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Add comprehensive motion models analysis, method comparison benchmarks, and robustness improvements #1

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11 changes: 10 additions & 1 deletion .gitignore
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Expand Up @@ -8,4 +8,13 @@ output/
build/
.vscode/
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# LaTeX auxiliary files (keep PDFs)
*.aux
*.log
*.out
*.toc
*.fls
*.fdb_latexmk
*.synctex.gz
108 changes: 108 additions & 0 deletions docs/MOTION_MODELS_README.md
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# Motion Models Analysis

This directory contains a comprehensive analysis of all motion model implementations in HGD.

## Files

- **motion_models_analysis.tex** - LaTeX source document analyzing all motion models
- **motion_models_analysis.pdf** - Compiled PDF document (16 pages)

## Overview

The document provides:

1. **Detailed analysis** of each motion model implementation:
- `d2q4_slow.py` - Reference Python implementation
- `d2q4_array.py` - Vectorized Python implementation
- `d2q4_array_v2.py` - Advanced Python with inertia support
- `d2q4_SA_array.py` - Alternative vectorized formulation
- `core.cpp` - Production C++ implementation
- `d2q4.cpp.dep` - Deprecated C++ implementation

2. **Physics characterization** including:
- Mathematical formulation of void motion
- Probability calculations for different directions
- Slope stability criteria
- Advection models (average_size, freefall, stress)

3. **Implementation features** including:
- Inertia support (present/absent)
- Parallelization strategies
- Memory usage
- Performance comparison

4. **Pros and cons** of each implementation

5. **Recommendations for stream_core** function:
- Three options ranging from minimal upgrade to full feature parity
- Specific implementation details for adding inertia support
- Validation and testing strategies

## Key Findings

### Inertia Implementations

Only the following models have proper inertia support:
- ✅ `d2q4_array_v2.py` - Full inertia with momentum transfer
- ✅ `d2q4.cpp.dep` - Deprecated but had inertia support
- ⚠️ `core.cpp` - Parameter exists but not fully implemented in `stream_core`

### Performance

Relative speed (approximate):
- `d2q4_slow.py`: 1× (baseline)
- `d2q4_array.py`: 10-50×
- `d2q4_array_v2.py`: 10-30×
- `d2q4_SA_array.py`: 5-20×
- `core.cpp`: 50-200×

### Recommendations

**For the `stream_core` function in `core.cpp`:**

The recommended approach is **Option 1: Minimal Upgrade** which includes:
1. Add full velocity field support (`u[i,j,k]`, `v[i,j,k]`)
2. Include inertia contribution to swap probabilities
3. Swap velocities with particles when inertia is enabled
4. Consider probabilistic swaps in inertia mode
5. Validate against `d2q4_array_v2.py`

This maintains C++ performance while adding the critical inertia feature that's currently missing.

## Compiling the Document

To recompile the LaTeX document:

```bash
cd docs
pdflatex motion_models_analysis.tex
```

Requirements:
- `texlive-latex-base`
- `texlive-latex-extra`

On Ubuntu/Debian:
```bash
sudo apt-get install texlive-latex-base texlive-latex-extra
```

## Citation

If you use this analysis in your research, please cite the HGD package:

```
Marks, B., Athani, S., & Li, J. (2024). Heterarchical Granular Dynamics (HGD).
https://github.com/benjym/HGD
```

## Contributing

If you find errors or have suggestions for improving this analysis, please:
1. Open an issue on GitHub
2. Submit a pull request with corrections
3. Contact the authors directly

## License

This documentation is provided under the same license as the HGD package (see LICENSE.txt in the root directory).
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