সংরক্ষণ করুন:
| প্রধান লেখক: | |
|---|---|
| বিন্যাস: | Recurso digital |
| ভাষা: | ইংরেজি |
| প্রকাশিত: |
Zenodo
2025
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://doi.org/10.5281/zenodo.17808122 |
| ট্যাগগুলো: |
ট্যাগ যুক্ত করুন
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সূচিপত্রের সারণি:
- <p>This paper extends the Chronos time-field framework by incorporating spatial dependence and Fourier-mode analysis into the coupled time field Θ(t, x) and density field ρ(t, x). Starting from a reaction–diffusion-type equation for ρ and a diffusion–relaxation equation for Θ, the system is linearized around a homogeneous equilibrium, yielding a 2×2 mode matrix M(k) for each wavenumber k.</p> <p>The dispersion relation λ±(k) derived from M(k) determines whether spatial perturbations grow or decay. In the symmetric parameter regime (Dρ = DΘ, κ = σ), the determinant simplifies to (κ + Dk²)² − CG, which is minimized at k = 0. This implies that global stability across all spatial modes is governed by the same Chronos threshold χ < 1 obtained in the homogeneous model. The Chronos constant χ thus controls stability universally, independent of wavelength.</p> <p>A verification protocol is provided to ensure that any researcher or automated reasoning system can independently confirm the linearization, mode matrix, dispersion relation, and Chronos threshold.</p>