N. E. Shapkina

Application of a 2D Model for Describing the Turbulent Transfer of CO2 in a Spatially Heterogeneous Vegetation Cover

A numerical 2D model of the turbulent transfer of CO2 in the air between a spatially heterogeneous vegetation cover and the atmospheric surface layer was developed. The model is based on the one-and-a-half closure scheme for averaged equations of hydrodynamics and diffusion of CO2 in the air. The model was applied to assess the possible influence of forest canopy heterogeneity on the turbulent regime and CO2 fluxes in the atmospheric surface layer. CO2 exchange was simulated both at the windward forest edge and around a forest clearing.

The application of the theory of contrast structures for describing wind field in spatially heterogeneous vegetation cover

The two-dimensional mathematical model based on the theory of contrast structures is proposed for solving the problem of the wind flow over some obstacles in the form of shelterbelt. With the help of numerical calculations the wind fields around the shelterbelts of different spatial sizes and vertical structures are obtained.

Mathematical modeling of waveguides with fractal insets

The paper is devoted to mathematical modeling of rectangular dielectric waveguides with local periodic and fractal insets. A three-dimensional scalar boundary-value problem for the Helmholtz equation is considered. The solution is obtained numerically by means of incomplete Galerkin method and finite-difference techniques. The transmission spectra for one-, two- and three-dimensional periodic and fractal insets are computed and compared with each other. Practical applications are suggested.

Optical diffraction on fractal lattices

The basic properties of fractals and fractal objects are described. Papers devoted to diffraction on fractal lattices are surveyed. The optical Fourier transform is considered as a method for determining the fractal dimension of a diffraction lattice.

Contemporary climate changes in the southwest of the Valdai Hills: A statistical analysis of the long-term dynamics of the air temperature

As the scientific community accepts the modern global climate changes, statistical analysis of a time series of hydrometeorological parameters becomes topical. A time series of air temperature was decomposed in this work; the decomposition allows one to distinguish regular, seasonal, and random components and to assess their statistical significance and adequacy to observation results. On the basis of a linear-regression model, a statistically significant increase in the annual average air temperature in the region under study was determined, both for the entire observation period and for separate months of the year.

An impact assessment of forest belts on the SO2 transport within the atmospheric boundary layer using a hydrodynamic model

A numerical two-dimensional hydrodynamic model was used to describe the influence of forest belts of different sizes on turbulent transport of SO2 within the atmospheric surface layer. The results of the model calculations showed that the presence of a forest belt results in an substantial reduction of the horizontal SO2 flux due to the decrease of the wind speed and the absorption of SO2 by tree crowns. The extinction coefficient of SO2 flux increases with an increase in the forest belt size and decrease with the pollution source height.

Analysis and synthesis of fractal antenna radiation patterns

A problem of fractal antenna radiation pattern synthesis is considered. The problem of synthesis of fractal antenna radiation patterns is solved for two kinds of antennas (discrete and linear) in one- and two- dimensional cases. With the use of the theory of fractal synthesis, new modes with new properties are obtained in fractal electrodynamics. Fractal radiation pattern synthesis was conducted by means of the Weierstrass function.

A Statistical Analysis of Cyclical Changes in the Time Series of Meteorological Parameters in the Southwest of the Valdai Hills

A statistical analysis of periodic and cyclical components of time series of meteorological parameters was conducted for the 40-year observation period in the southwest of the Valdai Hills by classic seasonal decomposition and Fourier analysis. The dependence of the obtained OLS estimates of linear-regression models of meteorological parameters on a length of the smoothing interval was analyzed. Cyclical fluctuations in the time series of temperature with periods of 8 and 3 years and those of rainfall with periods of 3.5 and 10.5 years were detected and analyzed.

The mathematical simulation of a diffracted field in the target area of a mirror collimator

A mathematical model of a mirror collimator with rounded edges is developed. The problem of calculating electromagnetic field components in the target area is solved by the method of integral equations. The results of numerical computations are presented.

A fractional order diffusion-wave equation for time-dispersion media

Electromagnetic fields in time-dispersion media with a power-law dependence on time are analyzed. It is shown that these media are fractal and their fractal dimension is determined. Equations for scalar and vector potentials are derived using analogues of Maxwell’s equations for these types of media with the use of Caputo fractional derivatives. Electromagnetic fields in a bounded domain are numerically calculated for arbitrary functions of charge and current.