论文标题
孤立磁域的渐近形状
Asymptotic shape of isolated magnetic domains
论文作者
论文摘要
我们研究了一个孤立的磁化域$ω\ subset \ mathbb {r}^n $的能量，$ n = 2,3 $。在非二敏变量中，由$ \ Mathcal {e}（ω）\ = \ \ int _ {\ Mathbb {r}^n} | \ nablaχ_Ω提供的能量\ dx + \ int _ {\ mathbb {r}^n} | \ nablah_Ω|^2 \ dx $$惩罚了域的界面区域以及相应的磁静力场的能量。在这里，磁电势$h_Ω$由$ΔH_Ω= \ partial_1χ_Ω$确定，对应于域内的均匀磁化。我们考虑宏观制度$ |ω| \ rightArrow \ infty $，我们得出紧凑性和$γ$ - 限制，该$限制是根据各向异性恢复配置的横截面面积制定的。然后，我们为极限问题提供解决方案。
We investigate the energy of an isolated magnetized domain $Ω\subset \mathbb{R}^n$ for $n=2,3$. In non-dimensionalized variables, the energy given by $$ \mathcal{E}(Ω) \ = \ \int_{\mathbb{R}^n} |\nabla χ_Ω| \ dx + \int_{\mathbb{R}^n} |\nabla h_Ω|^2 \ dx $$ penalizes the interfacial area of the domain as well as the energy of the corresponding magnetostatic field. Here, the magnetostatic potential $h_Ω$ is determined by $Δh_Ω= \partial_1 χ_Ω$, corresponding to uniform magnetization within the domain. We consider the macroscopic regime $|Ω| \rightarrow \infty$, in which we derive compactness and $Γ$-limit which is formulated in terms of the cross-sectional area of the anisotropically rescaled configuration. We then give the solutions for the limit problems.
