Epitaxy: the motion picture

The engineering of many modern electronic devices demands control over a crystal down to the thickness of a single layer of atoms—and future demands will be even more challenging. Such control is achieved by the method of crystal growth known as epitaxy, and that makes this method the subject of intense study. More than that, recent advances are revolutionizing our knowledge of how surfaces grow. In fact, growing surfaces show a beautifully rich variety of phenomena, many of which are only now beginning to be uncovered. In the past few years many surface imaging techniques have been used to give us a close look at how crystals grow—while they are growing. The purpose of this article will be to illustrate some of the ways real surfaces grow and change as revealed by some of the latest in situ microscopic imaging technologies.

It is often said that crystal growth is more of an art than a science. Here we will show that it is emphatically both.     

The two-dimensional quantum Euclidean algebra

The algebra dual to Woronowicz's deformation of the two-dimensional Euclidean group is constructed. The same algebra is obtained from SU _q (2) via contraction on both the group and algebra levels.     

A self-organizing network in the weak-coupling limit

We prove the existence of spatially localized ground states of the diffusive Haken model. This model describes a self-organizing network whose elements are arranged on a d-dimensional lattice with short-range diffusive coupling. The network evolves according to a competitive gradient dynamics in which the effects of diffusion are counteracted by a localizing potential that incorporates an additional global coupling term. In the absence of diffusive coupling, the ground states of the system are strictly localized, i.e. only one lattice site is excited. For sufficiently small non-zero diffusive coupling , it is shown analytically that localized ground states persist in the network with the excitations exponentially decaying in space. Numerical results establish that localization occurs for arbitrary values of in one dimension but vanishes beyond a critical coupling _c(d), when d> 1. The one-dimensional localized states are interpreted in terms of instanton solutions of a continuum version of the model.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Steady state analysis of an M/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.     

Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ _c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca₃Rh₄Sn₁₃, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ _c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca₃Rh₄Sn₁₃ has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.