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Random walks
Complexity Explorables
D Brockmann
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Modular hierarchical and power-law small-world networks bear structural optima for minimal first passage times and cover time
B F Maier
,
C Huepe
,
D Brockmann
Journal of Complex Networks 7 (6), 865-895
Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this …
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Cover time for random walks on arbitrary complex networks
B F Maier
,
D Brockmann
Physical Review E 96 (4), 042307
We present an analytical method for computing the mean cover time of a discrete-time random walk process on arbitrary, complex networks. The cover …
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Human mobility and spatial disease dynamics
D Brockmann
In Reviews of Nonlinear Dynamics and Complexity, H.G. Schuster (Ed.).
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Lévy flights in inhomogeneous media
D Brockmann
,
T Geisel
Phys. Rev. Lett. 90, 170601
We investigate the impact of external periodic potentials on superdiffusive random walks known as Lévy flights and show that even strongly …
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Lévy flights in external force fields: from models to equations
D Brockmann
,
I M Sokolov
Chemical Physics, 284 (1–2), 409--421
We consider different generalizations of the Fokker–Planck equation (FPE) devised to describe Lévy processes in potential force fields. We show that …
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