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Autore principale:	Boudreau
Natura:	Recurso digital
Lingua:	inglese
Pubblicazione:	Zenodo 2026
Soggetti:	magnetohydrodynamics, MHD simulation, magnetic field gradient, rotating systems, plasma physics, magnetic confinement, inertial systems, astrophysical fluids
Accesso online:	https://doi.org/10.5281/zenodo.19545232
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This work presents a simple experimental system (AMC – Auto Motor Core) consisting of a magnetically assisted rotor exhibiting stable rotation and extended spin-down time under ambient conditions. The system is fully consistent with classical physics and does not generate energy. Its behavior is attributed to reduced mechanical losses and structured magnetic field interactions. From this system, a local mathematical structure is derived based on magnetic energy gradients, leading to a phenomenological form that may be tested in magnetohydrodynamic (MHD) simulations. This work does not propose a new physical theory, but introduces a testable mathematical structure derived from an experimental system. <h2>1. Experimental Motivation</h2> The AMC system consists of: <ul> <li>a rigid rotor</li> <li>a structured magnetic field (segmented geometry)</li> <li>a passive gravitational preload</li> </ul> Observed behavior: <ul> <li>stable rotation without upper constraint</li> <li>extended spin-down time after initial impulse</li> <li>radial stability despite mechanical imperfections</li> </ul> These observations suggest the presence of an effective restoring mechanism linked to magnetic field gradients. <h2>2. Energy-Based Formulation</h2> Magnetic energy density: U_B = B² / (2 * mu0) Force derived from energy gradient: F = -grad(U_B) This gives: F ≈ -grad( B² / (2 * mu0) ) <h2>3. Local Radial Interpretation</h2> From the experimental behavior, a local restoring force can be approximated as: F_r ≈ - d/dr [ B² / (2 * mu0) ] This leads to an effective radial stiffness: k_B ≈ d²/dr² [ B² / (2 * mu0) ] <h2>4. Phenomenological Dynamic Model</h2> A local radial form can be written as: rho * d2r/dt2 + c * dr/dt + (k_eff - rho * Omega²) * r = 0 Where: <ul> <li>rho = local density</li> <li>r = radial displacement</li> <li>Omega = rotation rate</li> <li>c = dissipation coefficient</li> <li>k_eff = k_B + k_p + k_g</li> </ul> With: <ul> <li>k_B = magnetic contribution</li> <li>k_p = pressure-related contribution</li> <li>k_g = gravitational contribution</li> </ul> <h2>5. Stability Condition</h2> The system remains locally stable if: k_eff > rho * Omega² This condition is consistent with the observed stable rotation of the AMC rotor. <h2>6. Relation to MHD</h2> In magnetohydrodynamics: J x B = -grad( B² / (2 * mu0) ) + (B · grad) B / mu0 The first term corresponds to magnetic pressure gradients, which can act as a local restoring mechanism. <h2>7. Proposed Simulation Test</h2> This work proposes to evaluate whether a structure of the form: (k_eff - rho * Omega²) can generate observable effects such as: <ul> <li>local stabilization</li> <li>confinement</li> <li>coherent structure formation</li> </ul> in simulations involving: <ul> <li>rotating magnetized fluids</li> <li>plasma systems</li> <li>astrophysical environments</li> </ul> <h2>8. Scope and Limitations</h2> <ul> <li>No claim of new physics</li> <li>No direct equivalence with astrophysical systems</li> <li>The formulation is phenomenological and test-oriented</li> </ul> <h2>9. Key Statement</h2> This work proposes a testable mathematical structure derived from a real experimental system, rather than a purely theoretical model. <h2>10. Reference to Experimental System</h2> Radial Dynamics in AMC — Mathematical Structure 1. Centripetal force F_centripetal = mv²/r In AMC, part of this force is provided by the magnetic field gradient rather than the mechanical axis. 2. Radial equation of motion m·r̈ + c_r·ṙ + (k_r − m·ω²)·r = F_ext(t) where: <ul class="[li_&]:mb-0 [li_&]:mt-1 [li_&]:gap-1 [&:not(:last-child)_ul]:pb-1 [&:not(:last-child)_ol]:pb-1 list-disc flex flex-col gap-1 pl-8 mb-3"> <li class="whitespace-normal break-words pl-2">k_r = effective magnetic radial stiffness</li> <li class="whitespace-normal break-words pl-2">m·ω² = destabilizing centrifugal term</li> <li class="whitespace-normal break-words pl-2">c_r = radial damping</li> <li class="whitespace-normal break-words pl-2">F_ext(t) = external perturbations</li> </ul> 3. Stability condition k_r > m·ω² Satisfied across the observed speed range. 4. Link between k_r and field geometry k_r ≈ (V_actif / 2μ₀) · ∂²B²/∂r² 5. Coupled stabilization Two mechanisms combined: <ul class="[li_&]:mb-0 [li_&]:mt-1 [li_&]:gap-1 [&:not(:last-child)_ul]:pb-1 [&:not(:last-child)_ol]:pb-1 list-disc flex flex-col gap-1 pl-8 mb-3"> <li class="whitespace-normal break-words pl-2">Magnetic radial restoring force (k_r)</li> <li class="whitespace-normal break-words pl-2">Gyroscopic stabilization (L = I·ω, increasing with ω)</li> </ul> 6. MHD analogy J × B = −∇(B²/2μ₀) + (B·∇)B/μ₀ The first term shares the same mathematical structure as the radial restoring force in AMC. This is a structural analogy — not a physical equivalence.

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