Multifractal Properties of the Random Resistor Network

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/\nu$ to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E (Rapid Comm

Exact results and scaling properties of small-world networks

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance, $\bar{\ell}$, and its variance, $\sigma^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition

Video Pandemics: Worldwide Viral Spreading of Psy's Gangnam Style Video

Viral videos can reach global penetration traveling through international channels of communication similarly to real diseases starting from a well-localized source. In past centuries, disease fronts propagated in a concentric spatial fashion from the the source of the outbreak via the short range human contact network. The emergence of long-distance air-travel changed these ancient patterns. However, recently, Brockmann and Helbing have shown that concentric propagation waves can be reinstated if propagation time and distance is measured in the flight-time and travel volume weighted underlying air-travel network. Here, we adopt this method for the analysis of viral meme propagation in Twitter messages, and define a similar weighted network distance in the communication network connecting countries and states of the World. We recover a wave-like behavior on average and assess the randomizing effect of non-locality of spreading. We show that similar result can be recovered from Google Trends data as well.Comment: 10 page

Topological dragging of solitons

We put forward properties of solitons supported by optical lattices featuring topological dislocations, and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.Comment: 15 pages, 5 figures, to appear in Physical Review Letter

Elementary processes governing the evolution of road networks

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) `densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) `exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.Comment: 10 pages, 6 figure

Towards two-dimensional metallic behavior at LaAlO3/SrTiO3 interfaces

Using a low-temperature conductive-tip atomic force microscope in cross-section geometry we have characterized the local transport properties of the metallic electron gas that forms at the interface between LaAlO3 and SrTiO3. At low temperature, we find that the carriers do not spread away from the interface but are confined within ~10 nm, just like at room temperature. Simulations taking into account both the large temperature and electric-field dependence of the permittivity of SrTiO3 predict a confinement over a few nm for sheet carrier densities larger than ~6 10^13 cm-2. We discuss the experimental and simulations results in terms of a multi-band carrier system. Remarkably, the Fermi wavelength estimated from Hall measurements is ~16 nm, indicating that the electron gas in on the verge of two-dimensionality.Comment: Accepted for publication in Physical Review Letter

Phase diagram of the Bose-Hubbard Model on Complex Networks

Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last decade. Here we show that the phase diagram of the Bose-Hubbard model, an exclusively quantum mechanical phase transition, also changes significantly when defined on random scale-free networks. We present a mean-field calculation of the model in annealed networks and we show that when the second moment of the average degree diverges the Mott-insulator phase disappears in the thermodynamic limit. Moreover we study the model on quenched networks and we show that the Mott-insulator phase disappears in the thermodynamic limit as long as the maximal eigenvalue of the adjacency matrix diverges. Finally we study the phase diagram of the model on Apollonian scale-free networks that can be embedded in 2 dimensions showing the extension of the results also to this case.Comment: (6 pages, 4 figures

Spatio-temporal beam dynamics in multimode nonlinear optical fibers

ABSTRACT We overview recent advances in the spatio-temporal nonlinear dynamics of optical pulses propagating in multimode optical fibers. The Kerr effect leads to spatial beam self-cleaning in a graded-index multimode optical fiber, followed by sideband series generation spanning multiple octaves. Effectively single mode supercontinuum spanning from the visible to the mid-infrared was also demonstrated. Enhancement of Kerr beam self-cleaning was observed in active fiber with quasi-step index profile. Moreover, mutual self-cleaning was recently reported for both the fundamental and the second harmonic beams in optically poled multimode fibers with cubic and quadratic nonlinearity

Dynamical response and confinement of the electrons at the LaAlO3/SrTiO3 interface

With infrared ellipsometry and transport measurements we investigated the electrons at the interface between LaAlO3 and SrTiO3. We obtained a sheet carrier density of Ns~5-9x 10E13 cm^-2, an effective mass of m*~3m_e, and a strongly frequency dependent mobility. The latter are similar as in bulk SrTi1-xNbxO3 and therefore suggestive of polaronic correlations of the confined carriers. We also determined the vertical density profile which has a strongly asymmetric shape with a rapid initial decay over the first 2 nm and a pronounced tail that extends to about 11 nm.Comment: 4 pages, 3 figures, 1 EPAPS file (3 figures

Association between ambulatory 24-hour blood pressure levels and brain volume reduction: a cross-sectional elderly population-based study

Previous literature has shown mixed results regarding the association between blood pressure levels and brain volume reduction. The objectives of this study were to determine whether high blood pressure levels were associated with focal brain volume reduction and whether high blood pressure-related focal brain volume reduction was associated with a decline in executive function performance. On the basis of a cross-sectional design, 24-hour ambulatory blood pressure measurements, as well as brain morphology from 3-dimensional magnetic resonance images, were assessed among 183 participants (mean, 65 +/- 0.6 years; 62.4% women). Average levels of systolic and diastolic blood pressures, as well as dip, pulse pressure, and mean arterial blood pressure, were used as outcomes. Cortical gray and white matter volumes were determined by automatic calculation using Statistical Parametric Mapping segmentation. Folstein\u27s Mini-Mental State Examination, digit span, part B of Trail Making, and Stroop tests were used to assess executive function performance. Sex, use of antihypertensive drugs, duration of hypertension, leukoaraiosis, body mass index, education level, and total brain matter volume were used as potential confounders. A significant blood pressure-related decrease in gray matter volume of the left supplementary motor areas (Brodmann area 6) and of the left superior and middle frontal gyrus (Brodmann area 8) was shown. No significant decrease was found with white matter volume. Blood pressure-related decreases in gray matter volume were significantly associated with a decline in executive function performance. The association of high blood pressure with brain volume reduction may in part explain blood pressure-related cognitive decline leading to dementia