210 research outputs found
Application of the Gillespie algorithm to a granular intruder particle
We show how the Gillespie algorithm, originally developed to describe coupled
chemical reactions, can be used to perform numerical simulations of a granular
intruder particle colliding with thermalized bath particles. The algorithm
generates a sequence of collision ``events'' separated by variable time
intervals. As input, it requires the position-dependent flux of bath particles
at each point on the surface of the intruder particle. We validate the method
by applying it to a one-dimensional system for which the exact solution of the
homogeneous Boltzmann equation is known and investigate the case where the bath
particle velocity distribution has algebraic tails. We also present an
application to a granular needle in bath of point particles where we
demonstrate the presence of correlations between the translational and
rotational degrees of freedom of the intruder particle. The relationship
between the Gillespie algorithm and the commonly used Direct Simulation Monte
Carlo (DSMC) method is also discussed.Comment: 13 pages, 8 figures, to be published in J. Phys. A Math. Ge
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
Fractal Substructure of a Nanopowder
The structural evolution of a nano-powder by repeated dispersion and settling
can lead to characteristic fractal substructures. This is shown by numerical
simulations of a two-dimensional model agglomerate of adhesive rigid particles.
The agglomerate is cut into fragments of a characteristic size l, which then
are settling under gravity. Repeating this procedure converges to a loosely
packed structure, the properties of which are investigated: a) The final
packing density is independent of the initialization, b) the short-range
correlation function is independent of the fragment size, c) the structure is
fractal up to the fragmentation scale l with a fractal dimension close to 1.7,
and d) the relaxation time increases linearly with l.Comment: 4 pages, 8 figure
Movers and shakers: Granular damping in microgravity
The response of an oscillating granular damper to an initial perturbation is
studied using experiments performed in microgravity and granular dynamics
mulations. High-speed video and image processing techniques are used to extract
experimental data. An inelastic hard sphere model is developed to perform
simulations and the results are in excellent agreement with the experiments.
The granular damper behaves like a frictional damper and a linear decay of the
amplitude is bserved. This is true even for the simulation model, where
friction forces are absent. A simple expression is developed which predicts the
optimal damping conditions for a given amplitude and is independent of the
oscillation frequency and particle inelasticities.Comment: 9 pages, 9 figure
Towards a continuum theory of clustering in a freely cooling inelastic gas
We performed molecular dynamics simulations to investigate the clustering
instability of a freely cooling dilute gas of inelastically colliding disks in
a quasi-one-dimensional setting. We observe that, as the gas cools, the shear
stress becomes negligibly small, and the gas flows by inertia only. Finite-time
singularities, intrinsic in such a flow, are arrested only when close-packed
clusters are formed. We observe that the late-time dynamics of this system are
describable by the Burgers equation with vanishing viscosity, and predict the
long-time coarsening behavior.Comment: 7 pages, 5 eps figures, to appear in Europhys. Let
Breaking arches with vibrations: the role of defects
We present experimental results about the stability of arches against
external vibrations. Two dimensional strings of mutually stabilizing grains are
geometrically analyzed and subsequently submitted to a periodic forcing at
fixed frequency and increasing amplitude. The main factor that determines the
granular arch resistance against vibrations is the maximum angle among those
formed between any particle of the arch and its two neighbors: the higher the
maximum angle is, the easier to break the arch. Based in an analysis of the
forces, a simple explanation is given for this dependence. From this,
interesting information can be extracted about the expected magnitudes of
normal forces and friction coefficients of the particles conforming the arches
Marchenko-Ostrovski mappings for periodic Jacobi matrices
We consider the 1D periodic Jacobi matrices. The spectrum of this operator is
purely absolutely continuous and consists of intervals separated by gaps. We
solve the inverse problem (including characterization) in terms of vertical
slits on the quasimomentum domain . Furthermore, we obtain a priori two-sided
estimates for vertical slits in terms of Jacoby matrices
Dynamic regimes of hydrodynamically coupled self-propelling particles
We analyze the collective dynamics of self-propelling particles (spps) which
move at small Reynolds numbers including the hydrodynamic coupling to the
suspending solvent through numerical simulations. The velocity distribution
functions show marked deviations from Gaussian behavior at short times, and the
mean-square displacement at long times shows a transition from diffusive to
ballistic motion for appropriate driving mechanism at low concentrations. We
discuss the structures the spps form at long times and how they correlate to
their dynamic behavior.Comment: 7 pages, 4 figure
Guessing probability distributions from small samples
We propose a new method for the calculation of the statistical properties, as
e.g. the entropy, of unknown generators of symbolic sequences. The probability
distribution of the elements of a population can be approximated by
the frequencies of a sample provided the sample is long enough so that
each element occurs many times. Our method yields an approximation if this
precondition does not hold. For a given we recalculate the Zipf--ordered
probability distribution by optimization of the parameters of a guessed
distribution. We demonstrate that our method yields reliable results.Comment: 10 pages, uuencoded compressed PostScrip
Entropy and Long range correlations in literary English
Recently long range correlations were detected in nucleotide sequences and in
human writings by several authors. We undertake here a systematic investigation
of two books, Moby Dick by H. Melville and Grimm's tales, with respect to the
existence of long range correlations. The analysis is based on the calculation
of entropy like quantities as the mutual information for pairs of letters and
the entropy, the mean uncertainty, per letter. We further estimate the number
of different subwords of a given length . Filtering out the contributions
due to the effects of the finite length of the texts, we find correlations
ranging to a few hundred letters. Scaling laws for the mutual information
(decay with a power law), for the entropy per letter (decay with the inverse
square root of ) and for the word numbers (stretched exponential growth with
and with a power law of the text length) were found.Comment: 8 page
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