11,464 research outputs found
Efficient algorithm to study interconnected networks
Interconnected networks have been shown to be much more vulnerable to random
and targeted failures than isolated ones, raising several interesting questions
regarding the identification and mitigation of their risk. The paradigm to
address these questions is the percolation model, where the resilience of the
system is quantified by the dependence of the size of the largest cluster on
the number of failures. Numerically, the major challenge is the identification
of this cluster and the calculation of its size. Here, we propose an efficient
algorithm to tackle this problem. We show that the algorithm scales as O(N log
N), where N is the number of nodes in the network, a significant improvement
compared to O(N^2) for a greedy algorithm, what permits studying much larger
networks. Our new strategy can be applied to any network topology and
distribution of interdependencies, as well as any sequence of failures.Comment: 5 pages, 6 figure
Effect of particle polydispersity on the irreversible adsorption of fine particles on patterned substrates
We performed extensive Monte Carlo simulations of the irreversible adsorption
of polydispersed disks inside the cells of a patterned substrate. The model
captures relevant features of the irreversible adsorption of spherical
colloidal particles on patterned substrates. The pattern consists of (equal)
square cells, where adsorption can take place, centered at the vertices of a
square lattice. Two independent, dimensionless parameters are required to
control the geometry of the pattern, namely, the cell size and cell-cell
distance, measured in terms of the average particle diameter. However, to
describe the phase diagram, two additional dimensionless parameters, the
minimum and maximum particle radii are also required. We find that the
transition between any two adjacent regions of the phase diagram solely depends
on the largest and smallest particle sizes, but not on the shape of the
distribution function of the radii. We consider size dispersions up-to 20% of
the average radius using a physically motivated truncated Gaussian-size
distribution, and focus on the regime where adsorbing particles do not interact
with those previously adsorbed on neighboring cells to characterize the jammed
state structure. The study generalizes previous exact relations on monodisperse
particles to account for size dispersion. Due to the presence of the pattern,
the coverage shows a non-monotonic dependence on the cell size. The pattern
also affects the radius of adsorbed particles, where one observes preferential
adsorption of smaller radii particularly at high polydispersity.Comment: 9 pages, 5 figure
Shock waves on complex networks
Power grids, road maps, and river streams are examples of infrastructural
networks which are highly vulnerable to external perturbations. An abrupt local
change of load (voltage, traffic density, or water level) might propagate in a
cascading way and affect a significant fraction of the network. Almost
discontinuous perturbations can be modeled by shock waves which can eventually
interfere constructively and endanger the normal functionality of the
infrastructure. We study their dynamics by solving the Burgers equation under
random perturbations on several real and artificial directed graphs. Even for
graphs with a narrow distribution of node properties (e.g., degree or
betweenness), a steady state is reached exhibiting a heterogeneous load
distribution, having a difference of one order of magnitude between the highest
and average loads. Unexpectedly we find for the European power grid and for
finite Watts-Strogatz networks a broad pronounced bimodal distribution for the
loads. To identify the most vulnerable nodes, we introduce the concept of
node-basin size, a purely topological property which we show to be strongly
correlated to the average load of a node
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