2610.35270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35270},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Synchronization-controlled transport near an absorbing transition: Effective Enskog kinetic theory of a driven granular monolayer
AU - David González Méndez
AU - Rubén Gómez González
AU - Raphaël Maire
AU - Vicente Garzó
AU - Ignacio Pagonabarraga
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35270
UR - https://arxiv.org/abs/2610.35270
AB - Synchronization with vibrating boundaries can qualitatively alter the dynamics of confined granular fluids and control the collision-induced transfer of energy to horizontal motion. We develop an Enskog kinetic theory for the active phase of a driven granular monolayer within the framework of the Δ-model, which accounts for the transfer of energy from the vertical to the horizontal degrees of freedom of grains. Synchronization effects are incorporated through a state-dependent effective collision rule governed by the interplay between the local collision frequency and a characteristic synchronization time. A viscous drag force is also included to account for energy dissipation arising from interactions with the confining plates. Within this framework, we characterize the homogeneous active state and use it as the reference state for a Chapman--Enskog expansion. The solution of the Enskog equation to Navier--Stokes order then yields explicit expressions for the shear and bulk viscosities, the thermal conductivity, the diffusive heat coefficient, and the first-order contribution to the cooling rate, consistently accounting for inelasticity, damping, finite-density effects, and synchronization. Event-driven molecular-dynamics simulations show that the theory accurately describes the steady temperature and shear and bulk viscosities over a broad region of the active phase. Close to the discontinuous synchronization-controlled absorbing transition, deviations are mainly attributed to the mean-field coarse-graining of the microscopic synchronization dynamics: fluctuations of the collision-dependent injection amplitude and correlations between synchronization and pre-collisional velocities become increasingly important. These results provide a kinetic description of synchronization-controlled transport and delineate its range of validity near the absorbing transition.
ER -