Python

Python Projects Showcase

Welcome to my Python Projects Showcase! This portfolio features a selection of my projects developed using Python at Stanford University, illustrating my capabilities in software design, algorithm development, and simulation.

Pendulum-Projectile Simulation on Solar Planets

• Project Repository: View Project
• Description: A sophisticated simulation that combines the dynamics of pendulum motion with projectile motion in a solar system context.
• Course: Stanford University CS106A (2023)
• Frameworks & Libraries: Python 3, Canvas
• Key Features:
  • Realistic simulation of pendulum and projectile dynamics.

    

Finite Difference Method (FDM) for Heat Transfer

• Project Repository: View Project
• Description: A sophisticated implementation of the Finite Difference Method (FDM) that numerically solves heat transfer problems by approximating differential equations with difference equations.
• Course: Academic Project
• Frameworks & Libraries: Python 3, NumPy, Matplotlib
• Key Features:
  • Simulation of heat distribution in solid materials.
  • Simulation of deflection in solid bar.
  • Flexibility to analyze both cylindrical and spherical coordinate systems.

    

Heat Equation

The one-dimensional heat equation is: $$ \frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2} $$

Where:

• \( u \): temperature
• \( \alpha \): thermal diffusivity

Discretization Using FDM

The equation can be discretized as:

$$ \frac{u_i^{n+1} - u_i^n}{\Delta t} = \alpha \frac{u_{i+1}^n - 2u_i^n + u_{i-1}^n}{\Delta x^2} $$

Rearranged to:

$$ u_i^{n+1} = u_i^n + \frac{\alpha \Delta t}{\Delta x^2} (u_{i+1}^n - 2u_i^n + u_{i-1}^n) $$

Simplified Algorithm

1. Initialization: Define thermal properties \( h_a, T_a, k, g \).
2. User Input: Gather inputs like \( h_a, T_a, k, g, L, n \).
3. Discretization: $$ h = \frac{L}{n}, \quad s = -\frac{g \cdot h^2}{4k} \text{ (cylindrical)}, \quad s = -\frac{g \cdot h^2}{6k} \text{ (spherical)} $$
4. Matrix Setup: Construct \( \text{matA} \) with boundary conditions.
5. Matrix Construction: Append internal node coefficients \( a, b, c \) to \( \text{matA} \).
6. Constant Vector: Create \( \text{matB} \) with boundary values.
7. Matrix Calculations: Solve using: $$ u = \text{inmatA} \cdot \text{matB} $$
8. Visualization: Plot temperature distribution.
9. Execution: Run the algorithm.

Karel Robot (7 Mini Projects)

• Project Repository: View Projects
• Description: A series of seven mini-projects utilizing the Karel Robot programming environment to introduce fundamental programming concepts.
• Course: Stanford University CS106A (2023)
• Key Features:
  • Hands-on programming exercises including maze navigation and object manipulation.
  • Emphasis on logical thinking and problem-solving skills.
• Projects:
  • Beyond Fill Karel
  • Checkerboard Karel
  • Fill Karel
  • Jigsaw Karel
  • Piles
  • Spread Beepers
  • Stone Mason Karel

    

Graph Simulator

• Project Repository: View Project
• Description: A versatile graph simulation tool that allows users to visualize and manipulate graph structures interactively.
• Course: Stanford University CS106A (2023)
• Frameworks & Libraries: Python 3, Canvas
• Key Features:
  • Fourier Transform Visualization: Analyzing Signal Frequencies
  • Trigonometric Functions: Graphical Representations
  • Linear Algebra in Action: Visualizing Vectors and Matrices

    

Baby Snake

• Project Repository: View Project
• Description: A collection of engaging mini-games developed using Python, showcasing programming logic and design principles.
• Course: Stanford University CS106A (2023)
• Frameworks & Libraries: Python 3, Canvas
• Key Features:
  • Key Features: Classic gameplay with simple controls, colorful graphics, score tracking.