论文标题
反向时间中拓扑局部结构相互作用的动力学
Dynamics of interaction of topological localized structures in reversed time
论文作者
论文摘要
介绍了反向时间中拓扑孤子（2+1）的相互作用的数值模拟（2+1） - 二维O（3）非线性Sigma模型的结果。在第一阶段，开发了拓扑涡流的相互作用模型，其中，根据动态参数，其衰减过程中的过程中局部扰动和分阶段的歼灭。同样，考虑到拓扑涡流在与180度域壁相互作用过程中逐步消灭的模型。根据获得的模型，开发了反向时间中交互过程数值模拟的初始条件。得出了在局部扰动和辐射波的组合中完全恢复相互作用孤子的初始拓扑场的模型。此外，还获得了描述域壁平面及其随后发射的拓扑涡流的形成的模型。因此，确认了正在研究的现场理论模型的T传输特性。使用立体图投影的特性，根据有限差异方案理论的方法在分层空间中进行了数值计算。对拓扑涡流的Kronecker-HOPF指数的不同值进行了实验。提出了一个复杂的程序模块，该模块实现了一种特殊的算法，以计算在反向时间中时空拓扑结构相互作用的演变。
The results of numerical simulation of the interaction of topological solitons (2+1)-dimensional O(3) non-linear sigma model in reversed time are presented. At the first stage, models of interactions of topological vortices are developed, where, depending on the dynamic parameters, processes of their decay into localized perturbations and phased annihilation are observed. Also, models for the phased annihilation of topological vortices during their interaction with 180-degree domain walls are considered. On the basis of the models obtained, initial conditions for numerical simulation of interaction processes in reversed time are developed. The models describing the complete restoration of the initial topological field of interacting solitons at the combination of localized perturbations and radiation waves are obtained. Also, models are obtained that describe the formation of topological vortices in the plane of the domain wall and their subsequent emission. Thus, the T-invariance property of the field-theoretic model under study is confirmed. Numerical calculations were carried out in a stratified space on the basis of methods of the theory of finite difference schemes, using the properties of a stereo-graphic projection. The experiments were carried out for different values of the Kronecker-Hopf index of topological vortices. A complex program module is proposed that implements a special algorithm for the numerical calculation of the evolution of the interaction of space-time topological structures in reversed time.
