Anderson Localization of Classical Waves in Weakly Scattering Metamaterials

We study the propagation and localization of classical waves in one-dimensional disordered structures composed of alternating layers of left- and right-handed materials (mixed stacks) and compare them to the structures composed of different layers of the same material (homogeneous stacks). For weakly scattering layers, we have developed an effective analytical approach and have calculated the transmission length within a wide region of the input parameters. When both refractive index and layer thickness of a mixed stack are random, the transmission length in the long-wave range of the localized regime exhibits a quadratic power wavelength dependence with the coefficients different for mixed and homogeneous stacks. Moreover, the transmission length of a mixed stack differs from reciprocal of the Lyapunov exponent of the corresponding infinite stack. In both the ballistic regime of a mixed stack and in the near long-wave region of a homogeneous stack, the transmission length of a realization is a strongly fluctuating quantity. In the far long-wave part of the ballistic region, the homogeneous stack becomes effectively uniform and the transmission length fluctuations are weaker. The crossover region from the localization to the ballistic regime is relatively narrow for both mixed and homogeneous stacks. In mixed stacks with only refractive-index disorder, Anderson localization at long wavelengths is substantially suppressed, with the localization length growing with the wavelength much faster than for homogeneous stacks. The crossover region becomes essentially wider and transmission resonances appear only in much longer stacks. All theoretical predictions are in an excellent agreement with the results of numerical simulations.Comment: 19 pages, 16 figures, submitted to PR

Turing patterns in multiplex networks

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of an homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations

Generalized k-core percolation on correlated and uncorrelated multiplex networks

It has been recognized that multiplexes and interlayer degree correlations can play a crucial role in the resilience of many real-world complex systems. Here we introduce a multiplex pruning process that removes nodes of degree less than ki and their nearest neighbors in layer i for i=1,...,m, and establish a generic framework of generalized k-core (Gk-core) percolation over interlayer uncorrelated and correlated multiplex networks of m layers, where k=(k1,...,km) and m is the total number of layers. Gk-core exhibits a discontinuous phase transition for all k owing to cascading failures. We have unraveled the existence of a tipping point of the number of layers, above which the Gk-core collapses abruptly. This dismantling effect of multiplexity on Gk-core percolation shows a diminishing marginal utility in homogeneous networks when the number of layers increases. Moreover, we have found the assortative mixing for interlayer degrees strengthens the Gk-core but still gives rise to discontinuous phase transitions as compared to the uncorrelated counterparts. Interlayer disassortativity on the other hand weakens the Gk-core structure. The impact of correlation effect on Gk-core tends to be more salient systematically over k for heterogenous networks than homogeneous ones

Transient and steady-state shear banding in a lamellar phase as studied by Rheo-NMR

Flow fields and shear-induced structures in the lamellar (L-alpha) phase of the system triethylene glycol mono n-decyl ether (C10E3)/water were investigated by NMR velocimetry, diffusometry, and H-2 NMR spectroscopy. The transformation from multilamellar vesicles (MLVs) to aligned planar lamellae is accompanied by a transient gradient shear banding. A high-shear-rate band of aligned lamellae forms next to the moving inner wall of the cylindrical Couette shear cell while a low-shear-rate band of the initial MLV structure remains close to the outer stationary wall. The band of layers grows at the expense of the band of MLVs until the transformation is completed. This process scales with the applied strain. Wall slip is a characteristic of the MLV state, while aligned layers show no deviation from Newtonian flow. The homogeneous nature of the opposite transformation from well aligned layers to MLVs via an intermediate structure resembling undulated multilamellar cylinders is confirmed. The strain dependence of this transformation appears to be independent of temperature. The shear diagram, which represents the shear-induced structures as a function of temperature and shear rate, contains a transition region between stable layers and stable MLVs. The steady-state structures in the transition region show a continuous change from layer-like at high temperature to MLV-like at lower temperature. These structures are homogeneous on a length scale above a few micrometers

Multiplexing induced explosive synchronization in Kuramoto oscillators with inertia

Explosive synchronization (ES) of coupled oscillators on networks is shown to be originated from existence of correlation between natural frequencies of oscillators and degrees of corresponding nodes. Here, we demonstrate that ES is a generic feature of multiplex network of second-order Kuramoto oscillators and can exist in absence of a frequency-degree correlation. A monoplex network of second-order Kuramoto oscillators bearing homogeneous (heterogeneous) degree-distribution is known to display the first-order (second-order) transition to synchronization. We report that multiplexing of two such networks having homogeneous degree-distribution support the first-order transition in both the layers thereby facilitating ES. More interesting is the multiplexing of a layer bearing heterogeneous degree-distribution with another layer bearing homogeneous degree-distribution, which induces a first-order (ES) transition in the heterogeneous layer which was incapable of showing the same in the isolation. Further, we report that such induced ES transition in the heterogeneous layer of multiplex networks can be controlled by varying inter and intra-layer coupling strengths. Our findings emphasize on importance of multiplexing or impact of one layer on dynamical evolution of other layers of systems having inherent multiplex or multilevel architecture.Comment: 7 pages, 10 figure

Intrinsic degradation mechanism of nearly lattice-matched InAlN layers grown on GaN substrates

Thanks to its high refractive index contrast, band gap and polarization mismatch compared to GaN, In0.17Al0.83N layers lattice-matched to GaN are an attractive solution for applications such as distributed Bragg reflectors, ultraviolet light-emitting diodes, or high electron mobility transistors. In order to study the structural degradation mechanism of InAlN layers with increasing thickness, we performed metalorganic vapor phase epitaxy of InAlN layers of thicknesses ranging from 2 to 500 nm, on free-standing (0001) GaN substrates with a low density of threading dislocations, for In compositions of 13.5% (layers under tensile strain), and 19.7% (layers under compressive strain). In both cases, a surface morphology with hillocks is initially observed, followed by the appearance of V-defects. We propose that those hillocks arise due to kinetic roughening, and that V-defects subsequently appear beyond a critical hillock size. It is seen that the critical thickness for the appearance of V-defects increases together with the surface diffusion length either by increasing the temperature or the In flux because of a surfactant effect. In thick InAlN layers, a better (worse) In incorporation occurring on the concave (convex) shape surfaces of the V-defects is observed leading to a top phase-separated InAlN layer lying on the initial homogeneous InAlN layer after V-defects coalescence. It is suggested that similar mechanisms could be responsible for the degradation of thick InGaN layers

A geostrophic-like model for large Hartmann number flows

A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number (Ha >> 1). This is analogous to the case of low Ekman number rotating flows, with Ekman layers replacing Hartmann layers. This has been at the origin of the homogeneous model for flows in a rotating frame of reference, with its rich structure: geostrophic contours and shear layers of Stewartson, Munk and Stommel. In magnetohydrodynamics, the characteristic surfaces introduced by Kulikovskii play a role similar to the role of the geostrophic contours. However, a general theory for quasi two-dimensional magnetohydrodynamics is lacking. In this paper, a model is proposed which provides a general framework for quasi two-dimensional magnetohydrodynamic flows. Not only can this model account for otherwise disconnected past results, but it is also used to predict a new type of shear layer, of typical thickness Ha^{-1/4}