EQUATION REGISTRY

Candidate nonlinear longitudinal–transverse coupling

A lowest-order rotational scalar candidate, not uniquely derived from FCC or LVE.

Theory · CANDIDATE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 3

ASD-WEB-EM-041
η=−∇⋅uL,ΩT=∇×uT,LLT=−gLTη∣ΩT∣2\eta=-\nabla\cdot\mathbf u_L,\quad\boldsymbol\Omega_T=\nabla\times\mathbf u_T,\quad\mathcal L_{LT}=-g_{LT}\eta|\boldsymbol\Omega_T|^2

A lowest-order rotational scalar candidate, not uniquely derived from FCC or LVE.
Chapter reference: Final collected manuscript · Chapter 3, equations (3.74), (3.75) · ASD-BOOK-ddbade997b45

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ASD-WEB-EM-041 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

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Adopted source, conditions and previous versions

Final collected manuscript · Chapter 3, equations (3.74), (3.75)

A lowest-order rotational scalar candidate, not uniquely derived from FCC or LVE.

Conditions retained in this adoption

  • Vanishing boundary variations; constant g_LT, K_L and λ_T.
  • K_L>0 and λ_T≥2g_LT²/K_L
  • Minimize over η at fixed transverse intensity.

Specific unresolved source issues

  • Full gradient energy, microscopic parameters, long-range sources and stable configurations remain research tasks.

Source locators: p1240 · p1241 · p1243 · p1244 · p1245 · p1246 · p1249 · p1250 · p1251 · p1252 · p1284 · 最终合订稿 · 第三章式 (3.74)、(3.75)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

EM-f06476f55cae · 第三章 / Chapter 3 · (3.74)–(3.75), PDF p. 17

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No preceding equation is recorded in this index. Consult the source topic for definitions, geometry and model scope.

USED BY

Uses of this equation

Subsequent equationMutual response of the candidate couplingASD-WEB-EM-042Subsequent equationBoundedness of the local energy truncationASD-WEB-EM-043DocumentLongitudinal–Transverse Coupling
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