「wave equation」の検索結果

Expert-level differential equations knowledge. Use when working with ordinary differential equations, partial differential equations, systems of ODEs, Laplace transforms, Fourier methods, boundary value problems, stability analysis, or numerical methods for ODEs. Also use when the user mentions 'ODE', 'PDE', 'initial value problem', 'boundary value problem', 'Laplace transform', 'separation of variables', 'eigenvalue problem', 'heat equation', 'wave equation', 'Laplace equation', 'stability', or 'phase plane'.

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Work with the full set of Maxwell's equations in integral and differential form to analyze electromagnetic fields, waves, and energy transport. Use when applying Gauss's law, Faraday's law, or the Ampere-Maxwell law to boundary value problems, deriving the electromagnetic wave equation, computing Poynting vector and radiation pressure, solving for fields at material interfaces, or connecting electrostatics and magnetostatics to the unified electromagnetic framework.

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Simulate wave propagation — acoustic, electromagnetic, elastic, and quantum waves. FDTD, spectral methods, and absorbing boundary conditions for 1D/2D/3D wave equations with sources, scattering, and dispersion.

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Expert-level general relativity knowledge. Use when working with curved spacetime, Einstein field equations, geodesics, black holes, gravitational waves, cosmology, Schwarzschild metric, or tensor calculus. Also use when the user mentions 'Einstein field equations', 'curved spacetime', 'geodesic', 'black hole', 'event horizon', 'Schwarzschild', 'gravitational waves', 'spacetime curvature', 'Riemann tensor', 'metric tensor', 'cosmological constant', or 'gravitational lensing'.

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Algebra-driven API design with monoids, semigroups, and interpreters via algebraic equations

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Diagnose, fix, and improve IEEEtran LaTeX manuscripts using routed template, layout, float, equation, algorithm, table, bibliography, and PDF-compliance guidance. Use when fixing IEEE LaTeX compile errors, overfull boxes, float placement, two-column layout, figure sizing, tables, equations, algorithms, BibTeX, citation commands, template compliance, or final submission PDF checks.

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Expert-level electromagnetism knowledge. Use when working with electric fields, magnetic fields, Maxwell's equations, electromagnetic waves, circuits, Coulomb's law, Gauss's law, Faraday's law, Ampere's law, or electromagnetic induction. Also use when the user mentions 'electric field', 'magnetic field', 'Maxwell', 'Gauss law', 'Faraday', 'Ampere', 'capacitor', 'inductor', 'electromagnetic wave', 'Lorentz force', 'Poynting vector', or 'dielectric'.

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Expert-level quantum mechanics knowledge. Use when working with wave functions, Schrodinger equation, quantum states, operators, uncertainty principle, quantum tunneling, spin, angular momentum, perturbation theory, or quantum entanglement. Also use when the user mentions 'wave function', 'Schrodinger', 'Heisenberg', 'quantum state', 'eigenvalue', 'superposition', 'tunneling', 'spin', 'Hilbert space', 'Dirac notation', 'commutator', or 'quantum measurement'.

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Read, decompose, and analyze IEEE-style papers using routed technical-reading workflows. Use when extracting problem setting, object-method-condition logic, contributions, method pipeline, equations, datasets, baselines, metrics, ablations, limitations, replication details, citation role, related-work positioning, implementation notes, or reviewer-style assessment from a paper, PDF, abstract, or manuscript excerpt.

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Think and work like an expert Acoustics Physicist. Use when a task calls for Acoustics Physicist judgment. Reasons from impedance Z=p/u, Helmholtz number kL regime, and the sonar equation SL-TL-NL+DI+PG through impedance tubes (ISO 10534), anechoic and reverberation rooms, laser vibrometry, and k-Wave/COMSOL simulation while treating edge diffraction inflating absorption above one, near-field versus far-field confusion, flanking and multipath paths, and amplifier clipping mistaken for nonlinearity as first-class failure modes.

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。