AI 中文总结
本文提出一种基于动力系统思想的气体驱动数值算法，将移动沙发问题的几何优化转化为动力系统，实验可逼近Gerver沙发结果，还能估计不同角度走廊的最大沙发面积，发现43.327…°处的临界角及两侧主导模式切换的现象。
AI 中文摘要
本文提出一种基于动力系统思想的数值算法，用于求解移动沙发问题。通过引入由气体压力驱动的物理模型，我们将几何优化问题转化为动力系统。数值实验表明，该方法能有效逼近已知的Gerver沙发结果，并为不同角度走廊提供可能最大面积的数值估计。特别地，我们在43.327…°处观察到两种运动模式的交点，此处局部最大沙发面积为1.8674…，且在该临界角两侧主导模式发生切换。
英文摘要
This paper presents a numerical algorithm based on the idea of dynamical systems for solving the moving sofa problem. By introducing a physical model driven by gas pressure, we transform the geometric optimization problem into a dynamical system. Numerical experiments show that the method effectively approximates the known Gerver's sofa result, and provides numerical estimates of the possible maximum area for corridors with different angles. In particular, we observe an intersection of the two motion patterns at $43.327\ldots^\circ$, where the locally maximal sofa area is $1.8674\ldots$, and the dominant pattern switches on either side of this critical angle.
Comments19 pages, 14 figures
