Deduplicate mode machinery

[sergioald]

Summary

Deduplicates the shared modal root/coefficient machinery used by the free and periodic flow-field solvers.

Changed

• ldsfl/modes.py

  • adds a shared home for MATLAB-compatible quartic-root ordering;
  • adds shared modal coefficient precomputation;
  • adds the shared resonance flag helper.

• ldsfl/flowfield.py

  • imports the shared mode machinery instead of carrying a local copy;
  • preserves existing private helper names for compatibility with diagnostics/tests.

• ldsfl/flowfield_periodic.py

  • imports the same shared mode machinery instead of carrying a duplicate local copy.

• tests/test_mode_machinery_deduplication.py

  • verifies that the free and periodic flow paths use the same shared helpers;
  • checks that the shared precomputation returns finite modal arrays for the case-one parameters;
  • checks the MATLAB-style root-ordering sign convention.

Why

The free and periodic flow solvers duplicated the same mode machinery: quartic root solving, MATLAB-compatible root ordering, modal coefficient precomputation, and resonance flagging.

That duplication is risky after the recent resonance work because a future fix to one flow path could silently leave the other path inconsistent. A single shared implementation makes the numerical convention easier to audit and keeps the free and periodic paths aligned.

Validation

python -m py_compile ldsfl/modes.py ldsfl/flowfield.py ldsfl/flowfield_periodic.py tests/test_mode_machinery_deduplication.py
python -m pytest tests/test_mode_machinery_deduplication.py tests/test_resonance_diagnostics.py
python -m pytest
python -m run_ldsfl --base-dir . --cases 1 --max-steps 100 --no-plots

Notes

This is a refactor-only PR.

It does not change the morphodynamic update algorithm, curvature calculation, flow-field convolution implementation, resonance mathematics, stability diagnostics, CLI interface, GUI interface, output naming, fixture structure, or generated output format.