Numerical Modeling of Pollutant Dispersion and Oil Spreading by the Stochastic Discrete Particles Method

We consider two applications of the stochastic discrete particles method. The first one is concerned with the dispersion of a passive pollutant by a turbulent stream with a scale dependent diffusion coefficient. The second application deals with the problem of an oil spill spreading on the water surface described by transport–diffusion equation with a nonlinear diffusion coefficient. For the first problem we develop a discrete particles algorithm provided the diffusion coefficient obeys Richardson's "4/3" law and show good correspondence with the numerical and analytical results. The second problem is more involved and we develop a heuristic procedure based on the standard discrete particles random walk algorithm updating the dependence of each particle step variance on the dependent function. The obtained solution coincides well with analytical and direct one-dimensional finite-difference solutions both for instantaneous and continuous oil release.     

Effect of composition and structure of cobalt(II) complexes with oxyaldiminopropylaerosils on their catalytic activity in the decomposition of ozone

The composition, structure, and catalytic activity in low-temperature ozone decomposition were described for cobalt(II) complexes with oxyaldiminopropyl ligands achored to aerosil A-300 differing in the nature and position of the benzene ring substituent. The effect of the geometry of the coordination unit and electronic effects of the benzene ring substituents on the catalytic activity of the cobalt(II) complexes in ozone decomposition were established.     

Simulation of liquid cooling of an extruded sleeve plastic film

A mathematical model of a liquid cooling was considered for a tubular plastic film produced by extrusion down. The developed model allows for a preset film speed (extruder) and film parameters to determine a length of a cooling zone or for a preset length of the cooling zone calculation of maximum speed of the film with the preset parameters.     

Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups

In a series of our papers with Carlo Madonna (2002–2008), we described self-correspondences of a K3 surface over ℂ via moduli of sheaves with primitive isotropic Mukai vectors for the Picard number 1 or 2 of the K3 surfaces. Here we give a natural and functorial answer to the same problem for an arbitrary Picard number. As an application, we characterize, in terms of self-correspondences via moduli of sheaves, K3 surfaces with reflective Picard lattice, that is, when the automorphism group of the lattice is generated by reflections up to finite index. It is known since 1981 that the number of reflective hyperbolic lattices is finite. We also formulate some natural unsolved related problems.     

Abnormal reactions of 2‐methoxy‐4,9‐dimethyl‐1‐nitroacridine with selenous acid and selenium(IV) oxide. Synthesis of 1H‐selenopheno[2,3,4‐k,l]acridine‐1‐one: A new seleno‐containing ring system

Unusual course of the reaction was revealed on the oxidation of functionally substituted acridine containing the activated methyl groups by well‐known oxidants, such as selenous acid and selenium(IV) oxide. Treatment of 2‐methoxy‐4,9‐dimethyl‐1‐nitroacridine ( 5 ) with an excess of H₂SeO₃ in boiling ethanol gave a mixture of the normal reaction products, 2‐methoxy‐4‐methyl‐1‐nitro‐9‐formylacridine ( 11 ) (isolated yield 29%) and 2‐methoxy‐4‐methyl‐1‐nitroacridine‐9‐carboxylic acid ( 12 ) (36%), together with an abnormal product, 3‐methoxy‐5‐methyl‐1H‐selenopheno[2,3,4‐k,l]acridine‐1‐one ( 13 ) (21%), which is the first example of a new seleno‐containing ring system. With the use of SeO₂ the yield of selenolactone 13 was much lower. J. Heterocyclic Chem., 2011.     

Dielectric spectra of disordered ferroelectric systems: Polycrystals and composites

The dielectric spectra of heterogeneous systems that have very large dielectric constants and exhibit the Maxwell-Wagner relaxation are analyzed. The spectra of the disordered systems are found to be of a non-Debye type, and attempts to fit them using either the Cole-Cole or Davidson-Cole equations sometimes fail to produce satisfactory results. Experimental spectra of disordered systems are proved to be close to the spectra obtained by computer simulation of statistical mixtures and ferroelectric ceramics. A new formula is suggested to describe the dielectric relaxation in polycrystalline and composite materials, and reasons for the non-Debye nature of the dielectric spectra are examined.