Nonlinear Discrete Systems with Nonanalytic Dispersion Relations

A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz Ladik spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave evolution problem is a discrete version of the stimulated Raman scattering equations, and it is shown to be solvable for arbitrary boundary value of the two radiation fields and initial value of the medium state. The spectral transform is constructed on the basis of the D-bar approach.Comment: RevTex file, to appear in Journ. Math. Phy

Small-amplitude excitations in a deformable discrete nonlinear Schroedinger equation

A detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schr\"{o}dinger equation is performed. For generic deformations the system possesses "singular" points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicinity of the singular points are described by the Toda-lattice equation while away from the singular points are described by the Korteweg-de Vries equation. Depending on the value of the deformation parameter and of the background level several kinds of solutions are possible. In particular we delimit the regions in the parameter space in which dark solitons are stable in contrast with regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidly spreading solutions may exist.Comment: 18 pages (RevTex), 13 figures available upon reques

Studies of HT and HTO Behavior in the Vicinity of Long-Term Emission Source: Model - Experiment Intercomparison

There are presented in the research results of HT and HTO deposition and the model of HT (HTO) atmosphere concentration in the vicinity of a long-term HT and HTO emission source. Scavenging of HTO by precipitations was studied in 6 field experiments. The site of the scavenging experiments was around a 30 m emission source. The sampling arcs were chosen at 150-300 m from the base of the source to minimize dry deposition on the precipitation collectors. Data of the scavenging experiments are presented. Kinetics of HT deposition to soil through its oxidation has been studied in laboratory conditions. The activity of HTO converted in the soil sample during a certain period of time was used to determine the oxidation rate. This rate varies, depending on the catalytic and/or biological activity of the soil material. Theoretical considerations have shown that the deposition rate can be expressed by the effective rate of oxidation, which formally corresponds to the first-order HT oxidation. HT deposition rates are reported. The model, used for assessments, takes into account atmospheric dispersion, deposition and reemission. The model of HTO wet deposition is taken into account kinetics of HTO exchange between vapor and liquid phase with parameters such as rain drop spectra, rain intensity, condensation-evaporation on drop's interface. Gauss type formulae for continuous emission source is used to calculate HTO atmospheric concentration. Meteorological data are used as input parameters for modeling. The data presented on HT deposition to soil and HTO washout by precipitation is required for assessment of consequences of HT (HTO) release into the atmosphere

Effect of impregnation on the structure of niobium oxide/alumina catalysts studied by multinuclear solid-state NMR, FTIR, and quantum chemical calculations

Multinuclear solid-state 1H, 27Al, and 93Nb NMR experiments and DFT calculations were carried out for structura

Effect of Impregnation on the Structure of Niobium Oxide/Alumina Catalysts Studied by Multinuclear Solid-State NMR, FTIR, and Quantum Chemical Calculations

Multinuclear solid-state ¹H, ²⁷Al, and ⁹³Nb NMR experiments and DFT calculations were carried out for structural characterization of alumina-supported niobium oxide catalysts with high niobium content following an every stage in the catalyst preparation. It was found that the first stage of the impregnation procedure plays a key role in determining the catalyst structure and acidity. In order to monitor the presence in catalysts of aluminum niobate phase, AlNbO₄, a series of ²⁷Al and ⁹³Nb NMR experiments was performed for several different individual AlNbO₄ samples. Aluminum and niobium NMR parameters were determined for AlNbO₄, which crystal structure contains two different crystallographic sites for each element. The compound was investigated through a combination of experimental ⁹³Nb and ²⁷Al NMR spectroscopy methods at several magnetic field strengths (9.4, 11.7, 19.4, and 21.1 T) and complemented by ab initio quantum chemical calculations of NMR parameters for these nuclei. The chemical shielding and the quadrupole coupling tensor parameters were determined for both ⁹³Nb and ²⁷Al