All issues

The method of balanced identification was used to describe the response of Net Ecosystem Exchange of CO₂ (NEE) to change of environmental factors, and to fill the gaps in continuous CO₂ flux measurements in a sphagnum peat bog in the Tver region. The measurements were provided in the peat bog by the eddy covariance method from August to November of 2017. Due to rainy weather conditions and recurrent periods with low atmospheric turbulence the gap proportion in measured CO₂ fluxes at our experimental site during the entire period of measurements exceeded 40%. The model developed for the gap filling in long-term experimental data considers the NEE as a difference between Ecosystem Respiration (RE) and Gross Primary Production (GPP), i.e. key processes of ecosystem functioning, and their dependence on incoming solar radiation (Q), soil temperature (T), water vapor pressure deficit (VPD) and ground water level (WL). Applied for this purpose the balanced identification method is based on the search for the optimal ratio between the model simplicity and the data fitting accuracy — the ratio providing the minimum of the modeling error estimated by the cross validation method. The obtained numerical solutions are characterized by minimum necessary nonlinearity (curvature) that provides sufficient interpolation and extrapolation characteristics of the developed models. It is particularly important to fill the missing values in NEE measurements. Reviewing the temporary variability of NEE and key environmental factors allowed to reveal a statistically significant dependence of GPP on Q, T, and VPD, and RE — on T and WL, respectively. At the same time, the inaccuracy of applied method for simulation of the mean daily NEE, was less than 10%, and the error in NEE estimates by the method was higher than by the REddyProc model considering the influence on NEE of fewer number of environmental parameters. Analyzing the gap-filled time series of NEE allowed to derive the diurnal and inter-daily variability of NEE and to obtain cumulative CO₂ fluxs in the peat bog for selected summer-autumn period. It was shown, that the rate of CO₂ fixation by peat bog vegetation in August was significantly higher than the rate of ecosystem respiration, while since September due to strong decrease of GPP the peat bog was turned into a consistent source of CO₂ for the atmosphere.

Atherosclerotic diseases such as carotid artery diseases (CAD) and chronic kidney diseases (CKD) are the major causes of death worldwide. The onset of these atherosclerotic diseases in the arteries are governed by complex blood flow dynamics and hemodynamic parameters. Atherosclerosis in renal arteries leads to reduction in arterial efficiency, which ultimately leads to Reno-vascular hypertension. This work attempts to identify the localization of atherosclerotic plaque in human abdominal aorta — renal artery junction using Computational fluid dynamics (CFD).

The atherosclerosis prone regions in an idealized human abdominal aorta-renal artery junction are identified by calculating relevant hemodynamic indicators from computational simulations using the rheologically accurate shear-thinning Yeleswarapu model for human blood. Blood flow is numerically simulated in a 3-D model of the artery junction using ANSYS FLUENT v18.2.

Hemodynamic indicators calculated are average wall shear stress (AWSS), oscillatory shear index (OSI), and relative residence time (RRT). Simulations of pulsatile flow (f=1.25 Hz, Re = 1000) show that low AWSS, and high OSI manifest in the regions of renal artery downstream of the junction and on the infrarenal section of the abdominal aorta lateral to the junction. High RRT, which is a relative index and dependent on AWSS and OSI, is found to overlap with the low AWSS and high OSI at the cranial surface of renal artery proximal to the junction and on the surface of the abdominal aorta lateral to the bifurcation: this indicates that these regions of the junction are prone to atherosclerosis. The results match qualitatively with the findings reported in literature and serve as initial step to illustrate utility of CFD for the location of atherosclerotic plaque.

The article reports the findings of an investigation into pollution migration processes at the municipal solid waste (MSW) landfill located in the water protection zone of Lake Seliger (Tver Region). The distribution of pollutants is investigated and migration parameters are determined in field and laboratory conditions at the landfill site. A mathematical model describing physical and chemical processes of substance migration in soil strata is constructed. Pollutant migration is found to be due to a variety of factors. The major ones, having a significant impact on the migration of MSW ingredients and taken into account mathematically, include convective transport, diffusion and sorption processes. A modified mathematical model differs from its conventional counterparts by considering a number of parameters reflecting the decrease in the concentration of ammonium and nitrate nitrogen ions in ground water (transpiration by plant roots, dilution with infiltration waters, etc.). An analytical solution to assess the pollutant spread from the landfill is presented. The mathematical model provides a set of simulation models helping to obtain a computational solution of specific problems, vertical and horizontal migration of substances in the underground flow. Numerical experiments, analytical solutions, as well as field and laboratory data was studied the dynamics of pollutant distribution in the object under study up to the lake. A long-term forecast for the spread of landfill pollution is made. Simulation experiments showed that some zones of clean groundwater interact with those of contaminated groundwater during the pollution migration from the landfill, each characterized by a different pollutant content. The data of a computational experiments and analytical calculations are consistent with the findings of field and laboratory investigations of the object and give grounds to recommend the proposed models for predicting pollution migration from a landfill. The analysis of the pollution migration simulation allows to substantiate the numerical estimates of the increase in $NH_4^+$ and $NO_3^-$ ion concentration with the landfill operation time. It is found that, after 100 years following the landfill opening, toxic filtrate components will fill the entire pore space from the landfill to the lake resulting in a significant deterioration of the ecosystem of Lake Seliger.

In this work, we consider a special approximation of the general perturbation formula for the electromagnetic field by a set of electrically small inhomogeneities located in the domain of interest. The problem considered in this paper arises in many applications of technical electrodynamics, radar technologies and subsurface remote sensing. In the general case, it is formulated as follows: at some point in the perturbed domain, it is necessary to determine the amplitude of the electromagnetic field. The perturbation of electromagnetic waves is caused by a set of electrically small scatterers distributed in space. The source of electromagnetic waves is also located in perturbed domain. The problem is solved by introducing the far field approximation and through the formulation for the scatterer radar cross section value. This, in turn, allows one to significantly speed up the calculation process of the perturbed electromagnetic field by a set of a spherical inhomogeneities identical to each other with arbitrary electrophysical parameters. In this paper, we consider only the direct scattering problem; therefore, all parameters of the scatterers are known. In this context, it may be argued that the formulation corresponds to the well-posed problem and does not imply the solution of the integral equation in the generalized formula. One of the features of the proposed algorithm is the allocation of a characteristic plane at the domain boundary. All points of observation of the state of the system belong to this plane. Set of the scatterers is located inside the observation region, which is formed by this surface. The approximation is tested by comparing the results obtained with the solution of the general formula method for the perturbation of the electromagnetic field. This approach, among other things, allows one to remove a number of restrictions on the general perturbation formula for E-filed analysis.

Numerical modeling of turbulent flows requires finding the balance between accuracy and computational efficiency. For example, DNS and LES models allow to obtain more accurate results, comparing to RANS models, but are more computationally expensive. Because of this, modern applied simulations are mostly performed with RANS models. But even RANS models can be computationally expensive for complex geometries or series simulations due to the necessity of resolving the boundary layer. Some methods, such as wall functions and near-wall domain decomposition, allow to significantly improve the speed of RANS simulations. However, they inevitably lose precision due to using a simplified model in the near-wall domain. To obtain a model that is both accurate and computationally efficient, it is possible to construct a surrogate model based on previously made simulations using the precise model.

In this paper, an operator is constructed that allows reconstruction of the flow field obtained by an accurate model based on the flow field obtained by the simplified model. Spalart–Allmaras model with approximate nearwall domain decomposition and Spalart–Allmaras model resolving the near-wall region are taken as the simplified and the base models respectively. The operator is constructed using a local approach, i. e. to reconstruct a point in the flow field, only features (flow variables and their derivatives) at this point in the field are used. The operator is constructed using the Random Forest algorithm. The efficiency and accuracy of the obtained surrogate model are demonstrated on the supersonic flow over a compression corner with different values for angle $\alpha$ and Reynolds number. The investigation has been conducted into interpolation and extrapolation both by $Re$ and $\alpha$.

There are conditions of uneven combustion for tubular powder elements of large elongation used in artillery propelling charges. Here it is necessary to consider in parallel the processes of combustion and movement of powder gases inside and outside the channels of the powder tubes. Without this, it is impossible to adequately formulate and solve the problems of ignition, erosive combustion and stress-strain state of tubular powder elements in the shot process. The paper presents a physical and mathematical formulation of the main problem of the internal ballistics of an artillery shot for a charge consisting of a set of powder tubes. Combustion and movement of a bundle of powder tubes along the barrel channel is modeled by an equivalent tubular charge of all-round combustion. The end and cross-sectional areas of the channel of such a charge (equivalent tube) are equal to the sum of the areas of the ends and cross-sections of the channels of the powder tubes, respectively. The combustion surface of the channel is equal to the sum of the inner surfaces of the tubes in the bundle. The outer combustion surface of the equivalent tube is equal to the sum of the outer surfaces of the tubes in the bundle. It is assumed that the equivalent tube moves along the axis of the bore. The speed of motion of an equivalent tubular charge and its current position are determined from Newton’s second law. To calculate the flow parameters, we used two-dimensional axisymmetric equations of gas dynamics, for the solution of which an axisymmetric orthogonalized difference mesh is constructed, which adapts to the flow conditions. When the tube moves and burns, the difference grid is rearranged taking into account the changing regions of integration. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the Godunov problem of decay for an arbitrary discontinuity. The developed technique was used to calculate the internal ballistics parameters of an artillery shot. This approach is considered for the first time and allows a new approach to the design of tubular artillery charges, since it allows obtaining the necessary information in the form of fields of velocity and pressure of powder gases for calculating the process of gradual ignition, unsteady erosive combustion, stress-strain state and strength of powder elements during the shot. The time dependences of the parameters of the internal ballistics process and the distribution of the main parameters of the flow of combustion products at different times are presented.

Migration has a significant impact on the shaping of the demographic structure of the territories population, the state of regional and local labour markets. As a rule, rapid change in the working-age population of any territory due to migration processes results in an imbalance in supply and demand on labour markets and a change in the demographic structure of the population. Migration is also to a large extent a reflection of socio-economic processes taking place in the society. Hence, the issues related to the study of migration factors, the direction, intensity and structure of migration flows, and the prediction of their magnitude are becoming topical issues these days.

Mathematical tools are often used to analyze, predict migration processes and assess their consequences, allowing for essentially accurate modelling of migration processes for different territories on the basis of the available statistical data. In recent years, quite a number of scientific papers on modelling internal and external migration flows using mathematical methods have appeared both in Russia and in foreign countries in recent years. Consequently, there has been a need to systematize the currently most commonly used methods and tools applied in migration modelling to form a coherent picture of the main trends and research directions in this field.

The presented review considers the main approaches to migration modelling and the main components of migration modelling methodology, i. e. stages, methods, models and model classification. Their comparative analysis was also conducted and general recommendations on the choice of mathematical tools for modelling were developed. The review contains two sections: migration modelling methods and migration models. The first section describes the main methods used in the model development process — econometric, cellular automata, system-dynamic, probabilistic, balance, optimization and cluster analysis. Based on the analysis of modern domestic and foreign publications on migration, the most common classes of models — regression, agent-based, simulation, optimization, probabilistic, balance, dynamic and combined — were identified and described. The features, advantages and disadvantages of different types of migration process models were considered.

In Russian medicine two radiopharmaceuticals are currently used for radionuclide therapy of bone metastases: ⁸⁹Sr-chloride and ¹⁵³Sm-oxabifor. The first one has many side effects, so its use is limited. The second one is available only in clinics, its transportation to which does not take much time. Currently, the third radiopharmaceutical ¹⁸⁸Re-solerene is undergoing clinical trials. Due to the generator method of obtaining ¹⁸⁸Re, this radiopharmaceutical should become available for use in many regions of our country. Therefore, there is a need for a comparative analysis of the characteristics of these radiopharmaceuticals, including on the basis of mathematical modeling.

The article discusses the features of mathematical modeling the kinetics of osteotropic radiopharmaceutical drugs in the human body with bone metastases. Based on the four-compartment model, a complex of modeling and calculation of pharmacokinetic and dosimetric characteristics of radiopharmaceuticals for radionuclide therapy of bone metastases was developed and tested. Using clinical data, the transport constants of the model were identified and the individual characteristics of Russian radiopharmaceuticals labeled ⁸⁹Sr, 153Sm and ¹⁸⁸Re were calculated (effective half-lives, maximum activity in the compartments and the times of their achievement, absorbed doses to bone tissue and metastases, endosteal bone layer, red bone marrow, blood, kidneys and bladder). The time activity dependencies for all compartments of the model are obtained and analyzed. A comparative analysis of the pharmacokinetics and dosimetry of three radiopharmaceuticals (⁸⁹Sr-chloride, ¹⁵³Sm-oxabiphore, ¹⁸⁸Re-solerene) was carried out.

From a comparative analysis of the pharmacokinetic and dosimetric characteristics of these radiopharmaceutical drugs, it follows that the best of them for widespread use in many regions of our country should be ¹⁸⁸Re-solerene, taking into account the generator method of obtaining ¹⁸⁸Re in a hospital.

Rugose spiraling whitefly (RSW) is one of the major pests which affects the coconut trees. It feeds on the tree by sucking up the water content as well as the essential nutrients from leaves. It also forms sooty mold in leaves due to which the process of photosynthesis is inhibited. Biocontrol of pest is harmless for trees and crops. The experimental results in literature reveal that Pseudomallada astur is a potential predator for this pest. We investigate the dynamics of predator, Pseudomallada astur’s interaction with rugose spiralling whitefly, Aleurodicus rugioperculatus in coconut trees using a mathematical model. In this system of ordinary differential equation, the pest-predator interaction is modeled using Holling type III functional response. The parametric values are calculated from the experimental results and are tabulated. An approximate analytical solution for the system has been derived. The homotopy analysis method proves to be a suitable method for creating solutions that are valid even for moderate to large parameter values, hence we employ the same to solve this nonlinear model. The $\hbar$-curves, which give the admissible region of $\hbar$, are provided to validate the region of convergence. We have derived the approximate solution at fifth order and stopped at this order since we obtain a more approximate solution in this iteration. Numerical simulation is obtained through MATLAB. The analytical results are compared with numerical simulation and are found to be in good agreement. The biological interpretation of figures implies that the use of a predator reduces the whitefly’s growth to a greater extent.

This work is devoted to the study of the problem of modeling and analyzing complex oscillatory modes, both regular and chaotic, in systems of interacting populations in the presence of random perturbations. As an initial conceptual deterministic model, a Volterra system of three differential equations is considered, which describes the dynamics of prey populations of two competing species and a predator. This model takes into account the following key biological factors: the natural increase in prey, their intraspecific and interspecific competition, the extinction of predators in the absence of prey, the rate of predation by predators, the growth of the predator population due to predation, and the intensity of intraspecific competition in the predator population. The growth rate of the second prey population is used as a bifurcation parameter. At a certain interval of variation of this parameter, the system demonstrates a wide variety of dynamic modes: equilibrium, oscillatory, and chaotic. An important feature of this model is multistability. In this paper, we focus on the study of the parametric zone of tristability, when a stable equilibrium and two limit cycles coexist in the system. Such birhythmicity in the presence of random perturbations generates new dynamic modes that have no analogues in the deterministic case. The aim of the paper is a detailed study of stochastic phenomena caused by random fluctuations in the growth rate of the second population of prey. As a mathematical model of such fluctuations, we consider white Gaussian noise. Using methods of direct numerical modeling of solutions of the corresponding system of stochastic differential equations, the following phenomena have been identified and described: unidirectional stochastic transitions from one cycle to another, trigger mode caused by transitions between cycles, noise-induced transitions from cycles to the equilibrium, corresponding to the extinction of the predator and the second prey population. The paper presents the results of the analysis of these phenomena using the Lyapunov exponents, and identifies the parametric conditions for transitions from order to chaos and from chaos to order. For the analytical study of such noise-induced multi-stage transitions, the technique of stochastic sensitivity functions and the method of confidence regions were applied. The paper shows how this mathematical apparatus allows predicting the intensity of noise, leading to qualitative transformations of the modes of stochastic population dynamics.