723 research outputs found
Critical Exponents for Granular Phase Transitions
The solid--fluid phase transition of a granular material shaken horizontally
is investigated numerically. We find that it is a second-order phase transition
and propose two order parameters, namely the averaged kinetic energy and the
averaged granular temperature, to determine the fluidization point precisely.
It scales with the acceleration of the external vibration. Using this
fluidization point as critical point, we discuss the scaling of the kinetic
energy and show that the kinetic energy and the granular temperature show two
different universal critical point exponents for a wide range of excitation
amplitudes.Comment: 6 pages, including 6 figures. Uses Epic and EEpic macros (provided
Competition of mixing and segregation in rotating cylinders
Using discrete element methods, we study numerically the dynamics of the size
segregation process of binary particle mixtures in three-dimensional rotating
drums, operated in the continuous flow regime. Particle rotations are included
and we focus on different volume filling fractions of the drum to study the
interplay between the competing phenomena of mixing and segregation. It is
found that segregation is best for a more than half-filled drum due to the
non-zero width of the fluidized layer. For different particle size ratios, it
is found that radial segregation occurs for any arbitrary small particle size
difference and the final amount of segregation shows a linear dependence on the
size ratio of the two particle species. To quantify the interplay between
segregation and mixing, we investigate the dynamics of the center of mass
positions for each particle component. Starting with initially separated
particle groups we find that no mixing of the component is necessary in order
to obtain a radially segregated core.Comment: 9 pages, 12 figures (EPIC/EEPIC & EPS, macros included), submitted to
Physics of Fluid
Tumbling Motion of Elliptical Particles in Viscous Two-Dimensional Flow
The settling dynamics of spherical and elliptical particles in a viscous
Newtonian fluid are investigated numerically using a finite difference
technique. The terminal velocity for spherical particles is calculated for
different system sizes and the extrapolated value for an infinite system size
is compared to the Oseen approximation. Special attention is given to the
settling and tumbling motion of elliptical particles where their terminal
velocity is compared with the one of the surface equivalent spherical particle.Comment: 13 pages, 8 figures (within text), uses IJMPC macros (included
An exactly solvable model for driven dissipative systems
We introduce a solvable stochastic model inspired by granular gases for
driven dissipative systems. We characterize far from equilibrium steady states
of such systems through the non-Boltzmann energy distribution and compare
different measures of effective temperatures. As an example we demonstrate that
fluctuation-dissipation relations hold, however with an effective temperature
differing from the effective temperature defined from the average energy.Comment: Some further clarifications. No changes in results or conclusion
Phase separation of a driven granular gas in annular geometry
This work investigates phase separation of a monodisperse gas of
inelastically colliding hard disks confined in a two-dimensional annulus, the
inner circle of which represents a "thermal wall". When described by granular
hydrodynamic equations, the basic steady state of this system is an azimuthally
symmetric state of increased particle density at the exterior circle of the
annulus. When the inelastic energy loss is sufficiently large, hydrodynamics
predicts spontaneous symmetry breaking of the annular state, analogous to the
van der Waals-like phase separation phenomenon previously found in a driven
granular gas in rectangular geometry. At a fixed aspect ratio of the annulus,
the phase separation involves a "spinodal interval" of particle area fractions,
where the gas has negative compressibility in the azimuthal direction. The heat
conduction in the azimuthal direction tends to suppress the instability, as
corroborated by a marginal stability analysis of the basic steady state with
respect to small perturbations. To test and complement our theoretical
predictions we performed event-driven molecular dynamics (MD) simulations of
this system. We clearly identify the transition to phase separated states in
the MD simulations, despite large fluctuations present, by measuring the
probability distribution of the amplitude of the fundamental Fourier mode of
the azimuthal spectrum of the particle density. We find that the instability
region, predicted from hydrodynamics, is always located within the phase
separation region observed in the MD simulations. This implies the presence of
a binodal (coexistence) region, where the annular state is metastable. The
phase separation persists when the driving and elastic walls are interchanged,
and also when the elastic wall is replaced by weakly inelastic one.Comment: 9 pages, 10 figures, to be published in PR
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