Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2023 number 4

This Special issue of Russian Geology and Geophysics is a collection of papers on current problems of experimental mineralogy, petrology, and geochemistry discussed at the XVIII Russian Conference on Experimental Mineralogy (5-10 September 2022, Vinogradov Institute of Geochemistry, Irkutsk). The scope of considered issues ranges from laboratory modeling of mineral formation processes in different tectonic settings to technical mineralogy. The reported experiments are run at pressures and temperatures corresponding to crustal and mantle conditions.

Experimental studies aimed at determining the conditions for the formation of diamond and graphite as a result of the redox interaction of reduced mantle rocks and oxidized rocks of the slab in a wide temperature range, including the conditions of both "cold" and "hot" subduction, were carried out on a "split-sphere" multianvil high-pressure apparatus (BARS) in the (Fe,Ni)-(Mg,Ca)CO₃ system, at 6.3 GPa and 800-1550 °C for 35-105 h, using the «sandwich» assembly. We have established that the interaction of Fe,Ni metal and carbonate is due to the creation and propagation of a redox front, at rates from 1.3 (800 °C) to 118 µm/h (1550 °C). At T < 1200 °С, this interaction leads to the formation of alternating reaction zones (from the reduced center to the oxidized periphery): metal → metal + wüstite/magnesiowüstite → magnesiowüstite + graphite ± Mg,Fe,Ca carbonates → magnesite + aragonite. In this case, in the reduced part of the samples, the formation of a Ni,Fe metal phase strongly enriched in Ni (up to 65-70 wt.% vs. the initial 10 wt.%) was recorded. At higher temperatures, the formation of Fe,Ni metal-carbon (≥1200 °C) and carbonate (≥1330 °C) melts was observed. We have found that the presence of nickel precludes the formation of carbides in the reduced part of the sample and ensures stable diamond crystallization at 1400-1550 °C both in metal-carbon and carbonate melts. Our experiments demonstrate that diamonds from the metal-carbon melt are characterized by inclusions of taenite and magnesiowüstite. The morphology of these diamonds is determined by the {111} layer-by-layer grown faces, and their indicator characteristics are nitrogen-vacancy and nickel-related (884 nm) centers at 1400 °C or nickel-nitrogen centers (S3, 598 nm, 727 nm, 746 nm, etc.) at 1550 °C. For diamonds formed in the carbonate melt, the morphology is determined by the {100} and {111} (vicinal-growth) faces; carbonates are identified as inclusions; and nitrogen-vacancy centers H3, NV⁰, and NV^- are fixed in the photoluminescence spectra. Experiments show that the indicator of the metal-carbonate interaction temperature is the degree of structural perfection of graphite, which increases in the range of 800-1550 °C.

Subduction of marine carbonates is accompanied by numerous transformations and interactions, including reactions with reduced mantle rocks. At depths of 250-300 km, carbonates enter mantle zones where metallic iron can be stable. The interaction of carbonates with metals is one of the mechanisms of the release of elemental carbon and the formation of diamond. These processes are also accompanied by carbon isotope fractionation and can result in a significant isotopic heterogeneity of mantle carbon. In this work we study the partitioning of carbon isotopes between carbon and carbon-bearing phases obtained in experiments on the interaction of FeNi alloy with (Mg,Ca)CO₃, which simulates mantle-crust redox reactions in the temperature range 800-1550 °C and at a pressure of 6.3 GPa. It has been established that at 800-1000 °C, the carbon of carbonate is reduced at the metal/carbonate interface and dissolves in the FeNi alloy. This process leads to a 17-20 ‰ depletion of the metal in the heavy carbon isotope. At temperatures above 1330 °C, the fractionation of carbon isotopes between carbonate and metal-carbon melts is reduced to 8.5 ‰, approaching the thermodynamic calcite-cohenite isotope equilibrium. At temperatures above 1400 °C, diamond crystallizes from metal-carbon and carbonate melts, which leads to isotopic depletion of the metal-carbon melt. As a result, the measured carbon isotope fractionation between the carbonate and metal-carbon melts increases and moves away from the thermodynamic CaCO₃-Fe₃C equilibrium line. The carbonate-metal redox interaction is supposed to be one of the probable mechanisms of the formation of isotopically light carbon in the mantle at the expense of the marine carbonate sediments subducted into the mantle. This mechanism also provides the formation of anomalous isotopically heavy carbonates found in kimberlites of the Siberian Platform.

The composition of the fluid in carbonate- and chlorine-bearing pelite was experimentally studied at 3.0 GPa and 750 and 900 ºC, using the diamond trap method. The results of inductively coupled plasma atomic-emission spectrometry (ICP AES) data and mass balance calculations showed that a supercritical fluid formed in the studied system at 3.0 GPa and 750 °C. The fluid is Si- and Al-rich and contains 30–50 wt.% H₂O + CO₂ and up to 1 wt.% Cl. The contents of other major elements decrease in the order: K > Na > Сa ≈ Fe > Mg > Mn >> Ti ≈ P. Compared with supercritical fluids appeared in the systems pelite–H₂O and eclogite–H₂O, the fluid with high CO₂ and Cl contents is richer in Fe, Ca, Mg, and Mn but poorer in Si. Silicate melt generated in this system at 900 ºС has a composition typical of pelitic melt. Our experiments reveal a set of fingerprints of element fractionation between a supercritical fluid and solids forming an eclogite-like association, namely, high mobility of P, Sr, and B and low mobility of Li and S. Thus, a supercritical fluid compositionally similar to the pelitic melts generated in subduction zones can transfer significant amounts of both volatiles (H₂O, CO₂, Cl, and P) and major components to the regions of arc magma generation. It is important that supercritical fluids should have trace element signatures of diluted low-temperature fluids.

Alkaline chlorides are important constituents of carbonatitic inclusions in magmatic minerals from kimberlites and lamproites, mantle xenoliths from kimberlites, and diamonds from kimberlites and placers around the world. This indicates the participation of alkali chlorides, along with carbonates, in the processes of melting of mantle rocks, which makes it important to study chloride-carbonate systems at mantle pressures. In this work, we studied the phase relations in the NaCl-CaCO₃-MgCO₃ system at 3 GPa in the range of 800-1300 °С using a multianvil press. It has been found that the NaCl-CaCO₃ and NaCl-MgCO₃ binaries have the eutectic type of T-X diagram. The halite-calcite eutectic is situated at 1050 °C and Na2# = 36, while the halite-magnesite eutectic is located at 1190 °C and Na2# = 77, where Na2# = 2NaCl/(2NaCl + CaCO₃ + MgCO₃) · 100 mol.%. In the NaCl-CaCO₃-MgCO₃ ternary, subsolidus assemblages are represented by halite and calcium-magnesium carbonates. Just below solidus, two assemblages are stable: halite + magnesite + dolomite and halite + dolomite-calcite solid solution. The minimum on the liquidus/solidus surface corresponds to the halite-Ca_0.84Mg_0.16CO₃ dolomite eutectic, located at about 1000 °С with Na2#/Ca# = 34/84, where Ca# = Ca/(Ca + Mg) · 100 mol.%. At Ca# ≤ 73, the melting is controlled by the halite + dolomite = magnesite + liquid ternary peritectic, located at 1050 °C with Na2#/Ca# = 31/73. According to the data obtained, it can be assumed that at 3 GPa the solidi of NaCl-bearing carbonated peridotite and eclogite are controlled by the peritectic reaction halite + dolomite = magnesite + liquid, located at about 1050 °C. The melting is accompanied by the formation of a chloride-carbonate melt containing (wt.%): NaCl (35), CaCO₃ (56), and MgCO₃ (9).

Feldspar group minerals (feldspars) form up to 60 vol.% of the Earth’s crust. The knowledge of their stability under extreme conditions (high-pressure and high-temperature) allow to better understand the processes, that occur in the subduction and collision processes. This review focuses on the behavior of feldspars with paracelsian topology (seven mineral species: three borosilicates, two aluminosilicates and two beryllophosphates) at elevated temperatures and pressures. Partly, new data on high-temperature behavior of paracelsian BaAl₂Si₂O₈ (based on in situ high-temperature powder X-ray diffraction) provided. The high-temperature studies of 5 feldspar minerals with paracelsian topology (danburite, maleevite, pekovite, paracelsian, slawsonite) revealed that all of them are stable at least up to 800 °C. Among all of them only paracelsian undergoes polymorphic transition (at 930 °C), whereas all other minerals decompose or amorphisize. The structural deformations of these minerals demonstrate the different anisotropy degree upon heating, whereas the average volume expansion is similar for all of them (α_V = 23 ×10^-6 ºC^-1). High-pressure behavior was studied for six of seven minerals with paracelsian topology (danburite, meleevite, pekovite, paracelsian, slawsonite, hurlbutite). The studied minerals undergo transformations with the stepwise increasing of coordination number of frame-forming cations from 4 to 5 and 6 upon compression The discovering of unusual structural units under extreme conditions (e.g., fivefold-coordinated polyhedral) can influence on the concentration and transport processes of trace elements that should be taken into account when interpreting geochemical and geophysical data. The crystal structure stability range of studied minerals highly depends on the chemical composition of frame-forming cations: aluminosilicates are the least stable and undergo the phase transitions below 6 GPa; borosilicates preserve their initial crystal structure up to ~20 GPa; beryllium phosphates do not undergo phase transformations up to 75 GPa. It has been shown that transformations pathway of isostuctural compounds highly depends on the chemical composition of both extraframework and frame-forming cations that involves the difficulties with predictions of their behavior under extreme conditions.

We report new experimental data on the interaction of igneous melts with hydrogen at temperatures of 1100-1250 °C and hydrogen pressures of 1-100 MPa in strongly reducing conditions: f_O2 = 10^-12-10^-14. The experiments were conducted using an original high-gas-pressure unit equipped with a unique device that provides long-term experiments at high temperatures and pressures of hydrogen. The experiments used natural samples of igneous rocks: the magnesian basalt of the Northern Breakthrough of the Tolbachik Volcano (Kamchatka) and the andesite of the Avacha Volcano (Kamchatka). On the basis of the experiments, the following features of the process of interaction of hydrogen with igneous melts have been established: (1) Despite the high reduction potential of the H₂-igneous melt system, the reactions of hydrogen oxidation and complete reduction of oxides of metals of variable valence in the melt do not go to the end. The cessation of redox reactions in basaltic and andesitic melts is due to the formation of H₂O in the melt, which buffers the reduction potential of hydrogen; (2) The initially homogeneous igneous melt becomes heterogeneous: The formed H₂O dissolves in the melt and in the fluid phase (at first pure hydrogen), and melts of variable, more acidic composition and small metallic isolations of the liquation structure are formed; (3) The complex process of metal-silicate liquation in magmatic melts when they interact with hydrogen can be carried out at real magma temperatures in nature (≤1200 °C), significantly lower than the corresponding melting points of iron and its alloys with nickel and cobalt; (4) The structure and dimensions of the experimentally established metal isolations are consistent with natural data on the finds of small quantities of native metals, primarily iron and its alloys with nickel and cobalt, in igneous rocks of different compositions and genesis.

Distribution of a wide range of elements in the systems with magnetite, hematite and sphalerite is studied by the method of thermogradient hydrothermal synthesis combined with internal fluid sampling at 450 °C temperature and 100 MPa pressure. The distribution and cocrystallization coefficients are determined; the literature and original data on these coefficients are summarized. The possibility of obtaining the reproducible data on elements distribution in the mineral - solution system in the occurrence of many typomorphic elements is substantiated. This considerably increases the experiment efficiency. A significant advantage of using cocrystallization coefficients rather than "conventional" distribution coefficients expressed by the ratio of the element concentrations in crystal and solution (fluid) is shown. The features of behavior and occurrence of elements in hydrothermal systems are provided with physico-chemical evidence, through application of cocrystallization coefficients. The examples of the behavior of typomorphic trace elements in sphalerite are considered, which support the theoretical analysis. The major (Fe, Mn, Zn and possibly Cu) and secondary (Ti, V, Al, and Co) components of ore-forming solutions are estimated according to the compositions of magnetite and hematite from hydrothermal ore deposits of various types. The similarity in compositions of magnetite and hematite does not prove their coformation from a single fluid, quite the reverse, and this fact indicates different compositions of fluids from which the minerals were deposited.

The modeling experiments were conducted to study transport of ore-forming components in the lithosphere, taking into account the possibility of ore matter remobilization under endogenous conditions. The experiments, which included temperature gradient-based ones, were conducted at T = 500-680 °C and P = 1.5-5.0 kbar on high gas pressure devices (HGPD) in highly concentrated water-salt solutions of alkaline specifics. The experiments consisted of two stages. During the first stage, we tested the possibility of recrystallization of the ore matter of "black smokers" in the presence of basalt at 500 ℃ and 5 kbar and water-salt fluids at a concentration of up to 5 wt.%. At the second stage, mechanisms of ore-forming components transport ( P-T parameters: 450-650 ℃ and up to 5 kbar) were studied under conditions of a temperature gradient (0.3-0.4 °C/mm). The duration of the experiments was 14 days. The test products were: oceanic basalts, granite model mixtures (Fsp + Qz), as well as various sulfide minerals, oxides and noble metals (Au, Pt). It has been shown that at T 680-650 °C, intensive recrystallization and deposition of sulfide minerals (sphalerite, galena, chalcopyrite, pyrite, cooperite, etc.) along with feldspars, micas and quartz, takes place. Intensive transport of both the main petrogenic (Si, Ti, Al, Fe, Mn, Mg, Ca, Na, K) and ore-forming elements (Ni, Cu, Zn, As, Pb, Cd, Pt, Au, Hg, Bi), and a joint transport of silicate and ore matter is established. Some ore elements are either included into compositions of solid solutions or present as impurities in ore-forming minerals: Fe, Ni, Cu → pyrite, pyrrhotite; Pb, Au, As, Bi, Zn → galena; Zn, Cd, Fe, Mn, Cu → sphalerite; As → galena, orpiment, realgar, gold; Hg → gold. The obtained data attest to the possibility of modeling ore mineralization mechanisms. The experimental results apply to explain the genesis of the Zun-Kholba gold-quartz-sulfide deposit and describe the processes of epigenetic transformations of primary ores in polymetallic deposits, on the example of the Ozernoe Pb-Zn deposit. The discussed mechanisms can be extended to explain the genesis of other ore deposits occurring in the zones of tectonic-magmatic activation.

We consider high-purity quartzites of the Gargan quartz-bearing zone of East Sayan. The main productive varieties of quartzites have been identified. The structures, textures, chemical composition, and degree of enrichment of the quartzites and the mineral and fluid inclusions in them have been studied. Quartz concentrates of high and ultrahigh purity have been obtained from superquartzite and compact quartzite.

The form of the vibrational-rotational operator of kinetic energy for linear symmetric molecules of the A₂B₂ type in polyspherical non-orthogonal internal (bond lengths and angles between bonds) coordinates is obtained. Non-orthogonal coordinates have advantages in calculating the wave functions of heavy linear molecules, for example, C₂F₂, C₂Cl_2, and also simplify the calculation of the intensity of the lines of the vibrational-rotational spectra of molecules of this type. This work is a continuation of the previous work [1], in which the form of the kinetic energy operator in orthogonal coordinates was obtained. To verify the obtained expressions, the lower vibrational-rotational energy levels of the acetylene molecule were calculated.

Graphical resources on the continuum absorption of water vapor and its mixtures published in 2011-2020 are described. Summary tables are presented that characterize the main parameters of the absorption coefficients and transmission functions in different spectral intervals, the temperature dependence of the absorption coefficient, and the equilibrium constant of the water dimer formation reaction. The features of the study of the continuum absorption in published works in this time interval are noted. In a concise form, the results of the assessment of the quality of citing plots are presented, which are described by four qualitative and quantitative attributes. Three citation procedures are characterized, two of which are computerized. A method for estimating the difference between the citing and cited plots and examples of pairs "citing and cited plots" with a quantitative assessment of the difference are presented.

This work is a continuation of the paper "Measurements of atmospheric parameters along an extended paths. I. Acoustic measurements of turbulence and average wind speed" and is devoted to the results of optical measurements of atmospheric turbulence along horizontal atmospheric paths. These measurements were carried out to determine the effective mean values of atmospheric turbulence parameters along an optical radiation propagation path and the associated coherence length of optical waves propagating through the atmosphere. The path optical measurements were supported by AMK-03 acoustic weather station measurements. That made it possible to compare the local acoustic and optical measurements of turbulence with different optical meters.

The results of experimental studies of aerosol in the surface air layer in the southeastern part of the Crimean Peninsula at the background environmental monitoring station of the Vyazemsky Karadag scientific station from March 21 to June 17, 2020, are presented. The daily average mass concentration over aerosol for the entire measurement period ranged from 3 to 35 mg/m3, with an average value of 13 mg/m3. The exception was high concentrations of particles during the episode of 25–27.03.2020 (48, 195, and 49 mg/m3), when a extreme eastward transfer from sources in Kazakhstan (a dust storm on the Aral Sea) through Kalmykia to the Crimea took place. Taking into account this episode, the daily average aerosol mass concentration was 16 mg/m3. Days with different directions of air masses arrival, as well as days with the highest daily mean values of aerosol mass concentration were identified out of 89 observation days. For this sample (31 samples), the content of 64 chemical elements was determined in the samples. Accumulation of chemical elements in soil and in aerosol particles was estimated; clarks of chemical element concentrations in soil, aerosol concentration coefficients, and enrichment coefficients of chemical elements in aerosols were calculated. The dependences of the mass concentration and disperse and elemental composition of the surface aerosol on further aerosol migration are considered.

Water vapour plays a key role in different climate-forming processes at various altitudes of the Earth's atmosphere. Water vapour isotopologues monitoring provides information on the atmospheric hydrological cycle. It helps to study the processes associated with evaporation and condensation that control the humidity in the troposphere and water exchange between the troposphere and stratosphere. For the first time, temporal variability of water vapor isotopologues (H₂O and δD) in Peterhof in 2009-2020 were analyzed using ground-based measurements of solar IR radiation by the Bruker IFS 125HR Fourier spectrometer. For both H₂O and δD, the maximum values occur in summer, the minimum - in winter, while the largest variability of H₂O is observed in summer, and δD - in winter months due to the climatic features of St. Petersburg, i.e. the origin and history of incoming air masses. The database of water vapour isotopic composition in the vicinity of St. Petersburg can be used in models of the general circulation of the atmosphere to improve the accuracy of weather forecasting and long-term changes in the regional climate.

The results are presented of laboratory experiments to determine the characteristics of convective turbulence over a heated metal surface for various heights and temperatures by high-speed thermography. The study of convective turbulence characteristics was carried out using a high-speed infrared camera by shooting the temperature field of low-inertia paper targets suspended above the heated surface simultaneously over the entire vertical plane of the IR camera field of view. Based on fluctuations in the temperature field of the target surface, the heat transfer coefficient, the intensity level of the convective flow, the total flow, and the amount of heat generated during measurements at different heights above the surface are determined. The energy spectra of convective turbulence are plotted under various turbulent conditions. An analysis of the turbulence spectra showed the presence of an inertial interval with a slope close to the 8/3 power law for all considered heights above the heated surface, temperatures, and turbulence conditions. Characteristics of convective turbulence obtained can be used when testing various optical adaptive laser beam control systems, studying the propagation of vortex laser beams and combustion centers, which are also characterized by convective turbulence with a further transition to atmospheric turbulence induced by combustion energy.

Lidar is an important tool for studying atmospheric aerosol; it is widely used in studying the propagation of aerosol pollution in the atmosphere. During environmental monitoring, especially with a mobile lidar, it is important not only to detect a pollutant, but also to determine the spatial coordinates of its source and the propagation dynamics. In the work, we suggest a technique for calculating the coordinates of an object under study from the lidar coordinates, sensing direction, and the distance between the lidar and the object. The software implementation of the technique and an example of its application in the design of an auxiliary lidar system are described.

Changes in the oxygen (δ¹⁸O) and hydrogen (δD) isotope compositions of precipitation in Tomsk in the period from 2016 to 2020 are studied. It is found that the δ¹⁸O value varies in the range from -39.6 to +2.1‰, the average value over the entire period is -18 ± 6.8‰; the δD value varies in the range from -299 to -4.9‰, the average value is -118.7 ± 54.7‰. A Local Meteoric Water Line is calculated for the period from 2016 to 2020: δD = 7.43δ¹⁸O + 11.2; this equation indicates the predominance of evaporative fractionation. The dependence of the isotope composition of precipitation on temperature in Tomsk is derived: +0.47‰/°C for the δ¹⁸O value and +3.62‰/°C for the δD value. The main regions that provide atmospheric precipitation with different isotope compositions to Tomsk are identified based on the analysis of the airmass backward trajectories.

Gases desorbed by the vacuum method from the tree rings of discs of deciduous trees are measured. The content of residual gases vacuum-desorbed from tree rings is analyzed with an opto-acoustic gas analyzer with a tunable CO₂ laser. The chronologies of residual CO₂ and (CO₂ + H₂O) of some deciduous trees growing near the city of Tomsk (West Siberia) have been derived. All the chronologies are cyclic with pronounced 2-4-year cycles. A correlation was found between the content of gases and summer temperatures and precipitation. We believe that the annual distribution of residual gases in the discs reflects the pattern of annual release of the gases from the stems of the deciduous trees into the atmosphere.

The goal of this study is to develop hybrid composites to experimentally and numerically assess their behavior under a ballistic impact. The Al₂O₃ ceramic/woven fabric (Kevlar or UHMWPE) reinforced epoxy/Al-alloy multi-layered armours are developed. Simulation and ballistic test results show good agreement.

The lattice Boltzmann method (LBM) is a numerical scheme for solving fluid dynamics problems. One of the important and actively developing areas of LBM is correct construction of the scheme on non-uniform spatial grids. With non-uniform grids the total number of calculations can be significantly reduced. However, at the moment the construction of an LBM scheme near a boundary of grids with different spatial steps inevitably requires data interpolation, which can reduce the LBM approximation order and lead to violation of conservation laws. In this work, for the first time, we have developed and tested a method for constructing an athermal node-based LBM on non-uniform grids without interpolation, with the same time step for grids of different scales. The method is based on a two-stage transformation of populations corresponding to different on-grid stencils.

We have developed stochastic algorithms to simulate signals detected by a receiver of a laser navigation system designed for safe aircraft landing. Radiant flux and radiance at the receiver, as well as the contribution of radiation of different orders of scattering are estimated by a Monte Carlo method. Computation results show that the proposed algorithms allow one to study the efficiency of the laser navigation system in various conditions.

In this paper, an efficient numerical method which is a collocation method is considered in order to obtain numerical solutions of the KdV-Kawahara equation. The numerical method is based on a finite element formulation and a spline interpolation by trigonometric quintic B-spline basis. Firstly, the KdV-Kawahara equation is split into a coupled equation via an auxiliary variable as υ=u_xxx. Subsequently, a collocation method is applied to the coupled equation together with the forward difference and the Cranck-Nicolson formula. This application leads us to obtain an algebraic equation system in terms of time variables and trigonometric quintic B-spline basis. In order to measure the error between numerical solutions and exact ones, the error norms L₂ and L_∞. are calculated successfully. The results are illustrated by means of two numerical examples with their graphical representations and comparisons with other methods.

A comparative analysis of two algorithms for estimation of weighted mean particle flux - «by particles» and «by collisions» - is made on the basis of test problem solving for a single-speed particle propagation process with scattering and multiplication in a random medium. It is shown that the first algorithm is preferable for a simple estimation of the mean flux and the second one, for estimation of the parameters of a possible superexponential flux growth. Two models of the random medium are considered: a chaotic «Voronoi mosaic» and «a spherically layered mosaic». For a fixed mean correlation radius, the superexponential growth has been stronger for the layered mosaic.

The article considers the problem of calculating the phase probability density function of a phase-shift keying signal received under conditions of distortion and additive noise. This problem is reduced to an inverse problem, namely, to solving an integral equation of the convolution type. The functions included in the integral equation are analyzed. The case of equiprobable symbols, which is important from a practical point of view, is considered separately. Numerical simulation results are presented.

Based on the use of the geometric series theorem, we transform a linear Fredholm integral equation of the second kind defined on a large interval into an equivalent linear system of Fredholm integral equations of the second kind; then, we inflict a refinement in the way the investigated generalised iterative scheme approximates the sought-after solution. By avoiding to inverse a bounded linear operator, and computing a truncated geometric sum of the former's associated sequence of bounded linear operators instead, we notice that our approach furnishes a better performance in terms of computational time and error efficiency.

This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in R2. Both the spatially discrete and the fully discrete approximations are analyzed. We have used the standard continuous fitted finite element discretization for the space while, the backward Euler approximation is used for the time discretization. Due to the low regularity of the data of the problem, the solution possesses very low regularity in the entire domain. A priori error bounds in the L²(L²(Ω))-norm for both the spatially discrete and the fully discrete finite element approximations are derived under minimal regularity with the help of the L²-projection operator and the duality argument. Numerical experiments are performed to underline the theoretical findings. The interfaces are assumed to be smooth for our purpose.

The article solves the problem of determining the temperature on the inner wall of a hollow cylinder. Using a time Fourier transform, the problem is reduced to an ordinary differential equation, with the help of which the Fourier transform of an exact solution of the inverse boundary value problem is found. A projection regularization method is considered, which makes it possible to obtain a stable solution to the problem and an accurate in order of magnitude estimate of the error of the approximate solution. Since high accuracy requirements are imposed on solutions of such problems in numerical calculations, an algorithm is developed to improve the accuracy and reliability of processing the results of thermal test data. To check the performance of the algorithm, test calculations are carried out.

The study of alkali-resistant fungi was carried out for the first time on the coast of saline lakes in the south of the Trans-Baikal region on the territory of the Daursky Biosphere Reserve (lakes Zun-Torey, Khangei). Indicated changes in the structure of the community of alkali-resistant ascomycetes depended on local conditions. The coast of Khangei was devoid of halophites, but with a high content of Artemia eggs and was characterized by the absolute dominance of the alkaliphilic ascomycete Sodiomyces alkalinus (100 % occurrence) and Emericellopsis alkalina (80 %), with a minimum diversity of other fungi. S. alkalinus predominated (100 %) on the coast of Lake Zun-Torey in damp places without plants. Dark-colored fungi from Dothideomycetes (Alternaria, Neocamarosporium, etc.) predominated in the alkaline soil samples of this lake not far from the halophites, the occurrence of E. alkalina was 60 %, and S. alkalinus was not found here, but the high occurrence was shown for the other species from Plectosphaerellaceae (Chordomyces, Gibellulopsis). The distribution, substrate preferences, and functional roles of alkaliphilic and alkalitolerant fungi in extreme natural habitats with soda salinity are discussed in this paper.

The biodiversity of wood-destroying fungi on leguminous woody plants (LWP) growing in the Middle Urals has been studied for the first time. In the model region – Sverdlovsk province, from 2002 to 2022, there are 136 species of wood-destroying fungi were collected: 127 species of Basidiomycota and 9 species of Ascomycota. Fungi develop on 12 out of 20 species of LWP. The largest number of fungal species was found on the alien Caragana arborescens (115 species / 84.5 % of the total number of species), while on Caragana decorticans, C. ussuriensis, Laburnum alpinum two each, and one on Genista florida. 122 species of fungi were found on nine alien species of the LWP, which is 4.1 times more than on three native species. The largest number of substrate-specific fungal species develops on C. arborescens (85/62.5 %), while four on Chamaecytisus ruthenicus (2.9 %), three on Maackia amurensis (2.2 %), two each on Genista tinctoria and Robinia pseudoacacia (1.5 %), and one species on Caragana ussuriensis (0.7 %). Nectria cinnabarina develops on seven species of LWP, on six species – Xylodon sambuci, on four – Peniophora cinerea and Schizophyllum commune. In contrast, 71.3 % of fungal species were found on one LWP species, and 27.2 % of species are characterized by a single find. For the first time for Sverdlovsk province, 14 fungal species are indicated, of which 86 % were found in the parks of Ekaterinburg city, tree-lines along the roads, but only 14 % in natural conditions.

In order to reveal the latitudinal-zonal specificity for the distribution of species richness of the LWP associated mycobiota, we use Aphyllophoroids as the largest group of fungi among all analyzed (75 % of species), and Caragana arborescens, or Siberian pea tree, is the richest plant substrate. Changes in the fungal diversity were studied along a meridional transect stretching for 800 km. along 60° E, from the middle boreal subzone of Sverdlovsk province to the steppes of Chelyabinsk province (Russia) and Kostanay province (Kazakhstan). In each of the 5 vegetation zones/subzones, as well as in Ekaterinburg city, six sites were studied, the area of which varies from 0.9 to 6.8 ha. The aboveground phytomass of C. arborescens is maximal in the forest-steppe (8.9–11.7 t/ha), and minimal at the edges of transect (2.4–5.8 t/ha).A positive correlation was found between the aboveground plant phytomass and the species richness of mycobiota, while there was no correlation with climatic parameters. In Ekaterinburg city, where the Siberian pea tree phytomass is two times lower than in the forest-steppe, but the species richness of mycobiota is similar to the forest-steppe, is out of this pattern. A similar result was obtained for α-diversity (average number of fungal species on the sites and Shannon index) of mycobiota: an increase in indicators from the middle boreal subzone to the forest-steppe and a decrease in the steppe. The Whittaker and Czekanowski – Sørensen indices (β-diversity) increase towards the steppe, which is due to a strong relationship with the mean annual temperature and precipitation. A range of fungal species gravitating towards northern, southern and urbanized conditions has been revealed. In the north of transect, local species of fungi predominate, while in the south and in Ekaterinburg city, the role of biogeographically distant (alien) taxa is high. In this regard, the species composition of Siberian pea tree’s mycobiota is divided into two clusters – northern (boreal) and southern (nemoral-steppe) including Ekaterinburg city. To the south, species richness of pathogenic fungi increases, but this parameter does not correlate with the C. arborescens phytomass. In plantings of invasive Siberian pea tree, species richness of Poroid fungi is similar to Corticioid fungi at the local and regional level, which differs significantly from natural conditions. A high level of pathogenic fungi was also revealed compared to natural conditions. The results obtained can be used to optimize the concept development of Greenway planning in Ekaterinburg city and can help prevent a number of environmental problems arising after the “rapid” implementation of the strategy for the city development and surrounding areas.

Changes in the taxonomic structure of the fungal community during the processing of cow manure with straw using Eisenia fetida worms were studied using fundamentally different methods - cultural and metabarkoding (by amplification and high-performance sequencing of ITS2 rDNA). Significantly more fungal taxa have been identified in substrates and vermicompost by application of metabarkoding than by plating method (66 and 33 species, respectively). Single species were identified simultaneously by both methods. The method of metabarcoding revealed OTE of Ascomycota, Basidiomycota, Mortierellomycota, Chytridiomycota, Glomeromycota, Basidiobolomycota, Rozellomycota, Aphelidiomycota, fungi from Ascomycota, Basidiomycota, Mucoromycota were isolated by culture method. The species richness of the community decreased during the first 10-20 days of substrate processing, then grew and reached maximum values in the vermicompost (60 days). Both methods showed the dominance of ascomycetes at all stages of transformation of sunstrates by E. fetida. Metabarcoding showed the dominance of sordariomycetes of the order Sordariales (48-53 %), mainly Zopfiella spp., fungi of the orders Pezizales, Microascales, Hypocreales, Pleosporales, Chaetothyriales, Onygenales, Eurotiales had the representation at the level of several percents. The increase of the portion of Chytridiomycota in the community (from 1,1 to 3.2 %) was observed during vermicomposting. At the same time, the representation of fungi of Mortierellomycota (5.7 to 1,5 %) of genus Mortierella and Basidiomycota (from 8 and 21 to 3 %) decreased with an increase in their diversity. Among the basidiomycetes, Coprinellus marculentus, Coprinellus subdisseminatus, Coprinus annuloporus, Occultifur sp prevailed. According to the plating method, ascomycetes also prevailed during waste processing and in the vermicompost, but it were other species - Diplodascus geotrichum, genera Penicillium, Aspergillus, Talaromyces, Trichoderma, Fusarium, mucoromycetes of the genus Mucor and basidiomycetes - Filobasidium wieringae. Fungi capable of decomposition of various polymer compounds in waste, active destructors of lignocellulose have been identified. Coprophiles, keratinophiles, thermophilic and thermotolerant species, representatives of the genera Trichoderma, Penicillium, capable of determining the suppressive properties of vermicompost to phytopathogens and human pathogens were found. The differences in mycobiota during composting and vermicomposting of various wastes are considered.

The interaction in the system “epiphytic microorganisms - host plant-pathogen” was considered on the example of Scotch pine (Pinus sylvestris L.) seedlings which artificially infected with the facultative saprotroph Lophodermium seditiosum Minter, Staley & Millar. At the same time, the change of quantity of the epiphytic microorganisms, the composition and concentration of volatile compounds and the morphological parameters of pine in different variants of the experiment were studied. The influence of two factors on the studied characteristics was considered: L. seditiosum infection and the introduction of mycocompost into the soil. Classical phytopathological and microbiological methods were used. Volatile compounds were studied using chromato-mass spectrometry, phytoncide activity was studied using the Tokin method adapted to our conditions. At the stage of ascospore germination, an increase in the amount of volatile components released by the affected needles and a decrease in the number of those released by the roots of infected plants were noted. Against the background of changes in the composition of volatile compounds, an increase in the phytoncide activity of the leaf and root systems of plants with signs of the disease was found compared to specimens without signs of damage. This is also evidenced by the results of microbiological cultures: in the variants with infection, compared with the control, a significant decrease in the number of epiphytic microorganisms was noted. A significant increase in the mass of needles was noted in the variants with infection and with the adding of mycocompost, confirmed by ANOVA analysis. Registered correspond to Selye’s adaptive syndrome (activation of physiological processes at an early stage of adverse effects, followed by exhaustion of the body if the load continues).

The ability to determine the spatial distribution of rare fungal species is critical to understanding the environmental factors that affect them. Maximum entropy (MaxEnt) spatial distribution modeling solves this problem by allowing inferences about the distribution of species in a gradient of environmental factors based on occurrence data. To identify patterns of spatial distribution based on objective data, models of the potential geographical distribution of the rare polyporoid fungus of Picipes rhizophilus under current conditions (~1950-2000) and with predicted future climate changes (2100 AD) on a global scale were created. The species Picipes rhizophilus can develop in steppe habitats of both plains and mountains. Most of the known habitats of the species are found in the ecoregions that make up the Temperate grasslands, savannas and shrublands, Mediterranean Forests, woodlands and scrubs, and Deserts and xeric shrublands biomes. The species is not associated with forest biomes, but it can be represented in habitats located on their territory, subject to the processes of climate aridization and desertification. The species Picipes rhizophilus can develop in steppe habitats of both plains and mountains. Modeling the potential distribution of the species under the selected climatic scenario showed the dynamics of changes in its range. The species-friendly climate area will increase in the North American continent, while there will be no significant changes in Europe and adjacent areas of Africa. In the most favorable territory for the species, located in the basin of the Western Manych River, conditions will become less favorable. In the Asian part, there will be a local shift in the areas of potential distribution.

Data on the dynamics of rust fungi are presented on the example of the Skadovsky Zvenigorod Biological Station of Lomonosov Moscow State University. The survey was carried out by the route method in years 2011-2019 and 2021 during vegetative season. 81 species of rust fungi were recorded on the territory of the biological station, the number of species detected during one year varies from 36 to 56. The number of species detected per year shows a significant correlation (r = 0.76) with the G index calculated from temperature and rainfall in June and August. During each season there is a change in the dominant stages of rust fungi. Species with aeciospores (I) are more common in June, species with urediniospores (II) are more common in July, and species with teliospores (III)predominate in August. The number of species detected in stage II per month is mainly determined by the number of species identified in the previous month in stage I (r = 0.61). Similarly, the number of species detected in stage III in a month is predominantly determined by the number of species detected in the previous month in stage II (r = 0.85). The revealed dependencies correspond to the biology of the Pucciniales.

The taxonomic diversity of epiphytic myxomycetes on living woody plants in the arboretum of the Central Siberian Botanical Garden SB RAS was studied. The regularity of the distribution community of epiphytic myxomycetes by trunk height has been established. All samples of myxomycetes were obtained by cultivation moist chambers in Petri dishes in the laboratory. Bark sampling from live woody plants was carried out at the height of the trunks from 0 to 15 meters from the soil level. Nine species of deciduous woody introduced plants participated in the experiment: Fraxinus pennsylvanica, Prunus maackii, Populus alba, Salix alba, S. pentandra, S. triandra, Sorbus aucuparia, Tilia cordata, Junglans mandshuria. Fifty-one species of myxomycetes have been identified. The species composition of myxomycetes on the studied woody plants differs significantly from that on native tree species growing on the territory of the botanical garden. Two species have been identified as new to science from the genera Arcyria and Trichia, three species are new to Russia (Didymium clavodecus, D. ovoideum, D. synsporon), eighteen species are new to the Novosibirsk region. The change in the taxonomic composition of myxomycetes community′s correlates with the height from the soil surface. Representatives of the genus Perichaena are found at all altitudes, but the greatest species diversity is noted in the basal part. There are 7 species noted here, while the species of the genus Didymium have the maximum species diversity (6 species) at an altitude of 5 meters, including 3 species new to Russia, noted only at this altitude. The distribution of the number of collected samples by height showed that the bark of living woody plants is most abundantly populated at a height of 5 meters (72 samples) and in the basal part (50 samples).

Ecological and genetic characteristics of the phoma-like fungus Calophoma complanata were defined. C. complanata is a potential bioherbicide of the giant hogweed. An ecological analysis of the C. complanata sample collection sites showed this pathogen is found where the humidity is high, and the temperature is a lower than at other sites of phoma-like micromycetes. The growing degree days >10 ℃ (GDD) of the distribution of the species varies between 106.0 (Shetland) and 911.5 (Lublin, Poland) with rather low average of 570. The minimum and maximum Selyaninov hydrothermal coefficient on the boundary of the species area are 3.26 and 1.31, respectively, with the average of 1.9. The species area is characterized by long photoperiods. Classical morphological, histochemical, and molecular methods for founding C. complanata MF‑32.121 in plants were carried out. It is shown that this species, depending on the conditions, can be able to cause the Sosnowsky's hogweed disease, or turns to the endophytic lifestyle. We believe that this is one of the mechanisms that allow the pathogen to survive in harsh natural conditions. The obtained data allow to predict the effectiveness of mycoherbicides depending on environmental conditions, to assess the long-term risks associated with its application and to reveal the spectrum of non-target biological activities.

Based on the culture method and high-performance sequencing of the ITS2 rDNA site, the number of colony-forming units (CFU), taxonomic structure and species richness of fungal communities in the bottom ground of Lake Baikal from depths from 9 to 178 m were determined. 215 species of 138 genera of 50 orders of 22 classes of 6 divisions - Ascomycota, Basidiomycota, Mucoromycota, Mortierellomycota, Chytridiomycota, Glomeromycota have been identified. Only DNA barcoding allowed to detect representatives of the Phyla of Chytridiomycota, Glomeromycota and Rozellomycota. The cultural method and high-performance sequencing of the ITS2 rDNA site in the soil revealed 77 and 146 species, respectively, and only 8 species were established by both approaches. Most of the nucleotide sequences have not been identified to the level of families and species. There are representatives of various ecological and trophic groups - saprotrophs, pathogens, symbiotrophs in the mycobiota of the bottom grounds. These are mainly psychrotolerant organisms, among them there are facultative anaerobic species. Changes in the taxonomic structure of fungal communities depending on the depth and species, and able to function in soils, have been established. These are, in particular, Pseudeurotium bakeri, Pseudeurotium hygrophilum, Pseudogymnoascus pannorum, Pseudogymnoascus roseus, Trichoderma hamatum, Trichoderma harzianum, Trichoderma lixii, Trichoderma polysporum, Penicillium glandicola, Penicillium swiecickii, species of the genera Rhizophydium, Fusarium, Daldinia Mortierella, Coniochaeta, Cystobasidium, Mrakia, Rhodothorula, Solicoccozyma and a number of others. A collection of fungal strains isolated from the bottom soils of Lake Baikal has been created.

For the first time, the results of studying the long-term dynamics of the phytopathological state of alien tree and shrub plants (hereinafter as ATSP) in Ekaterinburg city (Russia, Ural) are presented. In connection with the active implementation of numerous landscaping programs, including the concept of the Greenway planning of Ekaterinburg city, over the past twenty years, a large number of ATSP seedlings have arrived in the city, which contributes to the penetration of many previously unknown species of alien and pathogenic fungi into the Urals, the number of which increases exponentially. On alien woody substrates, many species of local saprotrophic fungi exhibit pathogenic properties, which also contribute to a sharp increase in the pathogenic activity of urban mycobiota. A number of invasive fungal species cause mass diseases of woody plants and expand their trophic spectrum. Some invasive fungal species are expanding their invasive range into the natural forests. A list of ATSP species resistant to local and alien diseases, which are recommended for greening Ekaterinburg, is given. The applicability of the "sentinel plantations" technique for the early detection and localization of alien phytopathogens is discussed. Recommendations are given for the creation of a four-stage system of phytopathological monitoring of green urban spaces, which will contribute to the protection against penetration and the rapid detection of alien pathogenic fungi before diseases outbreaks.

At present, the taxonomy of fusarioid fungi has changed significantly due to the clarification of their taxonomic status by molecular genetic methods. This led to the emergence of new species / genera and the abolition of old ones. Data on the diversity and distribution of Fusarium species do not always correspond to modern taxonomy and require careful revision. In this work, we systematized long-term data on the species composition and specialization of fusarioid fungi associated with woody plants in Russia (Far East, Siberia, Northwestern region, Crimea). Molecular genetic identification of 53 isolates previously identified as Fusarium spp. was carried out. Using morphological characters, phylogenetic analysis, and ecological features, five Fusarium species complexes have been identified. 11 Fusarium species have been identified (F. acuminatum, F. avenaceum, F. equiseti, F. oxysporum, F. redolens, F. reticulatum, F. sambucinum, F. sporotrichioides, F. torulosum, F. tricinctum, F. venenatum) and 1 closely related species of the genus Neocosmospora (N. solani). On woody plants, the Fusarium tricinctum species complex is represented by the largest number of species: F. acuminatum, F. avenaceum, F. reticulatum, F. torulosum and F. tricinctum. The maximum number of isolates (17) belong to the F. avenaceum associated with various plants throughout the study area. In forest nurseries (Central and Southern Siberia) on juvenile plants with symptoms of mycosis, seven species of Fusarium and N. solani were identified. F. oxysporum, F. equiseti and N. solani were found only on seedlings of conifers in the first year of vegetation. In forest and park stands, where fusarioid fungi are predominantly saprotrophs and endophytes, nine Fusarium species were found, of which F. tricinctum, F. torulosum, F. venenatum and F. reticulatum were not isolated from pathological and seed material in forest nurseries.

On the example of spruce forests of the European taiga of Russia, the most important functional positions of wood-destroying fungi (DRFs) in the genesis of forest communities are described. In spruce forests, the age structures of forest stands, the extent of damage to forests by the DRG of the biotrophic complex, the volume of tree waste, and the participation of fungi of the xylotrophic complex in the decomposition of deadwood biomass by stages of decomposition were studied. The graphic version shows the structure of the process of formation of the biomass balance of the indigenous taiga spruce forest, based on differences in the time periods of accumulation and decomposition of the biomass of woody fractions of indigenous sustainable spruce forests. DRGs perform the task of coordinating the processes of accumulation and decomposition of forest biomass, maintaining its balance in the dynamics of the forest community to a state of optimal sustainability. The participation of wood-destroying fungi in the formation of structures of sustainable spruce forest formations should be considered as the main paradigm of their functional tasks in forest communities.