The paper is devoted to the study of a singular nonlinear second-order parabolic equation, which is called the porous medium equation or the nonlinear heat equation. One of the important classes of its solutions is he...
The paper is devoted to the study of a singular nonlinear second-order parabolic equation, which is called the porous medium equation or the nonlinear heat equation. One of the important classes of its solutions is heat waves propagating over a zero background with a finite velocity. This property is not typical for parabolic equations and is a consequence of singularity. The main object of study is exact solutions of mentioned type. A new way of separating variables is used to represent them. We obtain conditions when it is possible to make a reduction to the Cauchy problem for an ordinary second-order differential equation with a singularity. It is shown that the Cauchy problem describes a heat wave whose front moves exponentially. We construct a solution to the Cauchy problem as a power series and determine the cases when the series breaks off, i.e. the solution has the form of a polynomial, and the corresponding heat wave can be written explicitly. If the Cauchy problem cannot be explicitly integrated, the solution is constructed numerically. An algorithm based on the boundary element method is proposed. We perform a computational experiment and conclude the properties of the found solutions. Besides, the accuracy of the calculation results is analyzed.
The report addresses the application of ADSkit approach and related software tool for creating agent-based models describing the technical state dynamics of unique mechanical systems (UMS)s. UMSs are manufactured in v...
The report addresses the application of ADSkit approach and related software tool for creating agent-based models describing the technical state dynamics of unique mechanical systems (UMS)s. UMSs are manufactured in very few copies and furthermore the conditions of their exploitation can significantly diverse from each other. Also as a part of complex technical systems, UMS implements extreme technological operations. The step by step description of the ABSM development process for UMS is considered in the paper. In particular, the UMS ontology acts as a main source for model entities interpretation whereas their behavior mostly described in a rule-based or workflow manner. The testing simulations are carried out based on the ADSkit functionality related to the computational experiment management tool.
The data collected during various kinds of scientific research may be represented both by well known binary file formats and by custom formats specially developed for some unique device. While thorough understanding o...
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Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these nu...
This article discusses the implementation of the basic components of spatial data infrastructure for the implementation of interdisciplinary research. The main purpose of the components is to provide a common platform...
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Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a meth...
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The paper presents a problem formulation for the development of a theoretical and software framework for creating systems of data extraction from arbitrary spreadsheet tables. The problem covers the tasks of the autom...
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Charged wave packets with non-Gaussian spatial profiles are shown to possess intrinsic multipole moments. The magnetic dipole moment and the electric quadrupole moment are found for a wide class of packets, including ...
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Charged wave packets with non-Gaussian spatial profiles are shown to possess intrinsic multipole moments. The magnetic dipole moment and the electric quadrupole moment are found for a wide class of packets, including the vortex electrons with orbital angular momentum ℓ, the Airy beams, the so-called Schrödinger-cat states, and their generalizations. For the packets with no phase vortices, the electric quadrupole moment is shown to grow quadratically with the packet's width |Qαβ|∼eσ⊥2, while it is also |ℓ| times enhanced for the vortex beams. For available beams of electron microscopes, these multipole moments are relatively easily adjusted and can be quite large, which affects the packets' electromagnetic fields and also allows one to develop new diagnostic tools for materials science, atomic and molecular physics, nuclear physics, and so forth.
Nowadays geoportals provide some geospatial tools as services, usually implemented using the WPS standard. In this paper geoportal main principles are observed and existing methods and present technologies of classifi...
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