Synchronization of networks with variable local properties

We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical properties of the dynamics change when the clustering coefficient and the average shortest path length are varied. The results show that the onset of synchronization does depend on these properties, though the dependence is smooth. On the contrary, the appearance of complete synchronization is radically affected by the structure of the networks. Our study highlights the need of exploring the whole phase diagram and not only the stability of the fully synchronized state, where most studies have been done up to now.Comment: 5 pages and 3 figures. APS style. Paper to be published in IJBC (special issue on Complex Networks' Structure and Dynamics

The design of an automated verification of redundant systems

Handbook describes design processes, presents design considerations and techniques, gives tutorial material on implementation and methodology, shows design aids, illustrates use of design aids and application samples, and identifies general practices to be adhered to or avoided

Characterization of Fe-N nanocrystals and nitrogen–containing inclusions in (Ga,Fe)N thin films using transmission electron microscopy

Nanometric inclusions filled with nitrogen, located adjacent to FenN (n¼3 or 4) nanocrystals within (Ga,Fe)N layers, are identified and characterized using scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS). High-resolution STEM images reveal a truncation of the Fe-N nanocrystals at their boundaries with the nitrogen-containing inclusions. A controlled electron beam hole drilling experiment is used to release nitrogen gas from an inclusion in situ in the electron microscope. The density of nitrogen in an individual inclusion is measured to be 1.460.3 g/cm3. These observations provide an explanation for the location of surplus nitrogen in the (Ga,Fe)N layers, which is liberated by the nucleation of FenN (n>1) nanocrystals during growth

Dynamics of Impurity and Valence Bands in GaMnAs within the Dynamical Mean Field Approximation

We calculate the density-of-states and the spectral function of GaMnAs within the dynamical mean-field approximation. Our model includes the competing effects of the strong spin-orbit coupling on the J=3/2 GaAs hole bands and the exchange interaction between the magnetic ions and the itinerant holes. We study the quasi-particle and impurity bands in the paramagnetic and ferromagnetic phases for different values of impurity-hole coupling at the Mn doping of x=0.05. By analyzing the anisotropic angular distribution of the impurity band carriers at T=0, we conclude that the carrier polarization is optimal when the carriers move along the direction parallel to the average magnetization.Comment: 6 pages, 4 figure

Optimization of photon storage fidelity in ordered atomic arrays

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and "selective" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number $N_\mathrm{a}$ like $\sim (\log N_\mathrm{a})^2/N_\mathrm{a}^2$, and that, remarkably, an array of just $4 \times 4$ atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.Comment: paper is now identical to published versio

Explosive Synchronization Transitions in Scale-free Networks

The emergence of explosive collective phenomena has recently attracted much attention due to the discovery of an explosive percolation transition in complex networks. In this Letter, we demonstrate how an explosive transition shows up in the synchronization of complex heterogeneous networks by incorporating a microscopic correlation between the structural and the dynamical properties of the system. The characteristics of this explosive transition are analytically studied in a star graph reproducing the results obtained in synthetic scale-free networks. Our findings represent the first abrupt synchronization transition in complex networks thus providing a deeper understanding of the microscopic roots of explosive critical phenomena.Comment: 6 pages and 5 figures. To appear in Physical Review Letter