Results for “wave-equations”

Analyzes sound wave propagation, acoustic impedance, resonators, noise insulation, and musical instrument acoustics, with applications in concert halls, sonar, and noise barriers.

Creates realistic ocean and water wave effects for web using SVG filters (feTurbulence, feDisplacementMap), CSS animations, and layering techniques. Use for ocean backgrounds, underwater distortion, beach scenes, ripple effects, liquid glass, and water-themed UI. Activate on "ocean wave", "water effect", "SVG water", "ripple animation", "underwater distortion", "liquid glass", "wave animation", "feTurbulence water", "beach waves", "sea foam". NOT for 3D ocean simulation (use WebGL/Three.js), video water effects (use video editing), physics-based fluid simulation (use canvas/WebGL), or simple gradient backgrounds without wave motion.

Design, select, and analyze waveforms for radar, sonar, and active sensing using the Phased Array System Toolbox. Covers LFM, NLFM, FMCW, phase-coded, CW, stepped FM, custom IQ, ambiguity functions, sidelobe reduction, and Doppler tolerance. Key objects: phased.LinearFMWaveform, phased.NonlinearFMWaveform, phased.CustomFMWaveform, phased.PhaseCodedWaveform, phased.FMCWWaveform, phased.SteppedFMWaveform, phased.MFSKWaveform, phased.RectangularWaveform, nlfmspec2freq, shapespectrum, ambgfun, pambgfun, sidelobelevel, legendreseq, mlseq, radarWaveformGenerator.

Analyze AMS waveform data using Mixed-Signal Blockset utilities: phase noise measurement, clock jitter, anti-aliased resampling, timing measurements, lock time, INL/DNL, ADC/DAC calibration, HSpice import. Use when analyzing time-domain voltage from PLL/VCO/clock simulations, measuring phase noise from variable-step solver output, computing jitter, or resampling non-uniform data.

Compute aerospace environment properties including atmosphere (ISA, COESA, NRLMSISE-00, non-standard, CIRA), gravity (spherical harmonic, WGS84, zonal, centrifugal), horizontal wind (HWM), magnetic field (WMM, IGRF), geoid height, geocentric radius, space weather data, planetary ephemeris, Earth orientation (polar motion, nutation, delta-UT1, CIP). Use when computing atmospheric density, temperature, pressure, gravity vectors, wind profiles, magnetic field components, geoid undulation, solar flux indices, planet positions, or Earth orientation parameters for aerospace vehicle analysis, spacecraft environment modeling, or navigation corrections.

Equation component for rendering mathematical equations using KaTeX. Invoke when user needs to display mathematical formulas or LaTeX expressions in Naive UI.

Provides atomic motion rules, multi-phase scene blueprints, scene transitions, motion-design techniques, and runtime adapters (GSAP, Lottie, Three.js, Anime.js, CSS, WAAPI, TypeGPU) for composing animations with HyperFrames.

Solves equations, factors expressions, and analyzes algebraic structures including matrices, vector spaces, and group theory.

Interrogates research plans before evals or published claims, forcing explicit null hypotheses, confound checks, and data verification across four review waves.

Applies physical principles to model biological systems, including protein folding, membrane transport, molecular forces, and neural signaling.

Creates 3Blue1Brown-style animated explainer videos, algorithm visualizations, and math animations using Manim Community Edition.

Statistical visualization. Scatter, box, violin, heatmaps, pair plots, regression, correlation matrices, KDE, faceted plots, for exploratory analysis and publication figures.

Manim CE animations: 3Blue1Brown math/algo videos.

Computes derivatives, integrals, and solves calculus problems including optimization, Taylor series, and differential equations.

当意识到自己处于长期迷茫、缺乏动力阶段，需要系统性方法走出困境时

Builds statistical plots with the seaborn Python library and pandas DataFrame integration, on attractive matplotlib-based defaults. Use for quick exploration of distributions, relationships, and categorical comparisons — box plots, violin plots, swarm/strip plots, KDE/histograms, pair plots, joint plots, regression plots, correlation heatmaps, and faceted small multiples (relplot/displot/catplot/lmplot). For interactive/hover/zoom charts defer to alterlab-plotly; for exact journal/manuscript styling (column widths, point fonts, CMYK, vector export) defer to alterlab-scientific-viz; for low-level custom matplotlib figures defer to alterlab-matplotlib (seaborn integrates with it for fine-tuning). Part of the AlterLab Academic Skills suite.

Statistical visualization. Scatter, box, violin, heatmaps, pair plots, regression, correlation matrices, KDE, faceted plots, for exploratory analysis and publication figures.

Applied Optics Modeling Skill

Calculate portfolio risk metrics including VaR, CVaR, Sharpe, Sortino, and drawdown analysis. Use when measuring portfolio risk, implementing risk limits, or building risk monitoring systems.

Implements Manifold-Constrained Hyper-Connections (mHC) using Doubly Stochastic Matrices to improve deep learning stability.

Analyze and simulate options trading strategies using Black-Scholes pricing, Greeks calculation, and risk management guidance.

Manim CE animations: 3Blue1Brown math/algo videos.

Builds Vue 3 components with Composition API patterns, configures Nuxt 3 SSR/SSG projects, sets up Pinia stores, scaffolds Quasar/Capacitor mobile apps, implements PWA features, and optimises Vite builds.

Visualização estatística. Gráficos de dispersão, boxplots, violins, mapas de calor, matriz de pares, regressão, matrizes de correlação, KDE, gráficos facetados, para análise exploratória e figuras para publicação.

Measures the trade-off between computation time and energy consumption in mobile edge computing by computing a weighted sum of the two objectives, given system configuration parameters and per-user task characteristics.

Generate spectrograms and feature-panel visualizations from audio with the songsee CLI.

Balance game systems including difficulty curves, stat tuning, economy rates, matchmaking fairness, and player power progression. Use when tuning numbers and systems for fair, engaging gameplay. Also trigger for "game balance", "difficulty tuning", "stat balancing", "nerf", "buff", "power curve", or "difficulty curve".

Flamingo: A Visual Language Model for Few-Shot Learning

RF Toolbox and RF Blockset in MATLAB -- S-parameter I/O, network conversions (S/Z/Y/ABCD/T/H/G, mixed-mode), cascade/de-embedding, rfbudget analysis, circuit composition, matching networks, amplifier stability, mixer spurs, rational fitting, SI channels, baseband processing, Circuit Envelope simulation. Trigger: sparameters, Touchstone, .s2p, .s4p, rfplot, smithplot, rfparam, rfwrite, zparameters, yparameters, abcdparameters, s2sdd, cascadesparams, deembedsparams, rfbudget, noise figure, OIP3, IIP3, amplifier, modulator, nport, rffilter, attenuator, seriesRLC, shuntRLC, lcladder, txline, circuit, setports, clone, matchingnetwork, stabilityk, stabilitymu, powergain, gammams, gammaml, mixerIMT, OpenIF, rational, rationalfit, stepresp, txlineWRLGC, rf.Amplifier, rf.Mixer, rf.Filter, rf.Sparameter, rfsystem, RF Blockset.

Execute all plans in a phase with wave-based parallelization

Audits over-engineered codebases by factoring layers into live obligations, quotienting redundant distinctions, ablating unearned surface, and normalizing survivors while preserving required behavior. Produces an evidence-backed Reduction Certificate, cuts, migration phases, proof signals, and rollback.

Wilkinson, branchline, ratrace, directional couplers, corporate dividers, Rotman lenses for power splitting and beam-forming. TRIGGER: user asks to design, create, or analyze any coupler, splitter, power divider, combiner, or Rotman lens. Invoke BEFORE writing code — class names and design() availability vary per coupler type. SKIP: EM simulation/S-parameter extraction of an existing component (use matlab-analyze-em), building custom non-catalog geometry (use matlab-assemble-pcb-layout), material/stackup setup only (use matlab-manage-pcb-material), cascading multiple components (use matlab-integrate-pcb-circuit).

Analyzes stellar structure, galactic dynamics, orbital mechanics, gravitational lensing, cosmic microwave background, and exoplanet detection methods.

Advanced Optics Design Skill

Manim CE animations: 3Blue1Brown math/algo videos.