Singularity threshold of the nonlinear sigma model using 3D adaptive mesh refinement
Singularity threshold of the nonlinear sigma model using 3D adaptive mesh refinement
复制标题
使用 3D 自适应网格细化的非线性 sigma 模型的奇异阈值
DOI：
10.1103/physrevd.66.041703
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发表时间：
2002
影响因子：
5
通讯作者：
S. Liebling
中科院分区：
文献类型：
--
作者：
S. Liebling
采用自适应网格加密方法，计算了从$3+1$Minkowski空间到${S}^{3}，$的非线性Sigma模型的数值解。对于具有紧凑支持的初始数据，已知该模型有两个区域：一个是规则的初始数据形成奇点的区域，另一个是能量分散到无穷大的区域。这些区域之间的转变已经显示为球对称，以展示类似于引力理论中黑洞形成和扩散之间的阈值行为。在这里，我通过去掉球对称的假设来推广这一结果。演化表明，球对称临界解仍然是分离两个端态的中间吸引子。
Numerical solutions to the nonlinear sigma model, a wave map from $3+1$ Minkowski space to ${S}^{3},$ are computed in three spatial dimensions using adaptive mesh refinement. For initial data with compact support the model is known to have two regimes: one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.