边界层理论、强耦合级数和高阶行为
Boundary-Layer Theory, Strong-Coupling Series, and Large-Order Behavior
摘要：
格点的引入将连续介质中的奇异边界层问题转化为正则摄动问题。然而，离散问题的连续极限是非常不平凡的，并没有完全理解。本文探讨了两个奇异的边界层问题，从数学物理，瞬子问题和Blasius方程，并在每种情况下，检查两种策略，帕德重定和变分摄动理论，恢复的解决方案，连续问题的解决方案，从相关的离散问题。这两种方法都能得到很好的结果，但结果仍然偏离精确解。为了理解这一差异，对这两个问题的强耦合晶格展开进行了全面的高阶行为分析。
英文摘要：
The introduction of a lattice converts a singular boundary-layer problem in the continuum into a regular perturbation problem. However, the continuum limit of the discrete problem is extremely nontrivial and is not completely understood. This paper examines two singular boundary-layer problems taken from mathematical physics, the instanton problem and the Blasius equation, and in each case examines two strategies, Pade resummation and variational perturbation theory, to recover the solution to the continuum problem from the solution to the associated discrete problem. Both resummation procedures produce good and interesting results for the two cases, but the results still deviate from the exact solutions. To understand the discrepancy a comprehensive large-order behavior analysis of the strong-coupling lattice expansions for each of the two problems is done.
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