1,485 research outputs found
Microscopic origin of granular ratcheting
Numerical simulations of assemblies of grains under cyclic loading exhibit
``granular ratcheting'': a small net deformation occurs with each cycle,
leading to a linear accumulation of deformation with cycle number. We show that
this is due to a curious property of the most frequently used models of the
particle-particle interaction: namely, that the potential energy stored in
contacts is path-dependent. There exist closed paths that change the stored
energy, even if the particles remain in contact and do not slide. An
alternative method for calculating the tangential force removes granular
ratcheting.Comment: 13 pages, 18 figure
Shearing behavior of polydisperse media
We study the shearing of polydisperse and bidisperse media with a size ratio
of 10. Simulations are performed with a the two dimensional shear cell using
contact dynamics. With a truncated power law for the polydisperse media we find
that they show a stronger dilatancy and greater resistance to shearing than
bidisperse mixtures. Motivated by the practical problem of reducing the energy
needed to shear granular media, we introduce "point-like particles"
representing charged particles in the distribution. Even though changing the
kinematic behavior very little, they reduce the force necessary to maintain a
fixed shearing velocity.Comment: 17 pages, 15 figure
Fragmentation of a Circular Disc by Impact on a Frictionless Plate
The break-up of a two-dimensional circular disc by normal and oblique impact
on a hard frictionless plate is investigated by molecular dynamics simulations.
The disc is composed of numerous unbreakable randomly shaped convex polygons
connected together by simple elastic beams that break when bent or stretched
beyond a certain limit. It is found that for both normal and oblique impacts
the crack patterns are the same and depend solely on the normal component of
the impact velocity. Analysing the pattern of breakage, amount of damage,
fragment masses and velocities, we show the existence of a critical velocity
which separates two regimes of the impact process: below the critical point
only a damage cone is formed at the impact site (damage), cleaving of the
particle occurs at the critical point, while above the critical velocity the
disc breaks into several pieces (fragmentation). In the limit of very high
impact velocities the disc suffers complete disintegration (shattering) into
many small fragments. In agreement with experimental results, fragment masses
are found to follow the Gates-Gaudin-Schuhmann distribution (power law) with an
exponent independent of the velocity and angle of impact. The velocity
distribution of fragments exhibit an interesting anomalous scaling behavior
when changing the impact velocity and the size of the disc.Comment: submitted to J. Phys: Condensed Matter special issue on Granular
Medi
Steady state properties of a driven granular medium
We study a two-dimensional granular system where external driving force is
applied to each particle in the system in such a way that the system is driven
into a steady state by balancing the energy input and the dissipation due to
inelastic collision between particles. The velocities of the particles in the
steady state satisfy the Maxwellian distribution. We measure the
density-density correlation and the velocity-velocity correlation functions in
the steady state and find that they are of power-law scaling forms. The
locations of collision events are observed to be time-correlated and such a
correlation is described by another power-law form. We also find that the
dissipated energy obeys a power-law distribution. These results indicate that
the system evolves into a critical state where there are neither characteristic
spatial nor temporal scales in the correlation functions. A test particle
exhibits an anomalous diffusion which is apparently similar to the Richardson
law in a three-dimensional turbulent flow.Comment: REVTEX, submitted to Phys. Rev.
Thermodynamic Theory of Weakly Excited Granular Materials
We present a thermodynamic theory of weakly excited two-dimensional granular
systems from the view point of elementary excitations of spinless Fermion
systems. We introduce a global temperature T that is associated with the
acceleration amplitude \Gamma in a vibrating bed. We show that the
configurational statistics of weakly excited granular materials in a vibrating
bed obey the Fermi statistics.Comment: 12 pages, 1 figure, To Appear in Phys. Rev. Lett. April, 199
Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results
We study the response of a two-dimensional hexagonal packing of massless,
rigid, frictionless spherical grains due to a vertically downward point force
on a single grain at the top layer. We use a statistical approach, where each
mechanically stable configuration of contact forces is equally likely. We show
that this problem is equivalent to a correlated -model. We find that the
response is double-peaked, where the two peaks, sharp and single-grain diameter
wide, lie on the two downward lattice directions emanating from the point of
the application of the external force. For systems of finite size, the
magnitude of these peaks decreases towards the bottom of the packing, while
progressively a broader, central maximum appears between the peaks. The
response behaviour displays a remarkable scaling behaviour with system size
: while the response in the bulk of the packing scales as , on
the boundary it is independent of , so that in the thermodynamic limit only
the peaks on the lattice directions persist. This qualitative behaviour is
extremely robust, as demonstrated by our simulation results with different
boundary conditions. We have obtained expressions of the response and higher
correlations for any system size in terms of integers corresponding to an
underlying discrete structure.Comment: Accepted for publication in JStat; 33 pages, 10 figures; Section 2.2
reorganized and rewritten; Details about the simulation procedure added in
Sec.3.1. ; A new section, summarizing the final results and the calculation
procedure adde
Transitions in the Horizontal Transport of Vertically Vibrated Granular Layers
Motivated by recent advances in the investigation of fluctuation-driven
ratchets and flows in excited granular media, we have carried out experimental
and simulational studies to explore the horizontal transport of granular
particles in a vertically vibrated system whose base has a sawtooth-shaped
profile. The resulting material flow exhibits novel collective behavior, both
as a function of the number of layers of particles and the driving frequency;
in particular, under certain conditions, increasing the layer thickness leads
to a reversal of the current, while the onset of transport as a function of
frequency occurs gradually in a manner reminiscent of a phase transition. Our
experimental findings are interpreted here with the help of extensive, event
driven Molecular Dynamics simulations. In addition to reproducing the
experimental results, the simulations revealed that the current may be reversed
as a function of the driving frequency as well. We also give details about the
simulations so that similar numerical studies can be carried out in a more
straightforward manner in the future.Comment: 12 pages, 18 figure
Simulation of Flow of Mixtures Through Anisotropic Porous Media using a Lattice Boltzmann Model
We propose a description for transient penetration simulations of miscible
and immiscible fluid mixtures into anisotropic porous media, using the lattice
Boltzmann (LB) method. Our model incorporates hydrodynamic flow, diffusion,
surface tension, and the possibility for global and local viscosity variations
to consider various types of hardening fluids. The miscible mixture consists of
two fluids, one governed by the hydrodynamic equations and one by diffusion
equations. We validate our model on standard problems like Poiseuille flow, the
collision of a drop with an impermeable, hydrophobic interface and the
deformation of the fluid due to surface tension forces. To demonstrate the
applicability to complex geometries, we simulate the invasion process of
mixtures into wood spruce samples.Comment: Submitted to EPJ
Velocity and density profiles of granular flow in channels using lattice gas automaton
We have performed two-dimensional lattice-gas-automaton simulations of
granular flow between two parallel planes. We find that the velocity profiles
have non-parabolic distributions while simultaneously the density profiles are
non-uniform. Under non-slip boundary conditions, deviation of velocity profiles
from the parabolic form of newtonian fluids is found to be characterized solely
by ratio of maximal velocity at the center to the average velocity, though the
ratio depends on the model parameters in a complex manner. We also find that
the maximal velocity () at the center is a linear function of the
driving force (g) as with non-zero in
contrast with newtonian fluids. Regarding density profiles, we observe that
densities near the boundaries are higher than those in the center. The width of
higher densities (above the average density) relative to the channel width is a
decreasing function of a variable which scales with the driving force (g),
energy dissipation parameter () and the width of the system (L) as
with exponents and . A phenomenological theory based on a scaling argument is presented to
interpret these findings.Comment: Latex, 15 figures, to appear in PR
Static Friction Phenomena in Granular Materials: Coulomb Law vs. Particle Geometry
The static as well as the dynamic behaviour of granular material are
determined by dynamic {\it and} static friction. There are well known methods
to include static friction in molecular dynamics simulations using scarcely
understood forces. We propose an Ansatz based on the geometrical shape of
nonspherical particles which does not involve an explicit expression for static
friction. It is shown that the simulations based on this model are close to
experimental results.Comment: 11 pages, Revtex, HLRZ-33/9
- …