The minimization of mechanical work in vibrated granular matter

Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks

Non-equilibrium phase coexistence is commonly observed in both biological and artificial systems, yet understanding it remains a significant challenge. Unlike equilibrium systems, where free energy provides a unifying framework, the absence of such a quantity in non-equilibrium settings complicates their theoretical understanding. Granular materials, driven out of equilibrium by energy dissipation during collisions, serve as an ideal platform to investigate these systems, offering insights into the parallels and distinctions between equilibrium and non-equilibrium phase behavior. For example, the coexisting dense phase is typically colder than the dilute phase, a result usually attributed to greater dissipation in denser regions. In this article, we demonstrate that this is not always the case. Using a simple numerical granular model, we show that a hot solid and a cold liquid can coexist in granular systems. This counterintuitive phenomenon arises because the collision frequency can be lower in the solid phase than in the liquid phase, consistent with equilibrium results for hard-disk systems. We further demonstrate that kinetic theory can be extended to accurately predict phase temperatures even at very high packing fractions, including within the solid phase. Our results highlight the importance of collisional dynamics and energy exchange in determining phase behavior in granular materials, offering new insights into non-equilibrium phase coexistence and the complex physics underlying granular systems.

Geometry-controlled phase transition in vibrated granular media

We report experiments on the dynamics of vibrated particles constrained in a two-dimensional vertical container, motivated by the following question: how to get the most out of a given external vibration to maximize internal disorder (e.g. to blend particles) and agitation (e.g. to absorb vibrations)? Granular media are analogs to classical thermodynamic systems, where the injection of energy can be achieved by shaking them: fluidization arises by tuning either the amplitude or the frequency of the oscillations. Alternatively, we explore what happens when another feature, the container geometry, is modified while keeping constant the energy injection. Our method consists in modifying the container base into a V-shape to break the symmetries of the inner particulate arrangement. The lattice contains a compact hexagonal solid-like crystalline phase coexisting with a loose amorphous fluid-like phase, at any thermal agitation. We show that both the solid-to-fluid volume fraction and the granular temperature depend not only on the external vibration but also on the number of topological defects triggered by the asymmetry of the container. The former relies on the statistics of the energy fluctuations and the latter is consistent with a two-dimensional melting transition described by the KTHNY theory.

Particle Dynamics at the Onset of the Granular Gas-Liquid Transition

We study experimentally the dynamical behavior of few large tracer particles placed in a quasi-2D granular "gas" made of many small beads in a low-gravity environment. Multiple inelastic collisions transfer momentum from the uniaxially driven gas to the tracers whose velocity distributions are studied through particle tracking. Analyzing these distributions for an increasing system density reveals that translational energy equipartition is reached at the onset of the gas-liquid granular transition corresponding to the emergence of local clusters. The dynamics of a few tracer particles thus appears as a simple and accurate tool to detect this transition. A model is proposed for describing accurately the formation of local heterogeneities.

Patterns in magnetic granular media at the crossover from two to three dimensions

We perform three-dimensional particle-based simulations of confined, vibrated, and magnetizable beads to study the effect of cell geometry on pattern selection. For quasi-two-dimensional systems, we reproduce previously observed macroscopic patterns such as hexagonal crystals and labyrinthine structures. For systems at the crossover from two to three dimensions, labyrinthine branches shorten and are replaced by triplets of beads forming upright triangles which self-organize into a herringbone pattern. This transition is associated with increases in both translational and orientational orders.

Reduced Thermodynamic Description of Phase Separation in a Quasi-One-Dimensional Granular Gas

We describe simulations of a quasi-one-dimensional, vibrated granular gas which exhibits an apparent phase separation into a liquidlike phase and a gaslike phase. In thermal equilibrium, such a phase separation in one dimension is prohibited by entropic considerations. We propose that the granular gas minimizes a function of the conserved mechanical variables alone: the particle number and volume. Simulations in small cells can be used to extract the equation of state and predict the coexisting pressure and densities, as confirmation of the minimization principle. Fluctuations in the system manifest themselves as persistent density waves but they do not destroy the phase-separated state.

Phase separation in driven granular gases: exploring the elusive character of nonequilibrium steady states

The emergence of patterns and phase separation in many-body systems far from thermal equilibrium is discussed using the example of driven granular gases. It is shown that phase separation follows a similar mechanism as in the systems of active Brownian particles. Depending on the quantities chosen for observation, it may or may not be easy to find functionals analogous to the free energy in equilibrium statistical physics. We argue that although such functionals can always be derived from the dynamics, it is of only limited value for predicting relevant aspects of the nonequilibrium steady state of the system. Consequently, although there is indeed a 'principle' governing the selection of collective nonequilibrium steady states (and the corresponding large deviation functional can be identified), it is not generally useful for predicting the behaviour of the system.