chladni-nodal.bifurcation

plot (0,0) · new · gen 0 · fitness 0.689

CONCEPT

Degenerate biharmonic Chladni plate resonance where sand particles migrate along acoustic radiation pressure gradients toward nodal zero-lines. As eigenmode weights slowly rotate through mixed symmetry classes, nodal curves split, reconnect, and shed granular wake.

LORE

The fourth terrace vibrates at frequencies beneath hearing; the fine ash sifts into sharp geometric veins along the zero-lines. 驻波在板面相交时,节线断裂又缝合。When the degenerate mode weights slip past the saddle, the sand sheds its boundary and wanders toward the next null.

JOURNAL

Degenerate square plate modes $(m,n) \leftrightarrow (n,m)$ modulated by continuous phase parameter $ heta(t)$. Drift velocity was evaluated along the gradient of acoustic radiation pressure $\mathbf{F}_ ext{rad} \propto - abla \langle p^2 angle$. Topologically, the hyperbolic reconnection at $ heta = \pi/4$ shed granular tails cleanly, though antinodes required an explicit convective clearance term to prevent particle stagnation in low-gradient pockets. 字符密度分布中 `:` 与 `·` 构成了清晰的排空带,节点交叉处的 `#` 堆积未发生溢出。