Analyze Diffusion Dynamics
技能 已验证 活跃Analyze the dynamics of diffusion processes using stochastic differential equations, Fokker-Planck equations, first-passage time distributions, and parameter sensitivity analysis. Use when deriving probability density evolution for a continuous-time diffusion process, computing mean first-passage times for bounded diffusion, analyzing how drift and diffusion parameters affect process behavior, or validating closed-form solutions against stochastic simulation.
To provide a robust and executable framework for understanding the behavior of diffusion processes, enabling detailed analysis of probability density evolution and first-passage times.
功能
- Derive probability density evolution via Fokker-Planck equations
- Compute first-passage time distributions numerically and analytically
- Perform parameter sensitivity analysis on drift and diffusion coefficients
- Validate analytical solutions against Monte Carlo simulations
- Implement SDE models in Python with detailed procedural steps
使用场景
- Deriving probability density evolution for continuous-time diffusion processes
- Computing mean first-passage times for bounded diffusion
- Analyzing parameter effects on diffusion process behavior
- Validating closed-form solutions against stochastic simulations
非目标
- Fitting diffusion models to empirical data
- Real-time parameter estimation
- Analysis of non-Markovian processes
工作流
- Specify SDE Model
- Derive Fokker-Planck Equation
- Compute First-Passage Time Distributions
- Analyze Parameter Sensitivity
- Validate Analytics Against Numerical Simulation
实践
- Mathematical modeling
- Numerical methods
- Scientific simulation
- Code validation
先决条件
- Python 3.8+
- NumPy
- SciPy
- Matplotlib
安装
/plugin install agent-almanac@pjt222-agent-almanac质量评分
已验证类似扩展
Simulate Stochastic Process
97Simulate stochastic processes (Markov chains, random walks, SDEs, MCMC) with convergence diagnostics, variance reduction, and visualization. Use when generating sample paths for estimation, prediction, or visualization; when analytical solutions are intractable; running Monte Carlo estimation needing convergence guarantees; validating analytical results against empirical simulation; or sampling from complex posteriors via MCMC.
Performance Analysis
100Comprehensive performance analysis, bottleneck detection, and optimization recommendations for Claude Flow swarms
Oraclaw Decide
100为 AI 代理提供决策智能。分析选项、使用 PageRank 映射决策依赖关系、检测信息源冲突，并找出最重要的选择。
Session Logs
100Search and analyze your own session logs (older/parent conversations) using jq.
Presentation Structure
100关于演示文稿幻灯片格式、权重系统、导航和章节结构的知识
Compose Sacred Music
100Compose or analyze sacred music in Hildegard von Bingen's distinctive modal style. Covers modal selection, melodic contour (wide-range melodies), text-setting (syllabic and melismatic), neumatic notation, and liturgical context for antiphons, sequences, and responsories. Use when composing a new piece in Hildegardian style, analyzing an existing chant for structure and mode, researching medieval modal music, preparing to perform or teach Hildegard's music, or setting Latin sacred texts.