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PreprintarXiv licencearXiv

Weakly Nonlinear Analysis of Jammed Solids

  • Kota Noto
  • Harukuni Ikeda
  • Kuniyasu Saitoh
  • Hisao Hayakawa
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Abstract

We investigate the structural evolution in jammed solids by analyzing the eigenmodes of a generalized Hessian matrix that incorporates spatial modulation via wave numbers. Unlike the conventional Hessian, this generalized formulation captures linearly unstable modes through a Fourier-based extension of the Hessian matrix, enabling us to study responses beyond the mechanically stable regime. We demonstrate that the excitation of unstable eigenmodes leads to structural rearrangements independent of the initial perturbation by the simulation. Furthermore, we derive a weakly nonlinear amplitude equation to describe the growth and saturation of these unstable modes, analogous to the Landau equation. Our framework provides a pathway to understand instability-driven configuration changes in disordered solids.

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Cite

BibTeXRIS
BibTeX
@misc{noto2026weakly,
  title = {{Weakly Nonlinear Analysis of Jammed Solids}},
  author = {Kota Noto and Harukuni Ikeda and Kuniyasu Saitoh and Hisao Hayakawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.19818},
  eprint = {2607.19818},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.19818},
}
RIS
TY  - UNPB
TI  - Weakly Nonlinear Analysis of Jammed Solids
AU  - Kota Noto
AU  - Harukuni Ikeda
AU  - Kuniyasu Saitoh
AU  - Hisao Hayakawa
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2607.19818
UR  - https://arxiv.org/abs/2607.19818
AB  - We investigate the structural evolution in jammed solids by analyzing the eigenmodes of a generalized Hessian matrix that incorporates spatial modulation via wave numbers. Unlike the conventional Hessian, this generalized formulation captures linearly unstable modes through a Fourier-based extension of the Hessian matrix, enabling us to study responses beyond the mechanically stable regime. We demonstrate that the excitation of unstable eigenmodes leads to structural rearrangements independent of the initial perturbation by the simulation. Furthermore, we derive a weakly nonlinear amplitude equation to describe the growth and saturation of these unstable modes, analogous to the Landau equation. Our framework provides a pathway to understand instability-driven configuration changes in disordered solids.
ER  -