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Propagation of high-power phase-modulated femtosecond laser pulses in air is numerically simulated. Spatial modulation of the initial pulse wavefront is carried out using a programmable phase plate consisting of segments arranged in a checkerboard pattern with a variable wave phase jump. The self-focusing, filamentation and post-filamentation channeling of radiation for phase-modulating masks with different phase shifts at the boundaries of neighboring segments are studied within the numerical solution of the nonlinear Schrödinger equation for the time-averaged electric field amplitude. The filamentation domain in air for certain pulse phase modulation types is shown to be significantly shifted (along the coordinate) and elongated compared to an unmodulated pulse. In addition, it is found that the use of phase modulation makes it possible to reduce the angular divergence of high-intensity light channels generated during the post-filamentation propagation stage. This provides a possibility of self-channeling of radiation at distances multiple of the Rayleigh length.

The results of analysis of aerosol of an aqueous solution of NaCl by femtosecond-pulse laser-induced breakdown spectroscopy (FS-LIBS) are considered. The results of estimating the impurity (Na) concentration by the analytical pair method using the additive method are presented. The radiation of the atomic nitrogen ion N⁺ at a wavelength of 500.515 nm from atmospheric nitrogen molecules in the filamentation region was taken as the internal standard line. A possibility of estimating the concentration of the both desired substances, the radiation of which is recorded, and the compound containing it is shown. The results are of interest for the development of femtosecond lidar sensing methods.

The results of the laser granulometry of nanosize fraction of precipitated aerosols and UV spectrometry of water washes from the surfaces of needle of different age of four species of forest-forming plant species are analyzed. The phenolic compounds efflorescence activity on the needle surfaces is assessed for the period of winter dormancy of plants. A possibility of the secondary organic aerosols geeration as a result of photoactivated reactions between phenolic compounds and a precipitated aerosol substance has been shown. The possibility of secondary organic aerosols entering the winter forest canopy under the radiometric photophoresis is discussed. It is assumed that secondary aerosols photophoresis in the field of IR from the snow cover surface (“snow” photophoresis) can significantly affect the vertical transfer of secondary organic aerosols in the winter coniferous forest canopy.

The dependence of the intensity of emission lines Ca (393.3, 396.8, 422.6 nm), Mg (383.6 nm), and Na (589 nm) on the laser pulse duration in the method of filament-induced breakdown spectroscopy is investigated. The filament was excited in seawater aerosols droplets of 0.8-2 mm in size by laser pulses of 70, 230, 500, and 900 fs in duration at a constant pulse energy of 3.0 mJ. It is shown that with an increase in the laser pulse duration, the intensity of the emission lines of the studied elements increased, with the exception of the magnesium line. Optimal values of the laser pulse duration for the excitation of Ca, Mg, and Na lines in a seawater aerosol are derived.

The turbulence parameters obtained using lidar are compared with the parameters determined from the average values of velocity and temperature in the surface air layer. The results of observations of the structural constant of the refractive index C_n² obtained from the ratio of the turbulent lidar returns in the surface air layer when working along a slightly inclined sounding path are presented. A method for determining the rate of kinetic energy dissipation from lidar data has been tested.

In winters-springs 2010/2011 and 2019/2020, there were the strongest anomalies of ozone layer in the Arctic stratosphere in the total satellite era. They were due to extraordinarily strong and long-lived stratospheric polar vortices, entailing unprecedented chemical ozone destruction. The analysis of the TEMIS data indicates that the total ozone content (TOC) deviations from the multiyear (2003-2019 except 2011) average were from 37 to 44% in 2011 and from 45 to 55% in 2020 at Arctic observation stations; and from 27 to 36% in 2011 and from 27 to 32% in 2020 in the subarctic latitudes. Based on the Aura MLS data, the minimal temperatures were 8-12% below normal over the Arctic in 2011 and 8-13% below normal in 2020. The ozone concentration dropped to 23% of the multiyear average at an altitude of 20 km on March 22, 2011, and to 6% at an altitude of 19 km on April 15, 2020, for Alert. A detailed correlation analysis showed that the deviations in the concentrations of water vapor and ozone, water vapor and temperature, and ozone and temperature correlate stronger in 2020 than in 2011. The correlations decrease toward the vortex periphery owing to the exchange of air masses between the Arctic and middle latitudes, becoming weakly significant outside the Arctic circle.

Generation of fogs downstream of the Krasnoyarsk hydropower plant on the Yenisei River during 2020 is studied. Meteorological conditions at the time of fog generation were recorded on the geoportal developed by the authors; water temperatures were taken at a gauging station; fogs were recorded with the help of video surveillance cameras. Data analysis showed generation of advective cooling fogs in summer and advective steam fogs in winter, early spring, and autumn. Cooling fogs are generated due to the cooling of the moist air as the lower atmosphere interacts with a colder moving water surface. Steam fogs result from the advective cooling of water vapor on the river surface by the colder adjacent atmosphere. The spatial distribution of steam fogs was derived from remote sensing data.

This paper considers the problem of phases probability distribution function estimation for phase-shift-keying signals. The modulating sequence, and, accordingly, the values of the symbols phases, as well as the statistical characteristics of this sequence are unknown. The Fourier coefficients are calculated based on a limited sample for estimation of phases probability distribution function. In this case, the obtained Fourier coefficients are regularized. Application of multiparameter regularization for increasing the estimation accuracy are considered. The numerical simulation results are presented.

Resistance to HIV-1 disease developed by some exposed individuals has shown a promising sign in the fight against HIV-1 infection. Behavior change has also become one of the most important protection strategies against HIV-1 pandemic, but both of them have been widely neglected by mathematical modelers. In this paper, a new virus resistance HIV-1 mathematical model incorporating behavior change is formulated and analyzed rigorously for both partial and total abstinence cases. The calculated reproduction number is used to establish the local stability of the disease-free equilibrium points using the approach of Watmough and Driessche in both cases. Using appropriate demographic and epidemiological data for South Africa in the numerical simulation, the positive effect of behavior change in the midst of HIV-1 resistance is thoroughly examined, and this strategy is absolutely effective in dealing with the threat of HIV-1. This work also provides a better result than what is obtainable in the majority of the referenced related works.

In this work, we deal with a convex quadratic problem with inequality constraints. We use a logarithmic barrier method based on some new approximate functions. These functions have the advantage that they allow computing the displacement step easily and without consuming much time contrary to a line search method, which is time-consuming and expensive to identify the displacement step. We have developed an implementation with MATLAB and conducted numerical tests on some examples of considerable size. The obtained numerical results show the accuracy and efficiency of our approach.