Experimental study of the stochastic nature of the pulsation self-starting process in passive mode locking

We present an experimental study of the probabilistic nature of pulsation self-starting in passively mode-locked lasers. It is a Poissonian process that results from a noise-activated switching barrier. The switching rate from cw operation to pulsation when the laser pump level is turned on has an exponential dependence that is inversely proportional to the square of the laser power.     

Solitons in a linearly coupled system with separated dispersion and nonlinearity

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not "mixed" in a single nonlinear Schrodinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton's components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad "pedestal." This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.     

Nonlinear lattice dynamics of Bose-Einstein condensates

The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop "experimental" techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems-including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECs, in particular, due to their widely ranging and easily manipulated dynamical apparatuses-with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials-provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.     

Effect of adsorbed Sn on Ge diffusivity on Si(111) surface

The effect of adsorbed Sn as a surfactant on Ge diffusion on a Si(111) surface has been studied by Low Energy Electron Diffraction and Auger Electron Spectroscopy. The experimental dependence of Ge diffusion coefficients on the Si(111) surface versus temperature in the presence of adsorbed Sn atoms has been measured in the range from 300 to 650°C. It has been shown that at a Sn coverage of about 1 monolayer the mobility of Ge atoms increases by several orders of magnitude.      

Adsorption of hydrocarbons and various gases on Ni-SiO2 catalysts studied by high field magnetic methods

The adsorption of various gases (H₂, H₂S, alcanes, alcenes and alcynes containing up to five carbons, benzene, cyclohexane, cyclopentane, and some mixtures) on Ni-SiO₂ catalysts has been studied by measuring variations of saturation magnetization. The adsorption has been performed at ?78 °C and the system heated in steps. When coverage is small intermediate adsorbed compounds thermally stable have been detected. The observed bond number is even (2, 4, 6, 8) and it corresponds to strongly dehydrogenated states for alcanes, alcenes, cyclanes and benzene, and to an associative model for acetylene and propyne. Complete cracking occurs at relatively low temperatures (50 °C to 200 °C) with formation of Ni₃C and NiH: the greater the saturation of the hydrocarbon, the smaller its carbon number, and the lower is its cracking temperature. Sulfur of H₂S is rapidly and irreversibly dissolved into the bulk of nickel. These results which are not always in good agreement with those obtained by low field techniques, strongly supports the following view: nickel atoms, on which a molecule is adsorbed cease to participate to the collective magnetism.     

Single site spectra of Zn porphin in triphenylene

Single site spectra of Zn porphin in triphenylene have been recorded at low temperature. There were three principal site species, each of which had slightly different fluorescence and absorption spectra. Because the spectra of each site were separately recorded, the confusion which resulted from the spectra of multiple site species in previous studies was eliminated. Vibrational assignments in the ground and excited electronic states were made, and relative intensities of the spectral lines recorded. The general pattern of intensity of the spectra was in qualitative agreement with the theory of vibronic borrowing in the cyclic polyene model.     

The Euler-Maclaurin sum formula for an inner derivation

An operator form of the Euler-Maclaurin sum formula is obtained, expressing the sum of the Euler-Maclaurin infinite series in an inner derivation as the difference between a summation operator and an inner antiderivation, on a closed subalgebra of a Banach algebra.