Volume 10, no. 4Pages 132 - 144
Dynamics of Interaction of Bloch Type Domain Walls in a Two-Dimensional Nonlinear Sigma ModelF.Sh. Shokirov
Numerical simulation of the interaction of 180-degree Bloch-type domain walls in the phase space of the (2+1)-dimensional supersymmetric O(3) nonlinear sigma model is carried out. The method of numerical calculations is based on the special application of the properties of stereographic projection, where the projection of the isosphere onto the complex plane eliminates the problem of infinitely large quantities arising in the ordinary projection. Thus, the parametrization of the model under study in a complex form, necessary for the numerical approach, is realized, in which the singularity arising at the poles of the isosphere is overcome. A three-layer explicit difference scheme of the second order of accuracy with respect to time and coordinate on a five-point template is used. A complex programme module is proposed that implements the algorithm for the numerical calculation of space-time topological structures in three-dimensional lattices. The models of frontal collisions are obtained, where, depending on the dynamic parameters, processes of formation of bound (bion) states of domain walls, long-range models, passage of domain walls of magnetic domains through each other, as well as the formations of radially symmetric breathers are observed. Full text
- numerical simulation; interaction of domain walls; nonlinear sigma model; isotopic space.
- 1. Bar'yakhtar V.G., Ivanov B.A., Chetkin M.V. Dynamics of Domain Walls in Weak Ferromagnets. Physics-Uspekhi, 1985, vol. 28, no. 7, pp. 563-588. DOI: 10.1070/PU1985v028n07ABEH003871.
2. Volkov V.V., Bokov V.A. Domain Wall Dynamics in Ferromagnets. Physics of the Solid State, 2008, vol. 50, no. 2, pp. 199-228. DOI: 10.1134/S1063783408020017.
3. Filippov B.N. Static Properties and Nonlinear Dynamics of Domain Walls with a Vortexlike Internal Structure in Magnetic Films (Review). Low Temperature Physics, 2002, vol. 28, no. 10, pp. 707-738. DOI: 10.1063/1.1521291.
4. Muminov Kh.Kh., Shokirov F.Sh. [Dynamics of Interaction of Domain Walls in (2+1)-Dimensional Non-Linear Sigma Model]. Izvestiya AN RT [News of the Academy of Sciences of the Republic of Tajikistan], 2015, vol. 161, no. 4, pp. 57-64. (in Russian)
5. Muminov Kh.Kh., Shokirov F.Sh. Matematicheskoye modelirovaniye nelineynykh dinamicheskikh sistem kvantovoy teorii polya [Mathematical Modeling of Nonlinear Dynamical Systems of Quantum Field Theory]. Novosibirsk: Publishing House SB RAS, 2017. (in Russian)
6. Muminov Kh.Kh. [Multidimensional Dynamic Topological Solitons in a Nonlinear Anisotropic Sigma Model]. Doklady Akademii nauk Respubliki Tadzhikistan [Reports of the Academy of Sciences of the Republic of Tajikistan], 2002, vol. 45, no. 10, pp. 28-36. (in Russian)
7. Samarskiy A.A. The Theory of Difference Schemes. N.Y., Marcel Dekker, 2001.
8. Tikhonov A.N., Samarskiy A.A. Equations of Mathematical Physics. N.Y., Dover Publications, 2011.
9. Muminov Kh.Kh., Shokirov F.Sh. [Interactions of Dynamical and Topological Solitons in 1D Nonlinear Sigma Model]. Doklady Akademii nauk Respubliki Tadzhikistan [Reports of the Academy of Sciences of the Republic of Tajikistan], 2016, vol. 59, no. 3-4, pp. 120-126. (in Russian)
10. Shokirov F.Sh. [Mathematical Modeling of Breathers of Two-Dimensional O(3) Nonlinear Sigma Model]. Mathematical Modeling and Computational Methods, 2016, vol. 12, no. 4. pp. 3-16. (in Russian)
11. Belova T.I., Kudryavtsev A.E. Solitons and Their Interactions in Classical Field Theory. Physics-Uspekhi, 1997, vol. 40, no. 4, pp. 359-386. DOI: 10.1070/PU1997v040n04ABEH000227.
12. Gervais J.L, Jevicki A., Sakita B. Perturbation Expansion Around Extended-Particle States in Quantum Field Theory. Physical Review D, 1975, vol. 12, no 4, pp. 1038-1051.
13. Makhankov V.G. [Solitons and Numerical Experiments]. Fizika elementarnykh chastits i atomnogo yadra [Physics of Elementary Particles and Atomic Nuclei], 1983, vol. 14, no. 1, pp. 123-180. (in Russian)