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| Hlavní autor: | |
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| Médium: | Recurso digital |
| Jazyk: | |
| Vydáno: |
Zenodo
2025
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| Témata: | |
| On-line přístup: | https://doi.org/10.5281/zenodo.17849639 |
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- <p><strong>ΔΦ Branching Law v2.0 develops a universal rule governing the geometry of branching across biological, physical, fluid, and cosmic systems.</strong> Instead of treating bifurcation in vascular networks, bronchial trees, fungal hyphae, lightning forks, river deltas, plasma filaments, and cosmic web structures as unrelated domain-specific outcomes, this paper derives a single substrate-level law based on electrostatic tension redistribution.</p> <p>Using the core ΔΦ relation (ΔΦ = ρ v), the paper shows that division occurs when an incoming flux partitions into two outgoing pathways that minimize residual field tension. This produces the universal ΔΦ branching angle—<strong>68° to 74° with a mean of ~71.3°</strong>—and the conserved daughter-radius law <strong>r₁³ + r₂³ = r₀³</strong> across scales spanning 26 orders of magnitude. Comparative morphology demonstrates that biological bifurcation, laminar jet division, plasma filament splitting, and cosmic filament branching all obey these ΔΦ-driven equilibrium conditions.</p> <p>The manuscript provides the complete mathematical derivation of the ΔΦ branching law, outlines the energy minimization principle that determines branching angle, and establishes conservation rules governing radii, curvature, and flux ratios. It proposes five falsifiable tests, including biological imaging, fluid jet experiments, plasma arc manipulation, and astrophysical filament-geometry analysis.</p> <p><strong>ΔΦ Branching Law v2.0 completes the geometric triad of natural structure formation alongside ΔΦ Curvature Law v2.0 and ΔΦ Segmentation Law v2.0, demonstrating that branching is not an emergent adaptation but the equilibrium geometry of tension partitioning in the ΔΦ substrate.</strong></p>