In this paper we outline a certain way of understanding of macroscopically uncontrollable emergence of the so called Mannesmann effect by means of its induced controllable quantum-mechanical background. In other words, we factually present a modus operandi of how to avoid macroscopic models of specific atomic-level cavity origin based consequently on a classical fracture mechanics theory. Under such circumstances, the target solution of the controllable microscopic model cannot be determined, since it can obviously arise only as a macroscopic state of the structurally disturbed rolled metal semi-product during the Mannesmann process. We obtain this irrelevance of the target solution, using a very special kind of control of the famous Schrodinger equation employed as a fundamental model equation here. We show contextually that such control follows from some very elementary aspects of the group theory conditioning a physical meaning of the Schrodinger equation written in a controllable form. We specially emerge primary cyclic groups of symmetry of special solutions to the Schrodinger equation. Their imaginary part is given by a control satisfying the Klein-Gordon equation which can be driven (through a specific avoidance of the cyclic group Z4) into a connection with the characteristic series of primary cyclic groups and/or torsion groups respectively. We obtain a physically controllable special results representing a strange correspondence between a certain LET (Linear Energy Transfer) and “quantum-like” tunnelling interpreted for some “everyday” objects, particularly for the considered Mannesmann piercing process with a torsion known from metallurgy. The process violations are shown and further reflected via a standard finite element method (FEM) simulation.

中文翻译：

---

与原子级曼内斯曼效应耦合的薛定谔方程的一种可控性

在本文中，我们概述了通过其诱导的可控量子力学背景来理解所谓的曼内斯曼效应的宏观不可控出现的某种方式。换句话说，我们实际上提出了一种基于经典断裂力学理论的如何避免特定原子级腔起源的宏观模型的操作方法。在这种情况下，可控微观模型的目标解无法确定，因为它显然只能作为曼内斯曼过程中结构扰动的轧制金属半成品的宏观状态出现。我们使用对著名的薛定谔方程的一种非常特殊的控制来获得目标解的这种无关性，这里用作基本模型方程。我们在上下文中表明，这种控制来自群论的一些非常基本的方面，以可控形式写出薛定谔方程的物理意义。我们特地出现了薛定谔方程的特解的主循环对称群。它们的虚部由满足 Klein-Gordon 方程的控制给出，该方程可以被驱动（通过循环群 Z4 的特定避免）分别与主循环群和/或扭转群的特征级数连接。我们获得了一个物理上可控的特殊结果，代表了某个 LET（线性能量转移）和为一些“日常”物体解释的“类量子”隧道之间的奇怪对应，特别是对于所考虑的曼内斯曼穿孔工艺，该工艺具有冶金学已知的扭转。通过标准有限元方法 (FEM) 模拟显示并进一步反映过程违规。