Hydrodynamics of fluid-solid coexistence in dense shear granular flow

We consider dense rapid shear flow of inelastically colliding hard disks. Navier-Stokes granular hydrodynamics is applied accounting for the recent finding \cite{Luding,Khain} that shear viscosity diverges at a lower density than the rest of constitutive relations. New interpolation formulas for constitutive relations between dilute and dense cases are proposed and justified in molecular dynamics (MD) simulations. A linear stability analysis of the uniform shear flow is performed and the full phase diagram is presented. It is shown that when the inelasticity of particle collision becomes large enough, the uniform sheared flow gives way to a two-phase flow, where a dense "solid-like" striped cluster is surrounded by two fluid layers. The results of the analysis are verified in event-driven MD simulations, and a good agreement is observed

Universality of shear-banding instability and crystallization in sheared granular fluid

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier-Stokes'-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up-to the maximum packing density $\nu_{m}$) and the shear viscosity is allowed to diverge at a density $\nu_\mu$ ($< \nu_{m}$), with all other transport coefficients diverging at $\nu_{m}$. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respective Enskog values that diverge at $\nu_m$) can induce shear-banding instabilities, even though the original dense Enskog model is stable to such shear-banding instabilities. For any constitutive model, the onset of this shear-banding instability is tied to a {\it universal} criterion in terms of constitutive relations for viscosity and pressure, and the sheared granular flow evolves toward a state of lower "dynamic" friction, leading to the shear-induced band formation, as it cannot sustain increasing dynamic friction with increasing density to stay in the homogeneous state. A similar criterion of a lower viscosity or a lower viscous-dissipation is responsible for the shear-banding state in many complex fluids.Comment: 26 page

Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations

The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed analytic expression for the front diffusion coefficient in the weak noise limit. Here we test this theory in stochastic simulations involving reacting and diffusing particles on a one-dimensional lattice. We also investigate a small noise-induced systematic shift of the front velocity compared to the prediction from the spatially continuous deterministic reaction-diffusion equation.Comment: 5 pages, 5 figure

The Generation of the Distant Kuiper Belt by Planet Nine from an Initially Broad Perihelion Distribution

The observation that the orbits of long-period Kuiper Belt objects are anomalously clustered in physical space has recently prompted the Planet Nine hypothesis - the proposed existence of a distant and eccentric planetary member of our solar system. Within the framework of this model, a Neptune-like perturber sculpts the orbital distribution of distant Kuiper Belt objects through a complex interplay of resonant and secular effects, such that in addition to perihelion-circulating objects, the surviving orbits get organized into apsidally aligned and anti-aligned configurations with respect to Planet Nine's orbit. In this work, we investigate the role of Kuiper Belt initial conditions on the evolution of the outer solar system using numerical simulations. Intriguingly, we find that the final perihelion distance distribution depends strongly on the primordial state of the system, and demonstrate that a bimodal structure corresponding to the existence of both aligned and anti-aligned clusters is only reproduced if the initial perihelion distribution is assumed to extend well beyond $\sim 36$ AU. The bimodality in the final perihelion distance distribution is due to the existence of permanently stable objects, with the lower perihelion peak corresponding to the anti-aligned orbits and the higher perihelion peak corresponding to the aligned orbits. We identify the mechanisms which enable the persistent stability of these objects and locate the regions of phase space in which they reside. The obtained results contextualize the Planet Nine hypothesis within the broader narrative of solar system formation, and offer further insight into the observational search for Planet Nine.Comment: 7 pages, 6 figures, accepted for publication in the Astronomical Journa

Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?

We investigate shear-induced crystallization in a very dense flow of mono-disperse inelastic hard spheres. We consider a steady plane Couette flow under constant pressure and neglect gravity. We assume that the granular density is greater than the melting point of the equilibrium phase diagram of elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive relations all of which (except the shear viscosity) diverge at the crystal packing density, while the shear viscosity diverges at a smaller density. The phase diagram of the steady flow is described by three parameters: an effective Mach number, a scaled energy loss parameter, and an integer number m: the number of half-oscillations in a mechanical analogy that appears in this problem. In a steady shear flow the viscous heating is balanced by energy dissipation via inelastic collisions. This balance can have different forms, producing either a uniform shear flow or a variety of more complicated, nonlinear density, velocity and temperature profiles. In particular, the model predicts a variety of multi-layer two-phase steady shear flows with sharp interphase boundaries. Such a flow may include a few zero-shear (solid-like) layers, each of which moving as a whole, separated by fluid-like regions. As we are dealing with a hard sphere model, the granulate is fluidized within the "solid" layers: the granular temperature is non-zero there, and there is energy flow through the boundaries of the "solid" layers. A linear stability analysis of the uniform steady shear flow is performed, and a plausible bifurcation diagram of the system, for a fixed m, is suggested. The problem of selection of m remains open.Comment: 11 pages, 7 eps figures, to appear in PR

A stochastic model for wound healing

We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p near 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.Comment: 16 pages, 7 figure

Oscillatory instability in a driven granular gas

We discovered an oscillatory instability in a system of inelastically colliding hard spheres, driven by two opposite "thermal" walls at zero gravity. The instability, predicted by a linear stability analysis of the equations of granular hydrodynamics, occurs when the inelasticity of particle collisions exceeds a critical value. Molecular dynamic simulations support the theory and show a stripe-shaped cluster moving back and forth in the middle of the box away from the driving walls. The oscillations are irregular but have a single dominating frequency that is close to the frequency at the instability onset, predicted from hydrodynamics.Comment: 7 pages, 4 figures, to appear in Europhysics Letter