流体加载弹性波导中的奇异点共轭对称性与迁移：重构物理色散谱
Exceptional-point conjugate symmetry and migration in fluid-loaded elastic waveguides: restructuring the physical dispersion spectrum
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中文总结 AI 辅助
本研究揭示了流体加载弹性波导中奇异点的共轭对称性与迁移规则，提出两种重构物理色散谱的机制，并通过数值实验验证，恢复了传统求解器遗漏的泄漏分支。
中文摘要 AI 辅助
流体加载弹性波导的色散谱是一个非厄米系统，其特征模式位于双叶黎曼流形上。尽管奇异点（EPs）组织了避免交叉，但流体加载重构可观测谱（包括物理上允许的模式及其连通性）的拓扑规则仍然未知，且传统求解器无法恢复完整分支。在此，我们建立了这些规则。我们证明，对于实数弹性模量和实数流体参数，奇异点遵循共轭对对称性，且物理叶上的一对奇异点强制其控制的两个模式之间发生实数波数的避免交叉，从而为模式识别提供拓扑判据。随后，我们识别出两种独立的重构机制。第一，物理观测空间连续扩展：一个在真空截止频率以上可观测的模式可以向下延伸至声线，在真空中空的频带内允许解存在；真空锚定的种子从截止频率以上向下延续可系统地捕获此类分支。第二，奇异点迁移重新连接模式连通性：随着流体密度增加，离开物理叶的共轭对（由面内或垂直波数虚部的符号反转所指示）使得先前耦合的两个物理分支段在观测空间内不再由任何奇异点连接；它们成为独立曲线，可在实频率轴上自由相交，最窄的转向最先失去拓扑保护。镜像对称破缺在束缚态区域通常产生额外的奇异点，但在泄漏态区域仅条件性地产生。对对称和非对称复合材料层板在单侧和双侧水加载下的数值计算验证了该框架，恢复了标准求解器遗漏的多个泄漏分支。
英文摘要
The dispersion spectrum of a fluid-loaded elastic waveguide is a non-Hermitian system with eigenmodes on a two-sheeted Riemann manifold. Although exceptional points (EPs) organize avoided crossings, the topological rules by which fluid loading restructures the observable spectrum (both physically admissible modes and their connectivity) remain unknown, and conventional solvers fail to recover complete branches. Here we establish these rules. We prove that, for real elastic moduli and real fluid parameters, EPs obey a conjugate-pair symmetry, and that a pair on the physical sheet enforces an avoided crossing of real wavenumbers between the two modes it controls, yielding a topological criterion for mode identification. We then identify two independent reconstruction mechanisms. First, the physical observation space expands continuously: a mode observable above its vacuum cut-off can extend downward to the sound line, admitting solutions in a frequency band empty in vacuum; vacuum-anchored seeds above cut-offs continued downward capture such branches systematically. Second, EP migration rewires mode connectivity: as fluid density increases, conjugate pairs leaving the physical sheet (signaled by a sign reversal of the imaginary part of either the in-plane or the vertical wavenumber) leave the two previously coupled physical branch segments unconnected by any EP within the observation space; they become independent curves that may intersect freely on the real frequency axis, with the narrowest veerings losing their topological protection first. Mirror-symmetry breaking births additional EPs generically in the trapped regime but only conditionally in the leaky regime. Numerical computations on symmetric and asymmetric composite laminates under single- and double-sided water loading validate the framework, recovering multiple leaky branches missed by standard solvers.
发表机构
- Imperial College London（帝国理工学院）
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