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• Содержание выпуска •
• Artificial Intelligence, Intelligence Systems, Neural Networks •
• Software and Hardware for Distributed Systems and Supercomputers •
• Mathematical Foundations of Programming •
• Information Systems in Culture and Education •
• Healthcare Information Systems •
• Methods for Optimal Control and Control Theory •
• Mathematical Modelling •
Mathematical Modelling
Responsible for the Section: doctor of technical Sciences
Vladimir Gurman, candidate of technical Sciences Sergei Amelkin
On the left: assigned number of the paper, submission date, the number
of A5 pages contained in the paper, and the reference to the full-text
PDF
/r1/pdf.jpg) .
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Article #
25_2018
14
p.
/r1/pdf.jpg)
PDF |
submitted on 24th Oct 2018 displayed on
website on 05th
Nov
2018 Ilya Starodumov, Peter Galenko,
Nikolai Kropotin, Dmitri Alexandrov
On approximation of a periodic solution of the phase field
crystal equation in simulations by the finite
elements method
The paper presents a mathematical model of the phase
field crystal (PFC), describing the evolution
of the microstructure of matter during the
crystallization process. Such a model is expressed by a nonlinear
particle differential equation of the sixth
order in space and the second in time, for
the solution of which in recent years finite element computational
algorithms have been developed and guarantee
unconditional stability and second order of
convergence. However, due to the periodic nature of the solution of
the PFC problem, the accuracy of the
approximation of a numerical solution can vary
significantly with a change in the discretization parameters
of the simulated system.
Taking into account the high computational complexity of the PFC
problem in the three-dimensional formulation,
the determination of the discretization
criteria becomes an urgent practical issue. In this article, we
study the influence of finite element sizes
on the approximation of the solution of the PFC problem
for cases of a flat and spherical crystallization front. It
is shown that the excess of certain
dimensions of the final element leads to significant qualitative
changes in the numerical solution and, as a
consequence, to a sharp decrease in the accuracy
of the approximation. (In Russian).
Key words: crystal phase field method, numerical
calculations, finite elements, approximation. |
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article citation |
http://psta.psiras.ru/read/psta2018_4_265-278.pdf |
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DOI |
https://doi.org/10.25209/2079-3316-2018-9-4-265-278 |
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Article #
27_2018
11
p.
PDF |
submitted on 09th Nov 2018 displayed on
website on 17th Dec
2018 Artur Ovanesyan
About relationship between the need for medical care and the
distribution of life expectancy
The article considers the possibility of forecasting
the need for medical care of the population
using the density distribution of life expectancy
and the probabilistic dependence of the need for medical care
by age. The relationship between the
distribution of life expectancy and age distribution of
patients is established. It is expressed by the average life
expectancy.
An example of the distribution of life expectancy is given. It is
presented in graphical form, showing the form
of the found approximation together with the
actual data. By approximation, the distribution of life expectancy
is calculated.
The probability of dependence of the need for medical care by age is
given in the article on the basis of
statistical data, presented in graphical form. Since there
is a relationship between this dependence and the
distribution of patients by age, the
forecasting of the need for medical care is realized. Examples of
calculation for specific ages are given, the
possibility of calculation for all ages is indicated.
As a result, the study identified the possibility of predicting the
need for medical care on the basis of data on
life expectancy. (In Russian).
Key words: relationship of distributions, life expectancy, age
distribution, need for medical services. |
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article citation |
http://psta.psiras.ru/read/psta2018_4_307-317.pdf |
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DOI |
https://doi.org/10.25209/2079-3316-2018-9-4-307-317 |
• Artificial Intelligence, Intelligence Systems, Neural Networks •
• Software and Hardware for Distributed Systems and Supercomputers •
• Mathematical Foundations of Programming •
• Information Systems in Culture and Education •
• Healthcare Information Systems •
• Methods for Optimal Control and Control Theory •
• Mathematical Modelling •
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