The effects of forcing and dissipation on phase transitions in thin granular layers

Nonequilibrium steady states of vibrated inelastic frictionless spheres are investigated in quasi-twodimensional confinement via molecular dynamics simulations. The phase diagram in the densityamplitude plane exhibits a fluidlike disordered and an ordered phase with threefold symmetry, as well as phase coexistence between the two. A dynamical mechanism exists that brings about metastable traveling clusters and at the same time stable clusters with anisotropic shapes at low vibration amplitude. Moreover, there is a square bilayer state which is connected to the fluid by BKTHNY-type two-step melting with an intermediate tetratic phase. The critical behavior of the two continuous transitions is studied in detail. For the fluid-tetratic transition, critical exponents ofγ = 1.73, η4 ≈ 1/4, and z = 2.05 are obtained.

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“…Various aspects of the phase diagram have been reported previously [1,5,6,17,22,23], but a complete picture is lacking so far. In Fig.…”

Section: Phase Diagrammentioning

confidence: 99%

“…Critical density ρ4, parameter b, and critical exponentsγ and z of the fluid-tetratic transition for several amplitudes A obtained from fitting Eqs. (5),(6), and(8). Simulations at A = 0.03σ were performed with box size L = 120σ, simulations at other A were performed with L = 80σ.…”

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confidence: 99%

Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter

Schindler

Kapfer

2019

Phys. Rev. E

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“…The simulation methods that we used for DSMC and MD simulations are similar to those in our previous works and have been explained in detail elsewhere (Lobkovsky, Vega Reyes & Urbach 2009;Vega Reyes, Garzó & Santos 2011a;Vega Reyes, Santos & Garzó 2011b). We will briefly recall that DSMC yields an exact numerical solution of the corresponding kinetic equation (inelastic Boltzmann equation in this case), whereas MD yields a solution of the equations of motion of the particles.…”

Section: Simulation Detailsmentioning

confidence: 99%

Steady base states for non-Newtonian granular hydrodynamics

2013

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We study in this work steady laminar flows in a low density granular gas modelled as a system of identical smooth hard spheres that collide inelastically. The system is excited by shear and temperature sources at the boundaries, which consist of two infinite parallel walls. Thus, the geometry of the system is the same that yields the planar Fourier and Couette flows in standard gases. We show that it is possible to describe the steady granular flows in this system, even at large inelasticities, by means of a (nonNewtonian) hydrodynamic approach. All five types of Couette-Fourier granular flows are systematically described, identifying the different types of hydrodynamic profiles. Excellent agreement is found between our classification of flows and simulation results. Also, we obtain the corresponding non-linear transport coefficients by following three independent and complementary methods: (1) an analytical solution obtained from Grad's 13-moment method applied to the inelastic Boltzmann equation, (2) a numerical solution of the inelastic Boltzmann equation obtained by means of the direct simulation Monte Carlo method and (3) event-driven molecular dynamics simulations. We find that, while Grad's theory does not describe quantitatively well all transport coefficients, the three procedures yield the same general classification of planar Couette-Fourier flows for the granular gas. IntroductionThere have been in the recent years a large number of studies on the dynamics of granular gases, where 'granular gas' is a term used to refer to a low density system of many mesoscopic particles that collide inelastically in pairs. Due to inelasticity in the collisions, the granular gas particles tend to collapse to a rest state, unless there is some kind of energy input. In particular, Goldhirsch & Zanetti (1993) showed that clustering instabilities spontaneously appear in a freely evolving granular gas. Nevertheless, most situations of practical interest involve an energy input to compensate for the energy loss and sustain, in some cases, the 'gas' condition of the granular system. This type of problem has been extensively studied, giving rise to a subfield of granular dynamics: 'rapid granular flows ' (Jenkins & Savage 1983;Wang, Jackson & Sundaresan 1996;Goldhirsch 2003;Aranson & Tsimring 2006). Furthermore, it has been shown that rapid granular flows can attain steady states, some of which, under appropriate circumstances and for simple geometries, can give rise to laminar flows, in the same way as a regular gas does (see, for instance, the work by Tij, Tahiri, Montanero, Garzó, Santos & Dufty † Email address for correspondence: fvega@unex.es

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“…Among these, the difference in elastic properties may be less important compared to the others because forces acting upon interparticle collisions are too weak to cause non-linear deformation of the balls and it is known that the 2D melting behavior is not affected by the softness of the interaction potential [16]. A situation we consider is a single layer of monodisperse spheres, which is vibrated between two horizontal plates [30], unlike the above-mentioned previous works where bilayer formation is allowed [24][25][26][27][28][29]. The control parameters in our experiments are the energy input characterized by a dimensionless acceleration Γ and the area fraction of particles φ.…”

Section: Introductionmentioning

confidence: 99%

“…There were pioneering works on liquid-solid transitions of quasi-2D granular systems [24][25][26][27][28][29]. These studies showed interesting monolayer liquid-bilayer solid coexistence in a nonequilibrium steady state, in which the two phases have different granular temperatures.…”

Section: Introductionmentioning

confidence: 99%

Roles of Energy Dissipation in a Liquid-Solid Transition of Out-of-Equilibrium Systems

Komatsu

Tanaka

2015

Phys. Rev. X

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Self-organization of active matter as well as driven granular matter in nonequilibrium dynamical states has attracted considerable attention not only from the fundamental and application viewpoints but also as a model to understand the occurrence of such phenomena in nature. These systems share common features originating from their intrinsically out-of-equilibrium nature, and how energy dissipation affects the state selection in such nonequilibrium states remains elusive. As a simple model system, we consider a nonequilibrium stationary state maintained by continuous energy input, relevant to industrial processing of granular materials by vibration and/or flow. More specifically, we experimentally study roles of dissipation in self-organization of a driven granular particle monolayer. We find that the introduction of strong inelasticity entirely changes the nature of the liquid-solid transition from two-step (nearly) continuous transitions (liquid-hexatic-solid) to a strongly discontinuous first-order-like one (liquid-solid), where the two phases with different effective temperatures can coexist, unlike thermal systems, under a balance between energy input and dissipation. Our finding indicates a pivotal role of energy dissipation and suggests a novel principle in the self-organization of systems far from equilibrium. A similar principle may apply to active matter, which is another important class of out-of-equilibrium systems. On noting that interaction forces in active matter, and particularly in living systems, are often nonconservative and dissipative, our finding may also shed new light on the state selection in these systems.

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The effects of forcing and dissipation on phase transitions in thin granular layers

Cited by 22 publications

References 35 publications

Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter

Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter

Steady base states for non-Newtonian granular hydrodynamics

Roles of Energy Dissipation in a Liquid-Solid Transition of Out-of-Equilibrium Systems

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