Numerical Modeling of Self-Consistent Dynamics of Shallow and Ground Waters

A mathematical and numerical model of the joint dynamics of shallow and ground waters has been built, which takes into account the nonlinear dynamics of a liquid, water absorption from the surface into the ground, filtration currents in the ground, and water seepage from the ground back to the surface. The dynamics of shallow waters is described by the Saint-Venant equations, taking into account the spatially inhomogeneous distributions of the terrain, the coefficients of bottom friction and infiltration, as well as non-stationary sources and flows of water. For the numerical integration of Saint-Venant’s equations, the well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented as a software package “EcoGIS-Simulation” for high-performance computing on supercomputers with graphic coprocessors (GPU). The dynamics of groundwater is described by the nonlinear Bussensk equation, generalized to the case of a spatially inhomogeneous distribution of the parameters of the porous medium and the surface of the aquiclude (the boundary between water-permeable and low-permeable soils). The numerical solution of this equation is built on the basis of a finite-difference scheme of the second order of accuracy, the CUDA algorithm of which is integrated into the calculation module of the “EcoGIS-Simulation” software package and is consistent with the main stages of the CSPH-TVD method. The relative deviation of the numerical solution from the exact solution of the nonlinear Boussinesq equation does not exceed 10−4–10−5. The paper compares the results of numerical modeling of the dynamics of groundwater with analytical solutions of the linearized Bussensk equation used as calculation formulas in the methods for predicting the level of groundwater in the vicinity of water bodies. It is shown that the error of these methods is several percent even for the simplest case of a plane-parallel flow of groundwater with a constant backwater. Based on the results obtained, it was concluded that the proposed method for numerical modeling of the joint dynamics of surface and ground waters can be more versatile and efficient (it has significantly better accuracy and productivity) in comparison with the existing methods for calculating flooding zones, especially for hydrodynamic flows with complex geometry and nonlinear interaction of counter fluid flows arising during seasonal floods during flooding of vast land areas.

Exact Solutions of the Generalized Nonlinear Schrodinger Equation

In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sinecosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.

On the Use of the Wilcoxon Criterion in the Practice of Pedagogical Research

The article discusses the use of nonparametric measures of influence in pedagogical research. The Wilcoxon criterion for comparing indicators obtained as a result of measurements in a connected sample is highlighted. The necessary conditions for the application of the criterion, as well as the advantages of its use are indicated. The possibility of using the Wilcoxon criterion is illustrated by the example of determining the effectiveness of the proposed teaching methodology using the Uchi.ru online platform in educational activities. Most modern studies in the field of pedagogy and psychology, along with qualitative descriptions of the results of the research, actively use quantitative analysis. Last analysis includes processing of the data using methods of mathematical statistics. In order to show the effectiveness of the developed methodology for the learning process, it should be considered as a factor influencing changes in the studied trait. Further study of these changes allows the researcher to determine the statistical reliability (significance) of the influence of the factor under consideration. The subsequent analysis of the reliability of the influence of a particular factor, the comparison of the measure of influence of various factors is carried out using parametric (variance analysis) and nonparametric measures of influence (the sign criterion, the Wilcoxon criterion). This article discusses the use of nonparametric measures of influence in pedagogical research. The Wilcoxon criterion is selected for comparing the indicators obtained as a result of measurement in a connected sample and allowing to diagnose not only the direction of changes, but also their severity. The necessary conditions for the application of the criterion, as well as the advantages of its use, are indicated. The possibility of using the Wilcoxon criterion is illustrated by the example of determining the effectiveness of the proposed teaching methodology using the Uchi.ru online platform in educational activities. Conclusions are made about its inefficiency for mastering the material in mathematics for younger schoolchildren.

Influence of the Nonaxisymmetric Dark Halo Shape on Galaxies Outer Spiral Pattern Morphology

The results of numerical simulations of a gaseous galactic disk rotating in an external nonaxisymmetric potential of a dark halo are presented in the article. Analysis of two models of a nonaxisymmetric dark halo, in which a gaseous galactic disk rotates, has been carried out. In the first case, the halo is nonaxisymmetric within the optical radius of the disk, where the bulk of the visible matter of the galaxy is located, including the stellar disk. The model is ineffective for the external long-lived spiral structure formation in the disk periphery due to the nonaxisymmetry of dark halo. In the second series of calculations, we have employed the model with a symmetric halo inside the optical radius and a non-axisymmetric one outside of it. The results of the simulations confirm that nonaxisymmetry in the halo matter distribution is effectively generating the global spiral pattern at the periphery of the galaxy. One may observe such spiral structures in some galaxies, mainly in the ultraviolet range. Analysis of various model parameters has showed that the value of parameter " is the primary characteristic affecting the morphology of the forming spiral pattern. This value determines the degree of nonaxisymmetry of the halo. The Le parameter introduced in this work and responsible for the formation of small-scale structures in the transition region does not significantly affect the disk periphery. Moreover, the larger the value of Le, the smoother spirals are formed. As it has shown in this work the size of the computational grid does not significantly influence on the simulation results, revealing only small-scale structures which are not the subject of current work.

Modeling of Flooding of Settlements During the Spring Flood

The problem of flooding of territories with flood waters for settlements of the Volgograd region is considered. A numerical model of flood water dynamics is constructed, taking into account the topography of the terrain. The simulation is based on two-dimensional shallow water equations. For computational experiments, a parallel implementation of the numerical scheme CSPH-TVD for NVIDIA graphics accelerators with CUDA technology is used. The digital model of the river-bed and floodplain relief is based on spatial data SRTM3 and SRTMGL, topographic maps of the area, longitudinal profiles of rivers. The water flow rates for the Buzuluk and Perevozinka rivers are determined and a hydrograph of the Volga hydroelectric power station is constructed for the given probabilities of exceeding the water level. Flood maps were obtained for the following localities: Novoannisky, Berezovka 1st, kh. Vyazovka. The maximum values of the depths for 1 %, 3 %, 5 %, 10 %, 25 % and 50 % of water security are presented. An analysis of the flood situation was carried out and appropriate engineering and protective measures for settlements were proposed. At maximum flood water levels, residential buildings of kh. Berezovka 1-I are not subject to flooding. In order to minimize the negative impact for the city of Novoanninsky, it is proposed to carry out timely clearing of the river-bed of the Perevozinka river from congestion. To protect from flooding ch. Vyazovka it is recommended to use diversion dyke.

Forecasting the Risks of an Organization Operating Natural Gas Vehicles Using a Scoring Model of Logistic Regression in the Presence of Expert Restrictions

The paper proposes a method and describes a mathematical model for express analysis of the attractiveness of the operation of vehicles running on natural gas for a motor transport company. The proposed solution is based on a logistic regression scoring model used by banks to assess the creditworthiness of a borrower. To improve the quality of the results, the model is extended with a set of expert restrictions formulated in the form of rules. During the analysis, signs were identified that require quantization, since individual intervals of values ??turned out to be associated with risk in different ways. The developed mathematical model is implemented in the form of software in a high-level programming language, the information of the model is stored in a database management system and is integrated with an information system for supporting management decisions when operating vehicles on natural gas. The developed athematical model was tested on a test training sample. The test results showed a satisfactory accuracy of the proposed model at the level of 77 % without the use of expert restrictions and 79 % with their use. At the same time, the share of Type II errors was 2.7 %, and Type I errors were 7.2 %, which indicates that the model is quite conservative, and a relatively high proportion of vehicles that meet the requirements were rejected.

Numeric Low-Altitude Altimeter Modeling with Computation of Additional Modulation Frequencies Using a Genetic Algorithm

This study is concerned with the problem of increasing the accuracy of a low-altitude altimeter employing the frequency modulation principle. A way to suppress the “discrete error” of the altimeter by employing additional frequency modulation of the carrier wave and averaging the resulting counts is considered. The benefit of such approach is simplicity of technical implementation manifesting in minimal changes in the microwave path and the recording device, which needsto run in averaging count mode. This work presents a genetic algorithm for computing the array of additional modulation frequencies which can be used to reduce the mean square of the discrete error given a limited frequency band. Results of error calculations presented are obtained via mathematical modeling of the altimeter’s operation. It is shown that using additional modulation frequencies obtained by the genetic algorithm allows to reduce the average measurement error two times relatively to the linear modulation form without expanding the occupied frequency band.

Application of Computer Simulation Results and Machine Learning in the Analysis of Microwave Radiothermometry Data

This work was done with the aim of developing the fundamental breast cancer early differential diagnosis foundations based on modeling the spacetime temperature distribution using the microwave radiothermometry method and obtained data intelligent analysis. The article deals with the machine learning application in the microwave radiothermometry data analysis. The problems associated with the construction mammary glands temperature fields computer models for patients with various diagnostics classes, are also discussed. With the help of a computer experiment, based on the machine learning algorithms set (logistic regression, naive Bayesian classifier, support vector machine, decision tree, gradient boosting, Knearest neighbors, etc.) usage, the mammary glands temperature fields computer models set adequacy.

Asymptotics of the Spectrum of a Periodic Boundary ValueProblem for an Odd-Order Differential Operator

The spectrum of a differential operator of high odd order with periodic boundary conditions is studied. The asymptotics of the fundamental system of solutions of the differential equation defining the operator are obtained by the method of successive Picard approximations. With the help of this fundamental system of solutions the periodic boundary conditions are studied. As a result, the equation for the eigenvalues of the differential operator under study is obtained, which is a quasi-polynomial. The indicator diagram of this equation, which is a regular polygon, is investigated. In each of the sectors of the complex plane, defined by the indicator diagram, the asymptotics of the eigenvalues of the operator under study is found. An equation for the eigenvalues of the differential operator under study is derived. The indicator diagram of this equation has been studied. The asymptotics of the eigenvalues of the studied operator in different sectors of the indicator diagram is found.