5 research outputs found
Fragmentation Experiment and Model for Falling Mercury Drops
The experiment consists of counting and measuring the size of the many
fragments observed after the fall of a mercury drop on the floor. The size
distribution follows a power-law for large enough fragments. We address the
question of a possible crossover to a second, different power-law for small
enough fragments. Two series of experiments were performed. The first uses a
traditional film photographic camera, and the picture is later treated on a
computer in order to count the fragments and classify them according to their
sizes. The second uses a modern digital camera. The first approach has the
advantage of a better resolution for small fragment sizes. The second, although
with a poorer size resolution, is more reliable concerning the counting of all
fragments up to its resolution limit. Both together clearly indicate the real
existence of the quoted crossover.
The model treats the system microscopically during the tiny time interval
when the initial drop collides with the floor. The drop is modelled by a
connected cluster of Ising spins pointing up (mercury) surrounded by Ising
spins pointing down (air). The Ising coupling which tends to keep the spins
segregated represents the surface tension. Initially the cluster carries an
extra energy equally shared among all its spins, corresponding to the coherent
kinetic energy due to the fall. Each spin which touches the floor loses its
extra energy transformed into a thermal, incoherent energy represented by a
temperature used then to follow the dynamics through Monte Carlo simulations.
Whenever a small piece becomes disconnected from the big cluster, it is
considered a fragment, and counted. The results also indicate the existence of
the quoted crossover in the fragment-size distribution.Comment: 6 pages, 3 figure
Markov Properties of Electrical Discharge Current Fluctuations in Plasma
Using the Markovian method, we study the stochastic nature of electrical
discharge current fluctuations in the Helium plasma. Sinusoidal trends are
extracted from the data set by the Fourier-Detrended Fluctuation analysis and
consequently cleaned data is retrieved. We determine the Markov time scale of
the detrended data set by using likelihood analysis. We also estimate the
Kramers-Moyal's coefficients of the discharge current fluctuations and derive
the corresponding Fokker-Planck equation. In addition, the obtained Langevin
equation enables us to reconstruct discharge time series with similar
statistical properties compared with the observed in the experiment. We also
provide an exact decomposition of temporal correlation function by using
Kramers-Moyal's coefficients. We show that for the stationary time series, the
two point temporal correlation function has an exponential decaying behavior
with a characteristic correlation time scale. Our results confirm that, there
is no definite relation between correlation and Markov time scales. However
both of them behave as monotonic increasing function of discharge current
intensity. Finally to complete our analysis, the multifractal behavior of
reconstructed time series using its Keramers-Moyal's coefficients and original
data set are investigated. Extended self similarity analysis demonstrates that
fluctuations in our experimental setup deviates from Kolmogorov (K41) theory
for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references,
figures and major correction