| _version_ | 1866901783084793856 |
|---|---|
| author | Xu, Lingguang |
| author_facet | Xu, Lingguang |
| contents | <p>This paper extends the Missing-Tooth Law from optics and electronics to mechanics and thermodynamics.</p> <p>Classical mechanics defines work as W = F × s_net, which fails to account for continuous energy dissipation in static load-bearing (e.g., standing with a weight) or cyclic deformation (e.g., rolling tire) scenarios. This paper proposes a unified mechanism: under sustained loading or cyclic deformation, the energy stored during the loading phase cannot be fully recovered during unloading. The unrecovered fraction is dissipated as heat.</p> <p>The loss factor tanδ from materials science is introduced as the "Missing-Tooth Coefficient". A general formula for energy dissipation is established: E_diss = ∮ σ dε = (F × h) × tanδ. This formulation reduces to classical work when net displacement exists, and extends to internal work when there is no net displacement but continuous dissipation occurs.</p> <p>The Missing-Tooth Law reveals a cross‑domain universal principle: from engineering materials to biological systems, incomplete energy recovery during load‑unload or stress‑relaxation cycles is the common essence of energy dissipation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20163848 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Missing-Tooth Law: A Unified Mechanism of Energy Dissipation in Ordered Motion Xu, Lingguang <p>This paper extends the Missing-Tooth Law from optics and electronics to mechanics and thermodynamics.</p> <p>Classical mechanics defines work as W = F × s_net, which fails to account for continuous energy dissipation in static load-bearing (e.g., standing with a weight) or cyclic deformation (e.g., rolling tire) scenarios. This paper proposes a unified mechanism: under sustained loading or cyclic deformation, the energy stored during the loading phase cannot be fully recovered during unloading. The unrecovered fraction is dissipated as heat.</p> <p>The loss factor tanδ from materials science is introduced as the "Missing-Tooth Coefficient". A general formula for energy dissipation is established: E_diss = ∮ σ dε = (F × h) × tanδ. This formulation reduces to classical work when net displacement exists, and extends to internal work when there is no net displacement but continuous dissipation occurs.</p> <p>The Missing-Tooth Law reveals a cross‑domain universal principle: from engineering materials to biological systems, incomplete energy recovery during load‑unload or stress‑relaxation cycles is the common essence of energy dissipation.</p> |
| title | The Missing-Tooth Law: A Unified Mechanism of Energy Dissipation in Ordered Motion |
| url | https://doi.org/10.5281/zenodo.20163848 |