Cluster and group synchronization in delay-coupled networks

We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, we find that the master stability function shows a discrete rotational symmetry depending on the number of groups. The coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum, which helps to simplify the evaluation of the master stability function. Our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times, multiple coupling functions, but also with multiple kinds of local dynamics in the networks' nodes. We illustrate our results by calculating stability in the example of delay-coupled semiconductor lasers and in a model for neuronal spiking dynamics.Comment: 11 pages, 7 figure

Interrelation of work function and surface stability: the case of BaAl4

The relationship between the work function (Phi) and the surface stability of compounds is, to our knowledge, unknown, but very important for applications such as organic light-emitting diodes. This relation is studied using first-principles calculations on various surfaces of BaAl4. The most stable surface [Ba terminated (001)] has the lowest Phi (1.95 eV), which is lower than that of any elemental metal including Ba. Adding barium to this surface neither increases its stability nor lowers its work function. BaAl4 is also strongly bound. These results run counter to the common perception that stability and a low Phi are incompatible. Furthermore, a large anisotropy and a stable low-work-function surface are predicted for intermetallic compounds with polar surfaces.Comment: 4 pages, 5 figures, to be published in Chem. Ma

Stability Analysis of Spherically Symmetric Star in Scalar-Tensor Theories of Gravity

A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related to gravitation. There is an arbitrary function, the so-called coupling function, which determines the strength of the coupling between the gravitational scalar field and matter. Instability is induced by the scalar field for some ranges of the value of the first derivative of the coupling function. This instability leads to significant discrepancies with the results of binary-pulsar-timing experiments and hence, by the stability analysis, we can exclude the ranges of the first derivative of the coupling function in which the instability sets in. In this article, the constraint on the first derivative of the coupling function from the stability of relativistic stars is found. Analysis in terms of the quasi-normal mode frequencies accounts for the parameter dependence of the wave form of the scalar gravitational waves emitted from the Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.Comment: 17 pages, including 6 eps figures. Accepted for publication in Progress of Theoretical Physics. Grammatical errors correcte

A Stability Index for Local Effectivity Functions

We study the structure of unstable local effectivity functions defined for n players and p alternatives. A stability index based on the notion of cycle is introduced. In the particular case of simple games, the stability index is closely related to the Nakamura Number. In general it may be any integer between 2 and p. We prove that the stability index for maximal effectivity functions and for maximal local effectivity functions is either 2 or 3.Effectivity function, local effectivity function, acyclicity, stability index, Nakamura Number, acyclicity.