This repository contains Python code and notebooks developed during my PhD research, focused on the numerical modeling and simulation of a complex dynamical system governed by coupled differential equations.
The goal of this project was not to build a production-ready software package, but to explore system behavior across different regimes, study the impact of model assumptions, and analyze high-dimensional outputs through iterative computational experiments.
The system under study involves multiple interacting components with non-trivial dynamics that cannot be solved analytically. Understanding its behavior requires:
- Designing a numerical model
- Solving coupled ODEs across different parameter regimes
- Exploring large parameter spaces
- Analyzing and visualizing emergent behavior
The emphasis of this work is on the modeling approach and computational workflow rather than on domain-specific theoretical details.
This repository illustrates how I approach complex modeling problems using code:
- Translating an ill-defined research question into a concrete computational model
- Implementing numerical solvers and simulation pipelines in Python
- Running parameter scans to explore system behavior
- Analyzing and visualizing simulation outputs to extract trends and validate assumptions
- Iteratively refining the model based on results
The code reflects an exploratory research workflow and prioritizes clarity of logic and experimentation over software engineering completeness.
The repository contains three main notebooks, each addressing a different aspect of the modeling and numerical analysis. They can be read independently, depending on the part of the workflow of interest.
This notebook focuses on the numerical behavior of the coupled equations in the freeze-out regime, where interaction rates become inefficient compared to the expansion of the system.
It includes:
- definition of the coupled system of equations
- numerical integration using SciPy solvers
- visualization of freeze-out dynamics
- comparison of different freeze-out scenarios
- treatment of washout terms and their numerical impact
This notebook explores the generation of an asymmetry through competing dynamical processes.
It includes:
- importing and adapting thermally averaged interaction rates
- modeling of source terms responsible for asymmetry generation
- analysis of competing processes that create and erase asymmetries
- numerical integration over the relevant parameter and temperature ranges
- large parameter space scans
- visualizations highlighting regions of successful asymmetry generation
This notebook provides an end-to-end example combining multiple dynamical regimes.
It illustrates:
- how the system is adapted in different regimes depending on active interactions
- the complete numerical evolution of the system variables
- final plots summarizing the full simulation and analysis pipeline
- This code was developed for research purposes and reflects an exploratory workflow.
- It is not intended as a polished library or production system.
- The focus is on modeling choices, numerical experimentation, and analysis rather than on performance optimization or packaging.