Some properties of solutions for a fourth‐order parabolic equation

This paper is concerned with a fourth‐order parabolic equation in one spatial dimension. On the basis of Leray–Schauder's fixed point theorem, we prove the existence and uniqueness of global weak solutions. Moreover, we also consider the regularity of solution and the existence of global attractor. Copyright © 2012 John Wiley & Sons, Ltd.     

Quantum Wave Equation of Photon

In this paper, we give the quantum wave equations of single photon when it is in the vacuum and medium. With these wave equations, we can study light interference and diffraction with the approach of quantum theory, and also can study the quantum property of photon when it is in a general crystal and photonic crystal. Otherwise, it can be applied in quantum optics and condensed matter feld.     

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).