Stabilisation Dynamics VI: Domain Growth in Stabilisation Lattice Dynamics (Sub-Curvature Coarsening from Finite-Range Propagation)
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866901113206210560 |
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| author | Found, Luke |
| author_facet | Found, Luke |
| contents | <p>This paper investigates the dynamical formation and growth of domains in stabilisation lattice dynamics. Starting from disordered initial conditions, we measure the evolution of characteristic domain size using sign-field correlations.</p> <p>We find that domain growth follows an approximate power law L(t) ~ t^alpha with exponent alpha ≈ 0.39, which is smaller than the value expected for curvature-driven coarsening in standard ordering systems.</p> <p>This slower growth indicates that domain evolution is governed by finite-range stabilisation propagation rather than curvature-driven dynamics. Within the geometric stabilisation framework, ordering spreads through local basin interactions, leading to gradual, locally mediated coarsening consistent with a screened propagation mechanism.</p> <p>Together with previous results on probability, correlation, spatial propagation and the absence of criticality, these findings provide a unified geometric description of both static and dynamical structure formation in stabilisation systems.</p> <p>Subsequent work further extends this framework through operator-based resolution dynamics and phase structure.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19334759 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Stabilisation Dynamics VI: Domain Growth in Stabilisation Lattice Dynamics (Sub-Curvature Coarsening from Finite-Range Propagation) Found, Luke Stochastic Processes Statistical mechanics Dynamical systems Mathematical physics <p>This paper investigates the dynamical formation and growth of domains in stabilisation lattice dynamics. Starting from disordered initial conditions, we measure the evolution of characteristic domain size using sign-field correlations.</p> <p>We find that domain growth follows an approximate power law L(t) ~ t^alpha with exponent alpha ≈ 0.39, which is smaller than the value expected for curvature-driven coarsening in standard ordering systems.</p> <p>This slower growth indicates that domain evolution is governed by finite-range stabilisation propagation rather than curvature-driven dynamics. Within the geometric stabilisation framework, ordering spreads through local basin interactions, leading to gradual, locally mediated coarsening consistent with a screened propagation mechanism.</p> <p>Together with previous results on probability, correlation, spatial propagation and the absence of criticality, these findings provide a unified geometric description of both static and dynamical structure formation in stabilisation systems.</p> <p>Subsequent work further extends this framework through operator-based resolution dynamics and phase structure.</p> |
| title | Stabilisation Dynamics VI: Domain Growth in Stabilisation Lattice Dynamics (Sub-Curvature Coarsening from Finite-Range Propagation) |
| topic | Stochastic Processes Statistical mechanics Dynamical systems Mathematical physics |
| url | https://doi.org/10.5281/zenodo.19334759 |