the-observatory

Physics, Simulations & Applied Mathematics

A portfolio of interactive simulations, technical guides, and research notes — built for learning and sharing.

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Guides Reference & Theory
Fc
Particle Simulation
Cohesion Force Guide
Cohesive attraction between particles — distance thresholds, force profiles, and tuning parameters.
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ε
N-Body Simulation
Gravity Softening Guide
Preventing singularities in N-body simulations — softening length, force law modifications, and trade-offs.
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ω₀
Classical Mechanics
Harmonic Oscillator Guide
The simple harmonic oscillator from first principles — restoring force, angular frequency, energy, and phase space.
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Δ
Classical Mechanics
Damped Oscillator & Discriminant
Under-, over-, and critically-damped environments via the characteristic equation discriminant. Decay envelopes and Q-factor.
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η
Statistical Physics
Order Parameter Guide
What order parameters are, how they distinguish phases, and how they appear in Landau theory and simulation observables.
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∑
Notation
Math & Physics Notation — Cheat Sheet
Vectors, operators, Greek letters, decorators, subscript conventions, and famous constants — all in one place.
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γ
Special Relativity
The Lorentz Factor
What γ actually means — every symbol unpacked, three velocity regimes, and worked examples at ISS and GPS orbital speeds.
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s²
Special Relativity
The Spacetime Interval
The one quantity every observer agrees on — causal structure, Lorentz invariance, and a fully worked boost example with exact arithmetic.
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Δτ
Special Relativity
Time Dilation at Real Velocities
From picoseconds per day at walking speed to the GPS clock correction that keeps your maps accurate — SR and GR together.
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WIP - Simulations Interactive & Video
∿
Oscillations
Harmonic Oscillator
Real-time simulation of simple and damped harmonic motion with phase-space trajectory visualisation.
coming soon
⬡
N-Body
Particle Cohesion
N-body simulation exploring cohesive forces, cluster formation, and emergent structure.
Writing Blog & Essays
✍
Jan 2025  ·  Medium
Special relativity with Jupyter lab and Sympy
Using python tools to implement equations from relativistic physics.
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About Background

Hello! Welcome to my github homepage and portfolio. I'm a machine learning engineer and weekend physics enthusiast interested in the intersection of simulation, applied mathematics, and visualisation. This site collects work I build to deepen my own understanding — from first-principles derivations to running simulations of complex systems.

My code portfolio the-lab contains the underlying simulation engines and tooling.

</> the-lab in LinkedIn
Contact Get in touch
Open to opportunities in simulation engineering, scientific computing, and applied physics.
Feel free to reach out about feedback, projects, collaborations, or roles.
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