Growth and EPR properties of KSm(WO4)2 and KEr(WO4)2 single crystals

Growth conditions and electron paramagnetic resonance investigations of two well oriented KSm(WO₄)₂ and KEr(WO₄)₂ single crystals have been presented and discussed. Hyperfine structure of Sm³⁺ ion was detected and analyzed for angular and temperature dependences. EPR spectra of KEr(WO₄)₂ and its angular dependence showed the presence of 5 magnetically nonequivalent Er centers in the crystal. A change in the type of magnetic interactions was analyzed using mixed (Gaussian and Lorentzian) fits of the EPR spectra.     

Mathematical morphology operations with a comparator array processor

We present a demonstrator photonic system for mathematical morphology image processing. Optically interconnected arrays of differential pairs of optoelectronic transceivers realize morphological erosion and dilation in an 8x8 pixel size image.     

Analytical evaluation of bending loss oscillations in photonic crystal fibers

In this paper we present an analytical formula for bending loss oscillations in photonic crystal fibers (PCFs). We follow the approach originally adopted for conventional double-clad fibers and show that it can be applied to PCFs by substituting the structural parameters of the conventional fiber by their PCF counterparts. We then examine the spectral dependence of the critical bending radius and the position of the first order loss peak as a function of structural parameters of the PCF cladding such as the fill factor and the number of hole rings. Finally, we evaluate the precision of the analytical model by comparing the results to finite element calculations for a selection of PCF geometries.     

EPR and optical properties of KYb(WO4)2 and KTb0.2Yb0.8(WO4)2 single crystals

Well oriented KYb(WO₄)₂ and KTb_0.2Yb_0.8(WO₄)₂ single crystals have been investigated for their magnetic and optical properties using the Raman and EPR techniques. The registered EPR signal is dominated by three lines ascribed to ytterbium ions: one main and two satellites. Tb ions, although non-paramagnetic, distinctly modify magnetic properties of the KYb(WO₄)₂ single crystal. Basic parameters of the spin Hamiltonian, including Zeeman and hyperfine terms (g and A matrices) as well the spatial orientation between principal and crystallographic axes systems were determined for both crystals.     

Numerical analysis of apodized fiber Bragg gratings formation using phase mask with variable diffraction efficiency

Scalar diffraction theory is applied to analyze the intensity distribution in the fiber core during fiber Bragg grating (FBG) fabrication using an apodized phase mask. The averaged diffraction field distribution in fiber core was calculated as a function of optical fiber position. The results show that in a case of apodized FBGs fabrication, averaged field intensity profile, and thus refractive index changes in fiber core have complex form. Moreover, it was shown that the influence of optical fiber position behind the phase mask on average intensity distribution in fiber core decreases with increasing of its diameter.     

On homogenization of time-dependent random flows

We study a diffusion with a random, time dependent drift. We prove the invariance principle when the spectral measure of the drift satisfies a certain integrability condition. This result generalizes the results of [13, 7]. Received: 25 February 2000 / Revised version: 11 December 2000 /?Published online: 14 June 2001     

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in , where Ω is a bounded smooth domain in Rn, n?3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p=2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in and, uniformly with respect to the viscosity parameter, L^∞(Ω) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n=3,4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation.     

Complexity of networks II: The set complexity of edge‐colored graphs

We previously introduced the concept of “set‐complexity,” based on a context‐dependent measure of information, and used this concept to describe the complexity of gene interaction networks. In a previous paper of this series we analyzed the set‐complexity of binary graphs. Here, we extend this analysis to graphs with multicolored edges that more closely match biological structures like the gene interaction networks. All highly complex graphs by this measure exhibit a modular structure. A principal result of this work is that for the most complex graphs of a given size the number of edge colors is equal to the number of “modules” of the graph. Complete multipartite graphs (CMGs) are defined and analyzed. The relation between complexity and structure of these graphs is examined in detail. We establish that the mutual information between any two nodes in a CMG can be fully expressed in terms of entropy, and present an explicit expression for the set complexity of CMGs (Theorem 3). An algorithm for generating highly complex graphs from CMGs is described. We establish several theorems relating these concepts and connecting complex graphs with a variety of practical network properties. In exploring the relation between symmetry and complexity we use the idea of a similarity matrix and its spectrum for highly complex graphs. © 2012 Wiley Periodicals, Inc. Complexity, 2012