1,104 research outputs found
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 )
and the shear viscosity is allowed to diverge at a density (), with all other transport coefficients diverging at . 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 ) 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 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
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