The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.     

40 GHz Mode-Locked Semiconductor Lasers: Theory, Simulations and Experiment

We study both theoretically and experimentally typical operation regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz has been predicted theoretically and confirmed by measurements. Furthermore, we derive and apply a simplified Delay-Differential-Equation model which guides us to a qualitative analysis of bifurcations responsible for the appearance and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.     

Evolution of femtosecond laser-induced damage in doped GaN thin films

Mg- and Si-doped GaN layers deposited by metalorganic chemical vapor deposition method were irradiated with femtosecond pulse duration laser of three different wavelengths 1,030, 515 and 343 nm. Both single and multiple shot laser induced damage thresholds of doped GaN layers were evaluated and discussed. The scanning electron microscopy employed with electron beam induced current and energy dispersive X-ray techniques were used to study laser damage morphology. It was observed that ablated area and laser-induced damage increased with irradiation fluence. The mechanism of damage generation by Gaussian beam profile laser was considered.     

Dispersion production by semi-continuous radical vinyl acetate emulsion polymerization with silane co-monomer and characterization of final products

Vinyl acetate radical emulsion polymerization in water with GF51 silane co-monomer was performed by semi continuous way. The GF51 impacts on dispersion rheology as well on films and bonding strength properties were determined. It should be stated that even low quantities of GF51 (up to 6% from VAc) determined high viscosity of dispersions. The GF51 modified films have low water absorption and high affinity to glass. Molecular mass and thermal properties of GF51 modified polymers were determined accordingly.     

Mode transitions in distributed-feedback tapered master-oscillator power-amplifier: theory and experiments

Theoretical and experimental investigations have been carried out to study the spectral and spatial behavior of monolithically integrated distributed-feedback tapered master-oscillators power-amplifiers emitting around 973 nm. Introduction of self and cross heating effects and the analysis of longitudinal optical modes allows us to explain experimental results. The results show a good qualitative agreement between measured and calculated characteristics.     

Transition‐Metal‐Free Cross‐Coupling of Benzothiophenes and Styrenes in a Stereoselective Synthesis of Substituted (E,Z)‐1,3‐Dienes

A transition metal‐free one‐pot stereoselective approach to substituted (E,Z)‐1,3‐dienes was developed by using an interrupted Pummerer reaction/ligand‐coupling strategy. Readily available benzothiophene S‐oxides, which can be conveniently prepared by oxidation of the parent benzothiophenes, undergo Pummerer coupling with styrenes. Reaction of the resultant sulfonium salts with alkyllithium/magnesium reagents generates underexploited hypervalent sulfurane intermediates that undergo selective ligand coupling, resulting in dismantling of the benzothiophene motif and the formation of decorated (E,Z)‐1,3‐dienes.     

Versatile C(sp2)−C(sp3) Ligand Couplings of Sulfoxides for the Enantioselective Synthesis of Diarylalkanes

The reaction of chiral (hetero)aryl benzyl sulfoxides with Grignard reagents affords enantiomerically pure diarylalkanes in up to 98 % yield and greater than 99.5 % enantiomeric excess. This ligand coupling reaction is tolerant to multiple substitution patterns and provides access to diverse areas of chemical space in three operationally simple steps from commercially available reagents. This strategy provides orthogonal access to electron‐deficient heteroaromatic compounds, which are traditionally synthesized by transition metal catalyzed cross‐couplings, and circumvents common issues associated with proto‐demetalation and β‐hydride elimination.     

Well‐posedness,smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics

We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd.