Resonance tongues and patterns in periodically forced reaction-diffusion systems

Various resonant and near-resonant patterns form in a light-sensitive Belousov-Zhabotinsky (BZ) reaction in response to a spatially-homogeneous time-periodic perturbation with light. The regions (tongues) in the forcing frequency and forcing amplitude parameter plane where resonant patterns form are identified through analysis of the temporal response of the patterns. Resonant and near-resonant responses are distinguished. The unforced BZ reaction shows both spatially-uniform oscillations and rotating spiral waves, while the forced system shows patterns such as standing-wave labyrinths and rotating spiral waves. The patterns depend on the amplitude and frequency of the perturbation, and also on whether the system responds to the forcing near the uniform oscillation frequency or the spiral wave frequency. Numerical simulations of a forced FitzHugh-Nagumo reaction-diffusion model show both resonant and near-resonant patterns similar to the BZ chemical system

Magnetic properties of undoped Cu2O fine powders with magnetic impurities and/or cation vacancies

Fine powders of micron- and submicron-sized particles of undoped Cu2O semiconductor, with three different sizes and morphologies have been synthesized by different chemical processes. These samples include nanospheres 200 nm in diameter, octahedra of size 1 micron, and polyhedra of size 800 nm. They exhibit a wide spectrum of magnetic properties. At low temperature, T = 5 K, the octahedron sample is diamagnetic. The nanosphere is paramagnetic. The other two polyhedron samples synthesized in different runs by the same process are found to show different magnetic properties. One of them exhibits weak ferromagnetism with T_C = 455 K and saturation magnetization, M_S = 0.19 emu/g at T = 5 K, while the other is paramagnetic. The total magnetic moment estimated from the detected impurity concentration of Fe, Co, and Ni, is too small to account for the observed magnetism by one to two orders of magnitude. Calculations by the density functional theory (DFT) reveal that cation vacancies in the Cu2O lattice are one of the possible causes of induced magnetic moments. The results further predict that the defect-induced magnetic moments favour a ferromagnetically coupled ground state if the local concentration of cation vacancies, n_C, exceeds 12.5%. This offers a possible scenario to explain the observed magnetic properties. The limitations of the investigations in the present work, in particular in the theoretical calculations, are discussed and possible areas for further study are suggested.Comment: 20 pages, 5 figures 2 tables, submitted to J Phys Condense Matte

An MHD Model For Magnetar Giant Flares

Giant flares on soft gamma-ray repeaters that are thought to take place on magnetars release enormous energy in a short time interval. Their power can be explained by catastrophic instabilities occurring in the magnetic field configuration and the subsequent magnetic reconnection. By analogy with the coronal mass ejection (CME) events on the Sun, we develop a theoretical model via an analytic approach for magnetar giant flares. In this model, the rotation and/or displacement of the crust causes the field to twist and deform, leading to flux rope formation in the magnetosphere and energy accumulation in the related configuration. When the energy and helicity stored in the configuration reach a threshold, the system loses its equilibrium, the flux rope is ejected outward in a catastrophic way, and magnetic reconnection helps the catastrophe develop to a plausible eruption. By taking SGR 1806 - 20 as an example, we calculate the free magnetic energy released in such an eruptive process and find that it is more than $10^{47}$ ergs, which is enough to power a giant flare. The released free magnetic energy is converted into radiative energy, kinetic energy and gravitational energy of the flux rope. We calculated the light curves of the eruptive processes for the giant flares of SGR 1806 - 20, SGR 0526-66 and SGR 1900+14, and compared them with the observational data. The calculated light curves are in good agreement with the observed light curves of giant flares.Comment: Accepted to Ap

Time evolution, cyclic solutions and geometric phases for general spin in an arbitrarily varying magnetic field

A neutral particle with general spin and magnetic moment moving in an arbitrarily varying magnetic field is studied. The time evolution operator for the Schr\"odinger equation can be obtained if one can find a unit vector that satisfies the equation obeyed by the mean of the spin operator. There exist at least $2s+1$ cyclic solutions in any time interval. Some particular time interval may exist in which all solutions are cyclic. The nonadiabatic geometric phase for cyclic solutions generally contains extra terms in addition to the familiar one that is proportional to the solid angle subtended by the closed trace of the spin vector.Comment: revtex4, 8 pages, no figur

Harnessing heterogeneous social networks for better recommendations: A grey relational analysis approach

Most of the extant studies in social recommender system are based on explicit social relationships, while the potential of implicit relationships in the heterogeneous social networks remains largely unexplored. This study proposes a new approach to designing a recommender system by employing grey relational analysis on the heterogeneous social networks. It starts with the establishment of heterogeneous social networks through the user-item bipartite graph, user social network graph and user-attribute bipartite graph; and then uses grey relational analysis to identify implicit social relationships, which are then incorporated into the matrix factorization model. Five experiments were conducted to test the performance of our approach against four state-of-the-art baseline methods. The results show that compared with the baseline methods, our approach can effectively alleviate the sparsity problem, because the heterogeneous social network provides richer information. In addition, the grey relational analysis method has the advantage of low requirements for data size and efficiently relieves the cold start problem. Furthermore, our approach saves processing time, thus increases recommendation efficiency. Overall, the proposed approach can effectively improve the accuracy of rating prediction in social recommendations and provide accurate and efficient recommendation service for users