title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð²ÐµÑÑÐ¸Ð½Ðµ Ð´ÐµÑÐµÐºÑÐ° Ð½Ð° ÐºÑÐ°Ñ ÑÐ¾ÐºÐ¾Ð²ÐµÐ´ÑÑÐµÐ¹ ÑÐ¸Ð½Ñ Ð² 3D Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ Ð·Ð°Ð´Ð°ÑÐ¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Computational modeling of magnetic field diffusion at the peak of defect on the edge of current bus in a 3D statement of the problem
Creators: name: ÐÑÐµÐ²Ð½ÑÐºÐ¾Ð², ÐÐ¸ÐºÑÐ¾Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð¸Ð½ÑÐµÐ³ÑÐ°Ð» Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ
Ð´Ð²ÑÐ¼ÐµÑÐ½Ð°Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð´Ð¸ÑÑÑÐ·Ð¸Ñ
ÑÐºÐ¸Ð½-ÑÑÑÐµÐºÑ
ÑÐ¸Ð»ÑÐ½ÑÐµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÐµ Ð¿Ð¾Ð»Ñ
action integral
two-dimensional nonlinear diffusion
skin effect
strong magnetic fields

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: âÐ§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð²ÐµÑÑÐ¸Ð½Ðµ Ð´ÐµÑÐµÐºÑÐ° Ð½Ð° ÐºÑÐ°Ñ ÑÐ¾ÐºÐ¾Ð²ÐµÐ´ÑÑÐµÐ¹ ÑÐ¸Ð½Ñ Ð² 3D Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ Ð·Ð°Ð´Ð°ÑÐ¸â.
ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ ÑÐ¾ÐºÐ¾Ð²ÐµÐ´ÑÑÐµÐ¹ ÑÐ¸Ð½Ðµ Ñ Ð´ÐµÑÐµÐºÑÐ¾Ð¼ Ð² Ð²Ð¸Ð´Ðµ ÑÑÐµÑÐ¸Ð½Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°-Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ:
1. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ¾ÐºÐ° Ð² Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ ÑÐ¸Ð½Ðµ Ð±ÐµÐ· ÑÑÐµÑÐ° Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð¸ Ð½Ð°Ð³ÑÐµÐ²Ð°.
2. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ¾ÐºÐ° Ð² Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ ÑÐ¸Ð½Ðµ Ñ ÑÑÐµÑÐ¾Ð¼ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð¸ Ð½Ð°Ð³ÑÐµÐ²Ð°. 
3. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ¾ÐºÐ° Ð² Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ ÑÐ¸Ð½Ðµ Ñ ÑÑÐµÑÐ¾Ð¼ Ð¸ Ð±ÐµÐ· ÑÑÐµÑÐ° Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ Ð² Ð¿ÑÐ¾Ð²Ð¾Ð´Ð½Ð¸ÐºÐµ Ð¸ Ð½Ð°Ð³ÑÐµÐ²Ð°.
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description: The subject of the graduate qualification work is âNumerical modeling of mag-netic field diffusion at the apex of a defect on the edge of a busbar in a 3d statement of the problemâ.
The given work is devoted to the study of magnetic field diffusion in a flat current-carrying bus with a defect in the form of a crack. The tasks that were solved dur-ing the study:
1. The study of the distribution of current density in a flat bus without taking into account the magnetic field and heating.
2. The study of the distribution of current density in a flat bus taking into account the magnetic field and heating.
3. Comparison of the features of the distribution of current density in a flat bus with and without allowance for diffusion of the magnetic field in the conductor and heating.
The work was carried out on the territory of Peter the Great St. Petersburg Poly-technic University, where a significant part of the actual material was collected: test results of a current pulse of a flat bronze tire with a defect in the form of a crack. Cal-culations were made that clearly show how pressure is formed in a flat tire with a defect. The analysis was carried out by mathematical modeling using Comsol Multiphysics 5.4 software, using the resources of the Polytechnic supercomputer center: RSC Tornado (parameters of one node 2xCPU with 14 cores (2xXeone5-2697v3 2.6 GHz 64 GBRAM)).
As a result, the processes accompanying the flow of a current pulse were analyzed, thermodynamic calculations were carried out. Models have been constructed that show the formation and development of heating of a local site, with a temperature exceeding the melting temperature.