28 research outputs found
Sampling rare fluctuations of height in the Oslo ricepile model
We have studied large deviations of the height of the pile from its mean
value in the Oslo ricepile model. We sampled these very rare events with
probabilities of order by Monte Carlo simulations using importance
sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf
73}, 021303, 2006] that in steady state of the Oslo ricepile model, the
probability of large negative height fluctuations about
the mean varies as as with
held fixed, and .Comment: 7 pages, 8 figure
Probability distribution of residence-times of grains in sandpile models
We show that the probability distribution of the residence-times of sand
grains in sandpile models, in the scaling limit, can be expressed in terms of
the survival probability of a single diffusing particle in a medium with
absorbing boundaries and space-dependent jump rates. The scaling function for
the probability distribution of residence times is non-universal, and depends
on the probability distribution according to which grains are added at
different sites. We determine this function exactly for the 1-dimensional
sandpile when grains are added randomly only at the ends. For sandpiles with
grains are added everywhere with equal probability, in any dimension and of
arbitrary shape, we prove that, in the scaling limit, the probability that the
residence time greater than t is exp(-t/M), where M is the average mass of the
pile in the steady state. We also study finite-size corrections to this
function.Comment: 8 pages, 5 figures, extra file delete
Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure
We have studied precursors of the global failure in some self-organised
critical models of sand-pile (in BTW and Manna models) and in the random fiber
bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed
number of sand grains (heights) to any central site of the stable pile, the
local dynamics starts and continues for an average relaxation time (\tau) and
an average number of topplings (\Delta) spread over a radial distance (\xi). We
find that these quantities all depend on the average height (h_{av}) of the
pile and they all diverge as (h_{av}) approaches the critical height (h_{c})
from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim
(h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numerically
we find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for both
BTW and Manna model in two dimensions. In the strained RFB model we find that
the breakdown susceptibility (\chi) (giving the differential increment of the
number of broken fibers due to increase in external load) and the relaxation
time (\tau), both diverge as the applied load or stress (\sigma) approaches the
network failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c})
(-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). These
self-organised dynamical models of failure therefore show some definite
precursors with robust power laws long before the failure point. Such
well-characterised precursors should help predicting the global failure point
of the systems in advance.Comment: 13 pages, 9 figures (eps
Crises and collective socio-economic phenomena: simple models and challenges
Financial and economic history is strewn with bubbles and crashes, booms and
busts, crises and upheavals of all sorts. Understanding the origin of these
events is arguably one of the most important problems in economic theory. In
this paper, we review recent efforts to include heterogeneities and
interactions in models of decision. We argue that the Random Field Ising model
(RFIM) indeed provides a unifying framework to account for many collective
socio-economic phenomena that lead to sudden ruptures and crises. We discuss
different models that can capture potentially destabilising self-referential
feedback loops, induced either by herding, i.e. reference to peers, or
trending, i.e. reference to the past, and account for some of the phenomenology
missing in the standard models. We discuss some empirically testable
predictions of these models, for example robust signatures of RFIM-like herding
effects, or the logarithmic decay of spatial correlations of voting patterns.
One of the most striking result, inspired by statistical physics methods, is
that Adam Smith's invisible hand can badly fail at solving simple coordination
problems. We also insist on the issue of time-scales, that can be extremely
long in some cases, and prevent socially optimal equilibria to be reached. As a
theoretical challenge, the study of so-called "detailed-balance" violating
decision rules is needed to decide whether conclusions based on current models
(that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several
minor improvements along reviewers' comment
Trends in key soil parameters under conservation agriculture-based sustainable intensification farming practices in the Eastern Ganga Alluvial Plains
Key soil parameters, organic matter, soil pH and plant nutrients determine the capacity of a soil to sustain plant and animal productivity. Conservation agriculture (CA) and crop diversification or intensification may change these soil parameters positively or negatively, which eventually affect long-term sustainability. We monitored these key soil properties (at depths of 0-15 and 15-30 cm) under CA-based sustainable intensification practices: zero-till (ZT), and crop residue retention, and crop rotations on Inceptisols and Entisols in the Eastern Ganga Alluvial Plains from 2014 to 2017. The rainfall of this sub-tropical region is 1273-3201 mm. Soil organic carbon (C) ranged within 0.46-1.13% and generally followed (positive) rainfall gradients. At all sites, the soil under ZT tended to have higher organic C than conventional tillage (CT). Soil pH ranged within 5.7-7.8 across the region. At all sites, soil pH generally decreased under ZT compared to CT. This was most marked at some acidic soil sites where pH decreased by up to 0.4 units; the lower the initial soil pH, the higher was the decrease in pH under ZT practice. In contrast, the reverse trend was observed for soil organic C. Partial nutrient balances for N, P and K in rice-wheat and rice-maize systems were positive for N and P