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PreprintCC BY 4.0arXiv

Deformation-induced spectral softening drives phase separation on non-spherical membranes

  • Avraham Moriel
  • Howard A. Stone
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Abstract

Models of curvature-driven membrane sorting couple composition directly to membrane bending elasticity. Here we show that shape deformations can destabilize a homogeneous state without this composition-dependent mechanical coupling. We analyze the eigenspectrum of the Laplace-Beltrami operator on deformed spheres analytically, and verify it numerically. As the deformation amplitude increases, the spectral degeneracy breaks, and the lowest nonzero eigenvalue decreases substantially. Using Cahn-Hilliard dynamics, we show that this eigenvalue softening provides a purely geometric route to phase separation.

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Cite

BibTeXRIS
BibTeX
@misc{moriel2026deformationinduced,
  title = {{Deformation-induced spectral softening drives phase separation on non-spherical membranes}},
  author = {Avraham Moriel and Howard A. Stone},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16037},
  eprint = {2610.16037},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16037},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformation-induced spectral softening drives phase separation on non-spherical membranes
AU  - Avraham Moriel
AU  - Howard A. Stone
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16037
UR  - https://arxiv.org/abs/2610.16037
AB  - Models of curvature-driven membrane sorting couple composition directly to membrane bending elasticity. Here we show that shape deformations can destabilize a homogeneous state without this composition-dependent mechanical coupling. We analyze the eigenspectrum of the Laplace-Beltrami operator on deformed spheres analytically, and verify it numerically. As the deformation amplitude increases, the spectral degeneracy breaks, and the lowest nonzero eigenvalue decreases substantially. Using Cahn-Hilliard dynamics, we show that this eigenvalue softening provides a purely geometric route to phase separation.
ER  -