Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cascading failures in isotropic and anisotropic spatial networks induced
  by localized attacks and overloads   In this paper we study the Motter-Lai model of cascading failures induced by
overloads in both isotropic and anisotropic spatial networks, generated by
placing nodes in a square lattice and using various distributions of link
lengths and angles. Anisotropy has not been earlier considered in the
Motter-Lai model and is a real feature that may affect the cascading failures.
This could reflect the existence of a preferred direction in which a given
attribute of the system manifests, such as power lines that follow a city built
parallel to the coast. We show that the anisotropy causes a greater spread of
damage along the preferential direction of links. We also identify the critical
linear size, $l_c$, for a square shaped localized attack, which satisfies with
high probability that above $l_c$ the cascading disrupts the giant component of
functional nodes, while below $l_c$ the damage does not spread. We find that,
for networks with any characteristic link length, their robustness decreases
with the strength of the anisotropy. We show that the value of $l_c$ is finite
and independent of the system size (for large systems), both for isotropic and
anisotropic networks. Thus, in contrast to random attacks, where the critical
fraction of nodes that survive the initial attack, $p_c$, is usually below 1,
here $p_c = 1$. Note that the analogy to $p_c = 1$ is also found for localized
attacks in interdependent spatial networks. Finally, we measure the final
distribution of functional cluster sizes and find a power-law behavior, with
exponents similar to regular percolation. This indicates that, after the
cascade which destroys the giant component, the system is at a percolation
critical point. Additionally, we observe a crossover in the value of the
distribution exponent, from critical percolation in a two-dimensional lattice
for strong spatial embedding, to mean-field percolation for weak embedding.

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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin