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2026
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| Accés en línia: | https://doi.org/10.5281/zenodo.20175099 |
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| _version_ | 1866901757732323328 |
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| author | Aberg, Jesper |
| author_facet | Aberg, Jesper |
| contents | <p>This appendix extends the Dual-Field Interface Model (DFIM v4.0) into the domain of macroscopic fluid dynamics, proposing a geometric regularization of the incompressible Navier–Stokes equations. By projecting the 3-brane membrane dynamics onto a tangential fluid flow, the model demonstrates that the unchecked convective cascade—which threatens finite-time singularities in classical hydrodynamics—is naturally mitigated by the interface's native mechanics. The framework introduces a kinematically closed momentum sink driven by a strain-rate-dependent Landau–Zener leakage probability. When the Frobenius norm of the strain-rate tensor (<span class="math-inline">$|\mathbf{D}|$</span>) becomes critical, kinetic energy non-adiabatically leaks from the 3-brane into the bulk fields. This mechanism establishes strict Leray–Hopf energy bounds and satisfies the Beale–Kato–Majda (BKM) criterion by ensuring that nonlinear exponential dissipation strictly outpaces algebraic vortex stretching. The result guarantees the global existence of smooth solutions while perfectly recovering exact classical Navier–Stokes behavior in laminar regimes. The appendix provides the formal derivation, a proposed pseudo-spectral numerical protocol (Taylor–Green vortex), and falsifiable predictions for extreme laboratory turbulence.</p> <p> </p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20175099 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Appendix J: Effective 3-Brane Hydrodynamics and the Regularization of the Navier–Stokes Equations via DFIM Aberg, Jesper <p>This appendix extends the Dual-Field Interface Model (DFIM v4.0) into the domain of macroscopic fluid dynamics, proposing a geometric regularization of the incompressible Navier–Stokes equations. By projecting the 3-brane membrane dynamics onto a tangential fluid flow, the model demonstrates that the unchecked convective cascade—which threatens finite-time singularities in classical hydrodynamics—is naturally mitigated by the interface's native mechanics. The framework introduces a kinematically closed momentum sink driven by a strain-rate-dependent Landau–Zener leakage probability. When the Frobenius norm of the strain-rate tensor (<span class="math-inline">$|\mathbf{D}|$</span>) becomes critical, kinetic energy non-adiabatically leaks from the 3-brane into the bulk fields. This mechanism establishes strict Leray–Hopf energy bounds and satisfies the Beale–Kato–Majda (BKM) criterion by ensuring that nonlinear exponential dissipation strictly outpaces algebraic vortex stretching. The result guarantees the global existence of smooth solutions while perfectly recovering exact classical Navier–Stokes behavior in laminar regimes. The appendix provides the formal derivation, a proposed pseudo-spectral numerical protocol (Taylor–Green vortex), and falsifiable predictions for extreme laboratory turbulence.</p> <p> </p> <p> </p> |
| title | Appendix J: Effective 3-Brane Hydrodynamics and the Regularization of the Navier–Stokes Equations via DFIM |
| url | https://doi.org/10.5281/zenodo.20175099 |