Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index

Landau-Zener tunneling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave "acceleration" and thus induces strongly nonadiabatic Landau-Zener tunneling. Theoretically, the analysis is performed by considering a Schr?dinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.     

Optical necklace states in Anderson localized 1D systems

We report on the observation of nonlocalized modes or necklace states of light waves in disordered systems in the Anderson localized regime. The samples consist of positional-disordered binary multilayer systems. Anderson localized modes manifest themselves as narrow high-transmission peaks in the transmission spectrum, whereas the average of the logarithm of the transmission coefficient decreases linearly with thickness. Optical necklace states are observed as modes with a characteristic multiresonance time response and relatively fast decay time.     

A combinatorial characterization of quadrics

In this paper we prove that in a projective space of dimension three and orderq the two plane characterk-sets fork {q ²+ 1,(q+1)²} are of the same type as the elliptic or the hyperbolic quadric, respectively. As a corollary we obtain a characterization of the elliptic and the hyperbolic quadrics.     

Constructive techniques for approximating collocation linear systems

A high order discretization by spectral collocation methods of the elliptic problem $$\begin{gathered} \left\{ \begin{gathered} A_{A,b} u \equiv - \nabla [A(x)\nabla u(x)] + b(x)u(x) = c(x){\text{ on}}\;\Omega \; = ( - 1,1)^2 \hfill \\ u\left| {\partial \Omega \equiv 0,} \right. \hfill \\ \end{gathered} \right. \hfill \\ \hfill \\ \end{gathered} $$ is considered where A(x)=a(x)I ₂, x=(x ^[1],x ^[2]) and I ₂ denotes the 2×2 identity matrix, giving rise to a sequence of dense linear systems that are optimally preconditioned by using the sparse Finite Difference (FD) matrix-sequence {A _n } _n over the nonuniform grid sequence defined via the collocation points [11]. Here we propose a preconditioning strategy for {A _n } _n based on the “approximate factorization” idea. More specifically, the preconditioning sequence {P _n } _n is constructed by using two basic structures: a FD discretization of (1) with A(x)=I ₂ over the collocation points, which is interpreted as a FD discretization over an equidistant grid of a suitable separable problem, and a diagonal matrix which adds the informative content expressed by the weight function a(x). The main result is the proof that the sequence {P _n ^?1 A _n } _n is spectrally clustered at unity so that the solution of the nonseparable problem (1) is reduced to the solution of a separable one, this being computationally more attractive [2,3]. Several numerical experiments confirm the goodness of the discussed proposal.     

Synthesis and liquid crystalline properties of low molecular mass compounds containing the 1,4-bis(5-phenyl-1,3,4-oxadiazolyl)benzene unit

The synthesis and characterization of low molecular mass compounds containing 1,4-bis(5-phenyl-1,3,4-oxadiazolyl)benzene is reported. All compounds are fluorescent in solution. Due to the flat shape of the conjugated unit, smectic-like packing is observed at high temperatures for some of the synthesized compounds. Moreover the insertion of a lateral flexible alkoxy unit strongly destabilizes the smectic order whilst promoting the appearance of a nematic phase in the case of the shortest methoxy unit. The mesogenic character of this unit may be of interest in the synthesis of liquid crystalline polymeric systems, taking advantage of both the fluorescent properties and the peculiar molecular structure of the liquid crystalline state.     

Projective Planes, Coverings and a Network Problem

A problem concerning packet switched networks leads to a natural combinatorial design problem, whose solution involves (k, n)-arcs in projective planes, 3-dimensional linear codes, the theory of fractional matchings and designs which approximate projective planes.     

Application of direct nonlinear regression from single TG curve to compounds undergoing simple and complex thermal decompositions

Nonlinear regression of the basic kinetic equation was used to determine kinetic parameters of simple and complex decomposition processes related to some pesticides and pharmaceutical substances. The method for this calculation was carried out using a single TG curve. These values were compared with those obtained with model‐fitting and model‐free methods. Nonlinear regression method is able to define a single mechanism for compounds undergoing one or few steps of decomposition processes. For compounds that undergo many steps of decomposition processes, only the mechanisms of some of them can be hypothesized. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 611–622, 2003     

Paniceins,unusual aromatic sesquiterpenoids linked to a quinol or quinone system from the marine sponge Halichondria panicea

Five new substances, panicein-A, -B₁, -B₂, -B₃ and C, containing an aromatic sesquiterpenoid moiety linked to a quinol or a quinone system, have been isolated from the sponge Halichondria panicea. The structures of these compounds were elucidated from their chemical and spectral properties.