On the many-body problem with short-range interaction
The classical problem of the interaction of charged particles is considered in the framework of the concept of short-range interaction. Difficulties in the mathematical description of short-range interaction are discussed, for which it is necessary to combine two models, a nonlinear dynamic system d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Peoples’ Friendship University of Russia (RUDN University)
2022-02-01
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| Series: | Discrete and Continuous Models and Applied Computational Science |
| Subjects: | |
| Online Access: | http://journals.rudn.ru/miph/article/viewFile/30326/20363 |
| _version_ | 1818264856309006336 |
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| author | Mark M. Gambaryan Mikhail D. Malykh |
| author_facet | Mark M. Gambaryan Mikhail D. Malykh |
| author_sort | Mark M. Gambaryan |
| collection | DOAJ |
| description | The classical problem of the interaction of charged particles is considered in the framework of the concept of short-range interaction. Difficulties in the mathematical description of short-range interaction are discussed, for which it is necessary to combine two models, a nonlinear dynamic system describing the motion of particles in a field, and a boundary value problem for a hyperbolic equation or Maxwells equations describing the field. Attention is paid to the averaging procedure, that is, the transition from the positions of particles and their velocities to the charge and current densities. The problem is shown to contain several parameters; when they tend to zero in a strictly defined order, the model turns into the classical many-body problem. According to the Galerkin method, the problem is reduced to a dynamic system in which the equations describing the dynamics of particles, are added to the equations describing the oscillations of a field in a box. This problem is a simplification, different from that leading to classical mechanics. It is proposed to be considered as the simplest mathematical model describing the many-body problem with short-range interaction. This model consists of the equations of motion for particles, supplemented with equations that describe the natural oscillations of the field in the box. The results of the first computer experiments with this short-range interaction model are presented. It is shown that this model is rich in conservation laws. |
| first_indexed | 2024-12-12T19:41:33Z |
| format | Article |
| id | doaj.art-23ca2aceecf04f8e83749a69a2d81c5f |
| institution | Directory Open Access Journal |
| issn | 2658-4670 2658-7149 |
| language | English |
| last_indexed | 2024-12-12T19:41:33Z |
| publishDate | 2022-02-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Discrete and Continuous Models and Applied Computational Science |
| spelling | doaj.art-23ca2aceecf04f8e83749a69a2d81c5f2022-12-22T00:14:11ZengPeoples’ Friendship University of Russia (RUDN University)Discrete and Continuous Models and Applied Computational Science2658-46702658-71492022-02-01301526110.22363/2658-4670-2022-30-1-52-6120986On the many-body problem with short-range interactionMark M. Gambaryan0Mikhail D. Malykh1Peoples’ Friendship University of Russia (RUDN University)Peoples’ Friendship University of Russia (RUDN University); Meshcheryakov Laboratory of Information Technologies Joint Institute for Nuclear ResearchThe classical problem of the interaction of charged particles is considered in the framework of the concept of short-range interaction. Difficulties in the mathematical description of short-range interaction are discussed, for which it is necessary to combine two models, a nonlinear dynamic system describing the motion of particles in a field, and a boundary value problem for a hyperbolic equation or Maxwells equations describing the field. Attention is paid to the averaging procedure, that is, the transition from the positions of particles and their velocities to the charge and current densities. The problem is shown to contain several parameters; when they tend to zero in a strictly defined order, the model turns into the classical many-body problem. According to the Galerkin method, the problem is reduced to a dynamic system in which the equations describing the dynamics of particles, are added to the equations describing the oscillations of a field in a box. This problem is a simplification, different from that leading to classical mechanics. It is proposed to be considered as the simplest mathematical model describing the many-body problem with short-range interaction. This model consists of the equations of motion for particles, supplemented with equations that describe the natural oscillations of the field in the box. The results of the first computer experiments with this short-range interaction model are presented. It is shown that this model is rich in conservation laws.http://journals.rudn.ru/miph/article/viewFile/30326/20363many-body problemgalerkin methodshort-range interaction |
| spellingShingle | Mark M. Gambaryan Mikhail D. Malykh On the many-body problem with short-range interaction Discrete and Continuous Models and Applied Computational Science many-body problem galerkin method short-range interaction |
| title | On the many-body problem with short-range interaction |
| title_full | On the many-body problem with short-range interaction |
| title_fullStr | On the many-body problem with short-range interaction |
| title_full_unstemmed | On the many-body problem with short-range interaction |
| title_short | On the many-body problem with short-range interaction |
| title_sort | on the many body problem with short range interaction |
| topic | many-body problem galerkin method short-range interaction |
| url | http://journals.rudn.ru/miph/article/viewFile/30326/20363 |
| work_keys_str_mv | AT markmgambaryan onthemanybodyproblemwithshortrangeinteraction AT mikhaildmalykh onthemanybodyproblemwithshortrangeinteraction |