Asymptotic methods in the theory of nonlinear stochastic oscillations

We study applications of asymptotic methods of nonlinear mechanics and the method of Fokker-Planck-Kolmogorov equations to stochastic oscillations in quasilinear oscillating systems with random perturbations. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 510–518, October–December, 2007.     

Characterization of high-order harmonic radiation on femtosecond and attosecond time scales

We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky     

Dynamics of fluorescence of solid solutions of quantum dots and the organic dye DODCI: Experiment and numerical simulation

The fluorescence of solid solutions of CdSe/ZnS quantum dots and the organic dye DODCI is investigated. It is shown that nonradiative transfer of electronic excitation energy to dye molecules, which with some probability lose their acceptor properties as a result of photoisomerization or photodegradation, is responsible for a significant increase in the fluorescence intensity of a donor. The degree of polarization of the donor fluorescence attains values exceeding 0.5, which is due to the difference in the fluorescence quantum yields of donors with different orientations of the oscillator with respect to the electric vector of an excitation light wave. A numerical simulation of the experimentally observed dependences is performed.     

Interactions of surface states of copper with transition metals and cesium

The pseudopotential augmented-plane-wave method was used to study the surface structure of thin copper films with monolayers of Co, Ni, and Cs. Local densities of electron states, distributions of charge densities in the layers, and electron energy spectra are analyzed. The effect of adsorbates on the electronic properties of the Cu(001) surface and work function are discussed. Satisfactory agreement with available experimental data has been obtained.     

Reaction of aroyl- and hetaroyltrifluoroacetones with acylhydrazines: Regioselectivity and tautomerism of the condensation products

Acylhydrazines react with 1,3-diketones of the general formula CF₃COCH₂COR (where R is an aryl or hetaryl group) at both carbonyl groups. The reaction at the trifluoroacetyl group is favored by donor substituents in the aromatic ring of the 1,3-diketone or by the 2-furyl and, especially, 2-thienyl group as a hetaryl substituent, as well as by elevated temperature. The condensation products at the carbonyl group contiguous to the aryl or hetaryl ring have the structure of 5-hydroxy-4,5-dihydropyrazoles and do not undergo tautomeric transformations in solution. The condensation products at the trifluoroacetyl group have either 5-hydroxy-4,5-dihydropyrazole or hydrazone structure and give rise to ring-chain tautomeric equilibrium in solution. Electron-withdrawing substituents in the aromatic ring of the 1,3-dicarbonyl fragment and CDCl₃ as solvent favor formation of the cyclic tautomer. The state of the tautomeric equilibrium is weakly sensitive to structural variations in the hydrazine component.     

Circular dichroism spectra of langasite family crystals in the range of electronic transitions of structure defects

The absorption and circular dichroism spectra of langasite family crystals are studied. Wide bands in the range of 285–500 nm that are related to the structure lattice defects are found. For all the crystals, these bands are in approximately the same spectral region, have identical structures, and can be attributed to one type of defects formed by cation vacancies and excess oxygen atoms in the optically active positions.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

Spatial macroscopic structure of a pulsed microsecond discharge in barrier-metal gaps with a nonuniform electric field distribution

Electric and spatial characteristics of a pulse-periodic microsecond barrier discharge are investigated in different geometries—triangular prism, plate, and corrugated electrode—that are in contact with a dielectric plate and form a dihedral angle with it. It is established that, in the space of the dihedral angle, the regions of discharge represent alternating cylindrical layers with the axes lying on the contact line. The first conducting layer is formed at some distance from the contact edge of the electrode. The number of layers and their localization are determined by the angle formed between an electrode and the dielectric plate. A physical model explaining the main features of the structure formation is proposed.