The article is devoted to the numerical simulation of a nonlinear wave in a dissipative nondispersive medium described by the Burgers equation. Numerical solution of the Burgers equation at large values of viscosity r...
The article is devoted to the numerical simulation of a nonlinear wave in a dissipative nondispersive medium described by the Burgers equation. Numerical solution of the Burgers equation at large values of viscosity runs into serious difficulties. They are mainly associated with the presence of a small parameter at the highest derivative and, as a consequence, the appearance of regions of strong spatial inhomogeneity in the solution. Then the requirements imposed on the approximation properties of numerical methods sharply increase. In this work, the indicated difficulties are overcome and it is proposed to apply the spectral-grid method. For this, in the considered interval of integration, a grid is introduced, the requirements of the continuity of the solution itself and its first derivative are imposed at the inner nodes of the grid, and the corresponding boundary conditions are satisfied at the boundary nodes of the grid. The transition from one time layer to another is carried out according to the Adams-Beshfort scheme. A computational experiment was carried out in large-scale changes in characteristic parameters such as: viscosity, the number of Chebyshev polynomials and mesh elements, for different values of time and mesh steps in time. The calculation results show the high accuracy and efficiency of the spectral-grid method in solving the initial-boundary value problem for the Burgers equation.
This article proposes quantitative evaluation of quality pertaining to complex engineering systems at iron and steel works. It continues the cycle of research conducted by the authors on applying structural risk analy...
This article proposes quantitative evaluation of quality pertaining to complex engineering systems at iron and steel works. It continues the cycle of research conducted by the authors on applying structural risk analysis to various application tasks in the industry. An existing iron and steel works comprising 40 different workshops, which includes multiple various structures and elements, is taken as a complex engineering system. This approach is described for such a complex engineering system for the first time ever. Quality is suggested to be evaluated based on predominant aspects of quality whose indicators determine the risk of incidents, reliable operation of structures and elements as well as their economic efficiency. Calculation algorithm for evaluating quality at iron and steel works is presented. Real quantitative ratings of quality are obtained for the structure and the entire engineering system, in general. The obtained findings adequately match with the practical situation and known data. Such algorithm can also be applied to other complex engineering systems. Information provided in this article suggests the formation of scientific foundations of structural risk analysis as applicable to the problems of quantitative evaluation of quality pertaining to such systems.
Computer modeling is one of the approaches for investigation of structures and processes. The main component in the model study is the generation of the input flow, which forms the workload of the system. A random num...
Computer modeling is one of the approaches for investigation of structures and processes. The main component in the model study is the generation of the input flow, which forms the workload of the system. A random number generator is usually used to model the incoming program units. In this regards, the purpose of the article is to present developed software tools that form a model environment for generating stochastic flow when presenting workload of computer system. The software realization is made by using the tools of the program environment TryAPL2 which has a programming language APL2 for parallel processing. Initial analytical description is made based on preliminary discussion and formulation of the problem. The organization of the analytical modelling is based on presentation of program modules for generating random numerical sequences with the probability distributions most commonly used in computer systems. The experimental part is connected to determine program model of workload based on an analytical approximation and its implementation in two cases is presented.
The number of confirmed, deaths and recovered cases of Covid-19 *** period 08.03.2020 - 29.04.2021 *** are considered. Various smoothing techniques have been used to highlight the trend in data change. Confidence inte...
The number of confirmed, deaths and recovered cases of Covid-19 *** period 08.03.2020 - 29.04.2021 *** are considered. Various smoothing techniques have been used to highlight the trend in data change. Confidence intervals are obtained for daily and weekly deaths after 14 days based on confirmed cases to date. The Box-Cox transformed confirmed cases were modeled by regression with respect to three dummy variables related to working days and holidays, with errors following ARIMA(1,1,2)(2,0,0)7 model. For Box-Cox transformed deaths, three other dummy variables and lag 16 of transformed and smoothed confirmed cases were used. The regression errors follow ARIMA(1,1,2) model in which the MA(1) coefficient is set to 0. Fourteen daily forecasts are obtained which agree well with the respective test data sets.
In this paper we introduce the notion of derivation in product (direct product) of additively idempotent semirings. These semirings are useful and important tools in diverse areas such as design of switching circuits,...
In this paper we introduce the notion of derivation in product (direct product) of additively idempotent semirings. These semirings are useful and important tools in diverse areas such as design of switching circuits, automata theory, information systems, dynamic programming and decision theory. We study hereditary derivations, inner derivations and obtain a representation of an arbitrary derivations which are zero on the multipliers.
The announcement of the pandemic due to covid 19 requires a rapid transition to distance and e-learning, as well as blended learning. The contributions and differences of the different ways of learning are considered.
The announcement of the pandemic due to covid 19 requires a rapid transition to distance and e-learning, as well as blended learning. The contributions and differences of the different ways of learning are considered.
We consider two simple graphs G and H, the notation F → (G, H) means that for any red- blue coloring of all the edges of graph F contains either a red copy isomorphic to G or a blue copy isomorphic to H. A graph F is...
We consider two simple graphs G and H, the notation F → (G, H) means that for any red- blue coloring of all the edges of graph F contains either a red copy isomorphic to G or a blue copy isomorphic to H. A graph F is Ramsey (G, H)-minimal graph if F → (G, H) and for any edge e in F then F - e → (G, H). The set of all Ramsey minimal graphs for pair (G, H) is denoted by R(G, H). The Ramsey set for pair (G, H) is said to be Ramsey-finite or Ramsey-infinite if R(G, H) is finite or infinite, respectively. Several articles have discussed the problem of determining whether R(G, H) is finite (infinite). It is known that the set R(Pm, Pn), for 3 ≤ m ≤ n is Ramsey-infinite. Some partial results in R(P4, Pn), for n = 4 and n = 5 , have been obtained. Motivated by this, we are interested in determining graphs in R(P4, P6). In this paper, we determine some graphs of certain order in R(P4, P6).
In this work, the coefficient inverse problem of fluid filtration in fractured-porous media is numerically solved. The problem consists in identification cross-flow coefficient based on additional information about th...
In this work, the coefficient inverse problem of fluid filtration in fractured-porous media is numerically solved. The problem consists in identification cross-flow coefficient based on additional information about the solution of the direct problem. To solve the problem, two computational algorithms are proposed.
By numerically solving the Dirac equation, the energy levels of an electron in the 1S state of the hydrogen atom were determined for the actual for comparison possible values of the proton radius 0.8751, 0.8414, and 0...
By numerically solving the Dirac equation, the energy levels of an electron in the 1S state of the hydrogen atom were determined for the actual for comparison possible values of the proton radius 0.8751, 0.8414, and 0.8335 Fm under the assumption of an exponential distribution of its charge using the CODATA constants 2014 and 2019. The obtained values of the energy levels turn out to affect the correctness of extracting the proton radius from the experimental data at least to the same degree as other factors, for example, the corrections of quantum electrodynamics, which indicates possible ways to solve the riddle of the proton radius.
The article discusses the numerical modeling of the inverse problem of determining the kinematic viscosity for the vortex-current equation. To solve this differential problem, the least squares method is used, and the...
The article discusses the numerical modeling of the inverse problem of determining the kinematic viscosity for the vortex-current equation. To solve this differential problem, the least squares method is used, and the problem under study is reduced to finding the minimum of the functional. The formulation of the direct and inverse problems is presented. The inverse problem is approximated by finite differences and is solved by the sweep method. A computational experiment has been carried out illustrating the reconstruction of the value of the kinematic viscosity for the inverse problem at different values of the error level.
暂无评论