Erratum to Laplacian Instability of Planar Streamer Ionization Fronts—An Example of Pulled Front Analysis

Streamer ionization fronts are pulled fronts that propagate into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long-time attractor out of a continuous family. A stability analysis for perturbations in the transverse direction has to take these features into account. In this paper we show how to apply the Evans function in a weighted space for this stability analysis. Zeros of the Evans function indicate the intersection of the stable and unstable manifolds; they are used to determine the eigenvalues. Within this Evans function framework, we define a numerical dynamical systems method for the calculation of the dispersion relation as an eigenvalue problem. We also derive dispersion curves for different values of the electron diffusion constant and of the electric field ahead of the front. Numerical solutions of the initial value problem confirm the eigenvalue calculations. The numerical work is complemented with an analysis of the Evans function leading to analytical expressions for the dispersion relation in the limit of small and large wave numbers. The paper concludes with a fit formula for intermediate wave numbers. This empirical fit supports the conjecture that the smallest unstable wave length of the Laplacian instability is proportional to the diffusion length that characterizes the leading edge of the pulled ionization front. G. Derks acknowledges a travel grant of the Royal Society, which initiated this research, and a visitor grant of the Dutch funding agency NWO and the NWO-mathematics cluster NDNS⁺ to finish the work. The work was also supported by a CWI PhD grant for B. Meulenbroek.     

Inherently gain flattened L band TDFA based on W-fiber design

We present here a detailed theoretical analysis for realizing an inherently gain flattened L⁺ band thulium doped fiber amplifier (TDFA), based on a depressed inner-clad (W-fiber) design, wherein the inherent gain flattening is achieved by an optimized bend induced leakage loss. The leakage loss characteristics of W-fiber have been used to suppress higher wavelength amplified stimulated emission (ASE) in the designed TDFA, which otherwise depletes the population inversion in the amplifier, making it almost impossible to obtain high gain for wavelengths in and close to the conventional L-band. It has been shown through simulations that 20 dB net gain (±0.3 dB ripple) is achievable over 32 nm bandwidth (1604-1636 nm), using this design pumped with 160 mW of power. We also show that inherent gain flattening leads to redistribution of power among signal wavelengths, and hence an inherently gain-flattened TDFA is much more efficient as compared to a configuration that uses discrete filters for gain flattening. The net gain value and gain flattening of the designed TDFA module have been tested against tolerance with respect to fiber parameters as well as bend radius. This is for the first time to the authors knowledge that inherently gain flattened L⁺ band operation has been shown using TDFAs.     

Elaboration of corona functionalized regular unimolecular hyperbranched polystyrene nanoparticles

Functional arborescent graft polystyrenes prepared by the “graft-on-graft” technique, involving the iterative grafting of end functional polymer chains onto reactive polymer backbones were synthesized. The zero-generation comb polymers and then the first generation hyperbranched structures were obtained by the coupling reaction of living α-acetal polystyryllithium onto linear or comb chains of poly(chloroethyl vinyl ether) (PCEVE) of controlled D̄P̄_n and structure. Both the PS grafts and the PCEVE reactive backbones were synthesized individually by living polymerization techniques. Initiation of styrene polymerization from acetal functionalized lithium derivatives yield the ω-functionalization of all external polystyrene branches. Derivatization of these acetal branch termini allowed the generation of aldehyde, hydroxyl and carboxyl groups as well as the introduction of functional organic molecules at the periphery of the nanoparticles.     

Study of Mercurous Chloride Crystal Growth

In this work we deal with the mercurous chloride (Hg₂Cl₂) or calomel crystal growth in vapour phase by flux forced method, taking into account the total dissociation of calomel in mercury and mercuric chloride. The concentrations of mercury and mercuric chloride along the growth ampoule depend on the matter transport model from the source to sink. We use a molecular diffusion model of mercury and mercuric chloride through an immobile inert gas. The attempts of growth showed the key role of the concentrations of mercury and mercuric chloride as well as their ratio at the maximum of supersaturation.     

Polymer and organic molecules ordered via epitaxy: geometrical and molecular interactions

Control of structural order at the molecular level for both conventional linear polymers and conjugated polymers with valuable opto‐electronic properties has major consequence on the macroscopic properties of these polymers. Though the traditional means of orientation of polymer was mechanical deformation, presently extensive works are concerned with a more controlled way of orientation: epitaxial crystallisation. Most of the first documented examples of epitaxial growth of conventional polymers on single crystals followed the well‐established geometrical rules of best matching. However, recent examples show off more subtle rules of selection. Analogous cases, following or breaking the matching rules, have been observed for diacetylenes ordered via epipolymerisation on single crystals. Hereafter, representative examples of the structural matching rules are depicted first, and then recent examples, which depart from the simple geometrical fitting, are described. The analysis of the former leads to define the subtle matching rules applying for polymers linked to their conformational adaptability. The analysis of the latter gives the opportunity to discuss the relative influence of geometrical and molecular interactions between the deposit and the substrate.     

Triangulating a simple polygon in linear time

We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm. The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8700917.