This repository contains simulations of various physical systems using numerical methods.

This simulation models the spread of a disease through a population of agents in a 2D space. Key features include:

• Agent-based movement with linear trajectories and wall collisions
• Infection spread through proximity and contact
• Vaccination station where agents can get vaccinated
• Temporary immunity after recovery
• Real-time visualisation of:
  • Agent states (susceptible, infected, immune, vaccinated)
  • Infection and vaccination percentages over time

Parameters can be adjusted to study:

• Disease transmissibility
• Recovery time
• Vaccination effectiveness
• Population density
• Agent movement patterns

This simulation demonstrates the time evolution of a quantum wave packet in two dimensions. Features include:

• Free-particle Schrödinger equation solution using spectral methods
• Initial Gaussian wave packet with momentum
• Probability density visualisation
• Time evolution of the quantum state

The simulation helps visualise:

• Wave packet spreading
• Quantum interference
• Conservation of probability
• Phase evolution

This simulation shows the diffusion of heat in a 2D medium. Features include:

• Four initial temperature hotspots
• Heat equation solution using spectral methods
• Temperature distribution visualisation
• Time evolution of the temperature field

The simulation demonstrates:

• Heat conduction
• Temperature equilibration
• Diffusion patterns
• Conservation of energy

This simulation demonstrates the solution of the Poisson equation with moving source terms. Features include:

• Dynamic source terms that move in a periodic pattern
• Solution using spectral methods
• Potential field visualisation
• Time evolution of the electrostatic potential

The simulation helps visualise:

• Electrostatic potential distribution
• Source-sink dynamics
• Field propagation
• Boundary effects

Each simulation can be run using its respective Python script:

# Infection spread simulation
python Infection_Spread.py

# Schrödinger evolution
python Schrodinger_Evolution.py

# Heat diffusion
python Heat_Diffusion.py

# Poisson equation
python poissonSimulation.py

The simulations require the following Python packages:

• NumPy
• Matplotlib
• SciPy

• Uses agent-based modeling
• Implements spectral diffusion for infection spread
• Includes vaccination and immunity mechanics
• Real-time visualisation with matplotlib

• Solves the free-particle Schrödinger equation
• Uses Fast Fourier Transform for spectral methods
• Implements periodic boundary conditions
• Visualises probability density

• Solves the heat equation
• Uses spectral methods for efficient computation
• Implements periodic boundary conditions
• Visualises temperature distribution

• Solves the Poisson equation with moving sources
• Uses Fast Fourier Transform for spectral methods
• Implements periodic boundary conditions
• Visualises electrostatic potential distribution

Each simulation can be customised by adjusting parameters such as:

• Grid resolution
• Domain size
• Time step
• Physical constants
• Initial conditions

See the individual script files for detailed parameter descriptions and default values.