193 research outputs found
Bifurcation Diagram for Compartmentalized Granular Gases
The bifurcation diagram for a vibro-fluidized granular gas in N connected
compartments is constructed and discussed. At vigorous driving, the uniform
distribution (in which the gas is equi-partitioned over the compartments) is
stable. But when the driving intensity is decreased this uniform distribution
becomes unstable and gives way to a clustered state. For the simplest case,
N=2, this transition takes place via a pitchfork bifurcation but for all N>2
the transition involves saddle-node bifurcations. The associated hysteresis
becomes more and more pronounced for growing N. In the bifurcation diagram,
apart from the uniform and the one-peaked distributions, also a number of
multi-peaked solutions occur. These are transient states. Their physical
relevance is discussed in the context of a stability analysis.Comment: Phys. Rev. E, in press. Figure quality has been reduced in order to
decrease file-siz
Hysteretic clustering in granular gas
Granular material is vibro-fluidized in N=2 and N=3 connected compartments,
respectively. For sufficiently strong shaking the granular gas is
equi-partitioned, but if the shaking intensity is lowered, the gas clusters in
one compartment. The phase transition towards the clustered state is of 2nd
order for N=2 and of 1st order for N=3. In particular, the latter is
hysteretic. The experimental findings are accounted for within a dynamical
model that exactly has the above properties
Sudden Collapse of a Granular Cluster
Single clusters in a vibro-fluidized granular gas in N connected compartments
become unstable at strong shaking. They are experimentally shown to collapse
very abruptly. The observed cluster lifetime (as a function of the driving
intensity) is analytically calculated within a flux model, making use of the
self-similarity of the process. After collapse, the cluster diffuses out into
the uniform distribution in a self-similar way, with an anomalous diffusion
exponent 1/3.Comment: 4 pages, 4 figures. Figure quality has been reduced in order to
decrease file-siz
Yang-Lee zeroes for an urn model for the separation of sand
We apply the Yang-Lee theory of phase transitions to an urn model of
separation of sand. The effective partition function of this nonequilibrium
system can be expressed as a polynomial of the size-dependent effective
fugacity . Numerical calculations show that in the thermodynamic limit, the
zeros of the effective partition function are located on the unit circle in the
complex -plane. In the complex plane of the actual control parameter certain
roots converge to the transition point of the model. Thus the Yang-Lee theory
can be applied to a wider class of nonequilibrium systems than those considered
previously.Comment: 4 pages, 3 eps figures include
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
Dynamics of vibrofluidized granular gases in periodic structures
The behavior of a driven granular gas in a container consisting of
connected compartments is studied employing a microscopic kinetic model. After
obtaining the governing equations for the occupation numbers and the granular
temperatures of each compartment we consider the various dynamical regimes. The
system displays interesting analogies with the ordering processes of phase
separating mixtures quenched below the their critical point. In particular, we
show that below a certain value of the driving intensity the populations of the
various compartments become unequal and the system clusterizes. Such a
phenomenon is not instantaneous, but is characterized by a time scale, ,
which follows a Vogel-Vulcher exponential behavior. On the other hand, the
reverse phenomenon which involves the ``evaporation'' of a cluster due to the
driving force is also characterized by a second time scale which diverges at
the limit of stability of the cluster.Comment: 11 pages, 17 figure
Steady state representation of the homogeneous cooling state of a granular gas
The properties of a dilute granular gas in the homogeneous cooling state are
mapped to those of a stationary state by means of a change in the time scale
that does not involve any internal property of the system. The new
representation is closely related with a general property of the granular
temperature in the long time limit. The physical and practical implications of
the mapping are discussed. In particular, simulation results obtained by the
direct simulation Monte Carlo method applied to the scaled dynamics are
reported. This includes ensemble averages and also the velocity autocorrelation
function, as well as the self-diffusion coefficient obtained from the latter by
means of the Green-Kubo representation. In all cases, the obtained results are
compared with theoretical predictions
Motion of condensates in non-Markovian zero-range dynamics
Condensation transition in a non-Markovian zero-range process is studied in
one and higher dimensions. In the mean-field approximation, corresponding to
infinite range hopping, the model exhibits condensation with a stationary
condensate, as in the Markovian case, but with a modified phase diagram. In the
case of nearest-neighbor hopping, the condensate is found to drift by a
"slinky" motion from one site to the next. The mechanism of the drift is
explored numerically in detail. A modified model with nearest-neighbor hopping
which allows exact calculation of the steady state is introduced. The steady
state of this model is found to be a product measure, and the condensate is
stationary.Comment: 31 pages, 9 figure
On a new fixed point of the renormalization group operator for area-preserving maps
The breakup of the shearless invariant torus with winding number
is studied numerically using Greene's residue criterion in
the standard nontwist map. The residue behavior and parameter scaling at the
breakup suggests the existence of a new fixed point of the renormalization
group operator (RGO) for area-preserving maps. The unstable eigenvalues of the
RGO at this fixed point and the critical scaling exponents of the torus at
breakup are computed.Comment: 4 pages, 5 figure
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