Cluster synchronization in networks of distinct groups of maps

In this paper, we study cluster synchronization in general bi-directed networks of nonidentical clusters, where all nodes in the same cluster share an identical map. Based on the transverse stability analysis, we present sufficient conditions for local cluster synchronization of networks. The conditions are composed of two factors: the common inter-cluster coupling, which ensures the existence of an invariant cluster synchronization manifold, and communication between each pair of nodes in the same cluster, which is necessary for chaos synchronization. Consequently, we propose a quantity to measure the cluster synchronizability for a network with respect to the given clusters via a function of the eigenvalues of the Laplacian corresponding to the generalized eigenspace transverse to the cluster synchronization manifold. Then, we discuss the clustering synchronous dynamics and cluster synchronizability for four artificial network models: (i) p-nearest-neighborhood graph; (ii) random clustering graph; (iii) bipartite random graph; (iv) degree-preferred growing clustering network. From these network models, we are to reveal how the intra-cluster and inter-cluster links affect the cluster synchronizability. By numerical examples, we find that for the first model, the cluster synchronizability regularly enhances with the increase of p, yet for the other three models, when the ratio of intra-cluster links and the inter-cluster links reaches certain quantity, the clustering synchronizability reaches maximal.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

Pivotal role of ballistic and quasi-ballistic electrons on LED efficiency

Significant progress in the power conversion efficiency and brightness of InGaN-based light emitting diodes (LEDs) has paved the way for these devices to be considered for LED lighting. In this realm, however, the efficiency must be retained at high injection levels in order to generate the lumens required. Unfortunately, LEDs undergo a monotonic efficiency degradation starting at current densities even lower than 50 A/cm² which would hinder LED insertion into the general lighting market. The physical origins for the loss of efficiency retention are at present a topic of intense debate given its enormous implications. This paper reviews the current status of the field regarding the mechanisms that have been put forward as being responsible for the loss of efficiency, such as Auger recombination, electron overflow (spillover), current crowding, asymmetric injection of electrons and holes, and poor transport of holes through the active region, the last one being applicable to multiple quantum well designs. While the Auger recombination received early attention, increasing number of researchers seem to think otherwise at the moment in that it alone (if any) cannot explain the progressively worsening loss of efficiency reduction as the InN mole fraction is increased. Increasing number of reports seems to suggest that the electron overflow is one of the major causes of efficiency degradation. The physical driving force for this is likely to be the relatively poor hole concentration and transport, and skewed injection favoring electrons owing to their relatively high concentration. Most intriguingly there is recent experimental convincing evidence to suggest that quasi-ballistic electrons in the active region, which are not able to thermalize within the residence time and possibly longitudinal optical phonon lifetime, contribute to the carrier overflow which would require an entirely new thought process in the realm of LEDs.     

First-principles study of structural,electronic and optical properties of orthorhombic SrZrO3

We have investigated the structural parameters, electronic structure and optical properties of orthorhombic SrZrO₃ using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT). Our calculated structural parameters are in good agreement with the previous theoretical and experimental data. Band structure, density of states and chemical bonding have been systematically studied. Furthermore, the complex dielectric function, refractive index, extinction coefficient, optical reflectivity, absorption coefficient, loss function and optical conductivity are calculated, which show an optical anisotropy in the components of polarization directions (100), (010) and (001).     

Random approximations and random fixed point theorems for random 1-setn-contractive non-self-maps in abstract cones

In this paper, we will prove that the random version of Fan's Theorem [6, Theorem 2] is true for a random hemicompact 1-set-contractive map defined on a closed ball, a sphere and an annulus in cones. This class of random 1-set-contractive map includes random condensing maps, random continuous semicontractive maps, random LANE maps, random nonexpansive maps and others. As applications of our theorems, some random fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations, improvements or stochastic versions of the recent results obtained by many authors     

Automorphism Groups of Restricted Cartan-Type Lie Superalgebras

Let X denote the restricted Lie superalgebras of Cartan type W, S, H, or K over a field of characteristic p > 3, and 𝔄 the corresponding underlying superalgebra of X. Employing the invariance of the filtration of X we construct an isomorphism of Aut X to Aut(𝔄:X), the admissible automorphism group of the associative super-commutative superalgebra 𝔄. Moreover, it is proved that the group isomorphism above maps the standard normal series of Aut X to the one of Aut(𝔄:X), and also maps the homogeneous automorphism group of X to the admissible homogeneous automorphism group of 𝔄.