Synchronization-controlled transport near an absorbing transition: Effective Enskog kinetic theory of a driven granular monolayer

David González Méndez; Rubén Gómez González; Raphaël Maire; Vicente Garzó; Ignacio Pagonabarraga

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arXiv · 2610.35270

Synchronization-controlled transport near an absorbing transition: Effective Enskog kinetic theory of a driven granular monolayer

David González Méndez·Rubén Gómez González·Raphaël Maire·Vicente Garzó·Ignacio Pagonabarraga

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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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David González Méndez, Rubén Gómez González, Raphaël Maire, Vicente Garzó, Ignacio Pagonabarraga. 2026-10-26. Synchronization-controlled transport near an absorbing transition: Effective Enskog kinetic theory of a driven granular monolayer. https://arxiv.org/abs/2610.35270

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