论文标题
较高空间尺寸的局部径向滚动图案
Localized radial roll patterns in higher space dimensions
论文作者
论文摘要
局部滚动模式是在其中心表现出空间周期性轮廓的结构。当在一个空间维度的系统参数中遵循此类模式时，这些模式类似于周期性轮廓的空间间隔的长度保持界限，在这种情况下，分支形成封闭的有界曲线（“ Iselas”），或者长度增加到Infinity，以使分支在功能空间中没有结合的分支（“ Snaking”）。在两个空间维度中，数值计算表明，局部卷的分支表现出更为复杂的结构，在这种结构中均出现隔离和蛇的发生。在本文中，我们通过扰动分析分析了尺寸1+$ \ varepsilon $中局部径向滚动解决方案的分支结构，其中$ 0 <\ varepsilon \ ll1 $。我们的分析阐明了平面案例中可见的一些功能。
Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which these patterns resemble a periodic profile stays either bounded, in which case branches form closed bounded curves ("isolas"), or the length increases to infinity so that branches are unbounded in function space ("snaking"). In two space dimensions, numerical computations show that branches of localized rolls exhibit a more complicated structure in which both isolas and snaking occur. In this paper, we analyse the structure of branches of localized radial roll solutions in dimension 1+$\varepsilon$, with $0<\varepsilon\ll1$, through a perturbation analysis. Our analysis sheds light on some of the features visible in the planar case.
