27 research outputs found
The anatomy of urban social networks and its implications in the searchability problem
The appearance of large geolocated communication datasets has recently
increased our understanding of how social networks relate to their physical
space. However, many recurrently reported properties, such as the spatial
clustering of network communities, have not yet been systematically tested at
different scales. In this work we analyze the social network structure of over
25 million phone users from three countries at three different scales: country,
provinces and cities. We consistently find that this last urban scenario
presents significant differences to common knowledge about social networks.
First, the emergence of a giant component in the network seems to be controlled
by whether or not the network spans over the entire urban border, almost
independently of the population or geographic extension of the city. Second,
urban communities are much less geographically clustered than expected. These
two findings shed new light on the widely-studied searchability in
self-organized networks. By exhaustive simulation of decentralized search
strategies we conclude that urban networks are searchable not through
geographical proximity as their country-wide counterparts, but through an
homophily-driven community structure
Steep sharp-crested gravity waves on deep water
A new type of steady steep two-dimensional irrotational symmetric periodic
gravity waves on inviscid incompressible fluid of infinite depth is revealed.
We demonstrate that these waves have sharper crests in comparison with the
Stokes waves of the same wavelength and steepness. The speed of a fluid
particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
The adjoining cell mapping and its recursive unraveling, Part II: Application to selected problems
Several applications of the adjoining cell mapping technique are provided here by employing the adaptive mapping unraveling algorithm to analyze smooth and pathological autonomous dynamical systems. The performance of an implementation of recursive unraveling algorithm is also illustrated regarding its low memory requirements for computa- tional purposes when compared with the simple cell mapping method. The applications considered here illustrate the effectiveness of the adjoining cell mapping technique in its ability to determine limit cycles and to unravel nonstandard dynamics. The advantages of this new technique of global analysis over the simple cell mapping method are discussed
Spatial bifurcations of interfacial waves when the phase and group velocities are nearly equal
Steady waves at the interface between two immiscible and inviscid fluids of differing density are studied. The governing equations are reformulated as a spatial Hamiltonian system leading to new variational principles for uniform states and travelling waves. Analytical methods based on the properties of the Hamiltonian structure and numerical methods are used to find new branches of steady nonlinear interfacial waves in the
eighbourhood of the singularity c = cg. While the water-wave problem (upper fluid density negligible) near this singularity has received considerable attention the results for interfacial waves present some new features. The branches of travelling waves when plotted in ()-space, where and are related to the energy flux and flow force respectively, show new bifurcations in the context of hydrodynamic waves even at very low amplitudes. The secondary bifurcations are explained by a spatial analogue of the superharmonic instability. An interesting analogy is also found between the spatial bifurcations of travelling waves and the Kelvin–Helmholtz instability. The new branches of waves occur at physically realizable values of the parameters and therefore could have implications for interfacial waves in applications