The propensity for synchronization of complex networks with directed and weighted links is considered. We show that a weighting procedure based upon the global structure of network pathways enhances complete synchronization of identical dynamical units in scale-free networks. Furthermore, we numerically show that very similar conditions hold also for phase synchronization of nonidentical chaotic oscillators.

Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the refractive index are studied by using a two-component, highly symmetric version of Maxwell’s equations. The use of any slow varying amplitude approximation is avoided. Transfer matrices of sharp nonstationary interfaces are calculated explicitly, together with the amplitudes of all secondary waves produced in the scattering. Time-varying multilayer structures and spatiotemporal lenses in various configurations are investigated analytically and numerically in a unified approach. Several effects are reported, such as pulse compression, broadening and spectral manipulation of pulses by a spatiotemporal lens, and the closure of the forbidden frequency gaps with the subsequent opening of wave number band gaps in a generalized Bragg reflector.

Single‐phase multiferroic materials are of considerable interest for future memory and sensing applications. Thin films of Aurivillius phase Bi ₇ Ti ₃ Fe ₃ O ₂₁ and Bi ₆ Ti _2.8 Fe _1.52 Mn _0.68 O ₁₈ (possessing six and five perovskite units per half‐cell, respectively) have been prepared by chemical solution deposition on c‐plane sapphire. Superconducting quantum interference device magnetometry reveal Bi ₇ Ti ₃ Fe ₃ O ₂₁ to be antiferromagnetic (T_N = 190 K) and weakly ferromagnetic below 35 K, however, Bi ₆ Ti _2.8 Fe _1.52 Mn _0.68 O ₁₈ gives a distinct room‐temperature in‐plane ferromagnetic signature (M_s = 0.74 emu/g, μ₀H_c =7 mT). Microstructural analysis, coupled with the use of a statistical analysis of the data, allows us to conclude that ferromagnetism does not originate from second phase inclusions, with a confidence level of 99.5%. Piezoresponse force microscopy (PFM) demonstrates room‐temperature ferroelectricity in both films, whereas PFM observations on Bi ₆ Ti _2.8 Fe _1.52 Mn _0.68 O ₁₈ show Aurivillius grains undergo ferroelectric domain polarization switching induced by an applied magnetic field. Here, we show for the first time that Bi ₆ Ti _2.8 Fe _1.52 Mn _0.68 O ₁₈ thin films are both ferroelectric and ferromagnetic and, demonstrate magnetic field‐induced switching of ferroelectric polarization in individual Aurivillius phase grains at room temperature.

The propensity for synchronization is studied in a complex network of asymmetrically coupled units, where the asymmetry in a given link is determined by the relative age of the involved nodes. In growing scale-free networks, synchronization is enhanced when couplings from older to younger nodes are dominant. We describe the requirements for such an effect in a more general context and compare with the situations in nongrowing random networks with and without a degree ordering.

We consider a set of interacting phase oscillators, with a coupling between synchronized nodes adaptively reinforced, and the constraint of a limited resource for a node to establish connections with the other units of the network. We show that such a competitive mechanism leads to the emergence of a rich modular structure underlying cluster synchronization, and to a scale-free distribution for the connection strengths of the units.

Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior.