52 research outputs found
Rain: Relaxations in the sky
We demonstrate how, from the point of view of energy flow through an open
system, rain is analogous to many other relaxational processes in Nature such
as earthquakes. By identifying rain events as the basic entities of the
phenomenon, we show that the number density of rain events per year is
inversely proportional to the released water column raised to the power 1.4.
This is the rain-equivalent of the Gutenberg-Richter law for earthquakes. The
event durations and the waiting times between events are also characterised by
scaling regions, where no typical time scale exists. The Hurst exponent of the
rain intensity signal . It is valid in the temporal range from
minutes up to the full duration of the signal of half a year. All of our
findings are consistent with the concept of self-organised criticality, which
refers to the tendency of slowly driven non-equilibrium systems towards a state
of scale free behaviour.Comment: 9 pages, 8 figures, submitted to PR
Avalanche Merging and Continuous Flow in a Sandpile Model
A dynamical transition separating intermittent and continuous flow is
observed in a sandpile model, with scaling functions relating the transport
behaviors between both regimes. The width of the active zone diverges with
system size in the avalanche regime but becomes very narrow for continuous
flow. The change of the mean slope, Delta z, on increasing the driving rate, r,
obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the
continuous flow phase with an exponent theta given, paradoxically, only in
terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).Comment: Explanations added; relation to other model
Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile
We investigate the formation processes of a sandpile using numerical
simulation. We find a new relation between the fluctuation of the motion of the
top and the surface state of a sandpile. The top moves frequently as particles
are fed one by one every time interval T. The time series of the top location
has the power spectrum which obeys a power law, S(f)~f^{\alpha}, and its
exponent \alpha depends on T and the system size w. The surface state is
characterized by two time scales; the lifetime of an avalanche, T_{a}, and the
time required to cause an avalanche, T_{s}. The surface state is fluid-like
when T_{a}~T_{s}, and it is solid-like when T_{a}<<T_{s}. Our numerical results
show that \alpha is a function of T_{s}/T_{a}.Comment: 15 pages, 13 figure
Slowly driven sandpile formation with granular mixtures
We introduce a one-dimensional sandpile model with different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial when N=1, but for N=2 we observe four broad classes of sandpile structure in different regions of the parameter space. We describe and explain the behaviour of each of these classes, giving quantitative analysis wherever possible. The behaviour of sandpiles with N>2 essentially consists of combinations of these four classes. We investigate the model's robustness and highlight the key areas that any experiment designed to reproduce these results should focus on
Coiling Instability of Multilamellar Membrane Tubes with Anchored Polymers
We study experimentally a coiling instability of cylindrical multilamellar
stacks of phospholipid membranes, induced by polymers with hydrophobic anchors
grafted along their hydrophilic backbone. Our system is unique in that coils
form in the absence of both twist and adhesion. We interpret our experimental
results in terms of a model in which local membrane curvature and polymer
concentration are coupled. The model predicts the occurrence of maximally tight
coils above a threshold polymer occupancy. A proper comparison between the
model and experiment involved imaging of projections from simulated coiled
tubes with maximal curvature and complicated torsions.Comment: 11 pages + 7 GIF figures + 10 JPEG figure
Internal avalanches in a pile of superconducting vortices
Using an array of miniature Hall probes, we monitored the spatiotemporal
variation of the internal magnetic induction in a superconducting niobium
sample during a slow sweep of external magnetic field. We found that a sizable
fraction of the increase in the local vortex population occurs in abrupt jumps.
The size distribution of these avalanches presents a power-law collapse on a
limited range. In contrast, at low temperatures and low fields, huge avalanches
with a typical size occur and the system does not display a well-defined
macroscopic critical current.Comment: 5 pages including 5 figure
Viscous stabilization of 2D drainage displacements with trapping
We investigate the stabilization mechanisms due to viscous forces in the
invasion front during drainage displacement in two-dimensional porous media
using a network simulator. We find that in horizontal displacement the
capillary pressure difference between two different points along the front
varies almost linearly as function of height separation in the direction of the
displacement. The numerical result supports arguments taking into account the
loopless displacement pattern where nonwetting fluid flow in separate strands
(paths). As a consequence, we show that existing theories developed for viscous
stabilization, are not compatible with drainage when loopless strands dominate
the displacement process.Comment: The manuscript has been substantially revised. Accepted in Phys. Rev.
Let
Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice
We present a two-dimensional system which exhibits features of self-organized
criticality. The avalanches which occur on the surface of a pile of rice are
found to exhibit finite size scaling in their probability distribution. The
critical exponents are = 1.21(2) for the avalanche size distribution and
= 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches
is studied leading to a fractal dimension of the active sites of =
1.58(2). Using a set of scaling relations, we can calculate the roughness
exponent = 0.41(3) and the dynamic exponent = 1.56(8). This result is compared with that obtained from a power
spectrum analysis of the surface roughness, which yields = 0.42(3) and
= 1.5(1) in excellent agreement with those obtained from the scaling
relations.Comment: 7 pages, 8 figures, accepted for publication in PR
Simulating temporal evolution of pressure in two-phase flow in porous media
We have simulated the temporal evolution of pressure due to capillary and
viscous forces in two-phase drainage in porous media. We analyze our result in
light of macroscopic flow equations for two-phase flow. We also investigate the
effect of the trapped clusters on the pressure evolution and on the effective
permeability of the system. We find that the capillary forces play an important
role during the displacements for both fast and slow injection rates and both
when the invading fluid is more or less viscous than the defending fluid. The
simulations are based on a network simulator modeling two-phase drainage
displacements on a two-dimensional lattice of tubes.Comment: 12 pages, LaTeX, 14 figures, Postscrip
Fine Structure of Avalanches in the Abelian Sandpile Model
We study the two-dimensional Abelian Sandpile Model on a square lattice of
linear size L. We introduce the notion of avalanche's fine structure and
compare the behavior of avalanches and waves of toppling. We show that
according to the degree of complexity in the fine structure of avalanches,
which is a direct consequence of the intricate superposition of the boundaries
of successive waves, avalanches fall into two different categories. We propose
scaling ans\"{a}tz for these avalanche types and verify them numerically. We
find that while the first type of avalanches has a simple scaling behavior, the
second (complex) type is characterized by an avalanche-size dependent scaling
exponent. This provides a framework within which one can understand the failure
of a consistent scaling behavior in this model.Comment: 10 page
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