「conservation laws」の検索結果

Deep symmetries and unifying principles — gauge theory, Lie groups, Noether's theorem, and the Standard Model. Constructs field theories from symmetry requirements, derives conservation laws, and traces force unification. Use when working with gauge symmetry, Lie groups (U(1), SU(2), SU(3)), conservation laws via Noether's theorem, the Higgs mechanism, or Standard Model structure.

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Discover conserved quantities and symmetries from trajectory data. Identifies energy, momentum, angular momentum, and custom invariants using neural networks and symbolic methods. Inspired by Noether's theorem.

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Think and work like an expert Mathematical Modeler. Use when a task calls for Mathematical Modeler judgment. Reasons from nondimensionalization, conservation/positivity laws, and minimal-viable model structure through mechanistic ODE/PDE, stochastic, and agent-based formulations, profile-likelihood and Fisher-information identifiability, and Sobol/Morris sensitivity analysis, while treating sloppy unidentifiable parameters, structural model uncertainty, and out-of-regime extrapolation as first-class failure modes.

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Think and work like an expert Electrical Engineer. Use when a task calls for Electrical Engineer judgment. Reasons from Kirchhoff's laws, Maxwell's quasi-static limit, energy conservation, and LTI superposition through SPICE loop-gain and corner analysis, Bode gain/phase-margin checks, impedance-controlled layout, and IEC 62368/CISPR compliance, while treating unmodeled PCB parasitics, ground-return loops, protection let-through energy versus semiconductor SOA, and probe-artifact confounders as first-class failure modes.

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Expert-level classical mechanics knowledge. Use when working with Newton's laws, kinematics, dynamics, energy, momentum, rotational motion, oscillations, gravitation, Lagrangian mechanics, or Hamiltonian mechanics. Also use when the user mentions 'force', 'torque', 'momentum', 'energy conservation', 'simple harmonic motion', 'projectile', 'friction', 'center of mass', 'moment of inertia', 'Lagrangian', or 'Hamiltonian'.

日本語の概要は準備中です。原文の説明を表示しています。