RZ Rui Zhang Academic portfolio
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Mathematics · Physics · Scientific Computing · Trumpet

Rui Zhang

Mathematics and Physics student at UCL, interested in scientific computing, mathematical modelling, computational physics, and trumpet performance.

View projects & outputs Explore music work Contact

4

featured projects

3

writing notes

2

reports/artifacts

2

music record

Portfolio map

Three public routes, one coherent profile

Use the tabs to see how the site separates academic evidence, music records, and collaboration enquiries without mixing their purposes.

Learning Route

Mathematics, physics, and scientific computing as a path

The learning route explains the story behind the module choices: foundations, methods, advanced physics, numerical computation, and research preparation.

Open learning route
  • UCL Mathematics and Physics course map from Year 1 foundations to Year 3 specialisation.
  • Current numerical work on the one-dimensional Schrodinger equation and oscillator models.
  • PDE/modelling work through tumour-growth modelling and Gray-Scott reaction-diffusion.

Current desk

What is active right now

These are not generic interests; they are the current threads that should turn into notes, figures, reports, or cleaned public repositories.

Computational quantum mechanics

1-D Schrodinger equation and oscillator models

In progress

Building toward a reproducible numerical note with finite-difference discretisation, eigenvalue checks, plots, and clear limits.

HPC / PDE patterns

Gray-Scott reaction-diffusion

Summer-school thread

Tracking parameter sweeps, timestep stability, array implementation, and performance-aware simulation habits.

Quantum computing

IBM Qiskit summer-school learning log

Learning notes

Recording core concepts and small original exercises without reposting restricted course material.

Mathematical exposition

Lagrangian mechanics LaTeX report

Published artifact

Converted a Year 1 presentation into a public PDF and LaTeX source for a durable portfolio record.

Learning route

A learning route from formal modules to reproducible computing

The course map keeps UCL mathematics and physics modules connected to public projects, reports, and self-study in scientific computing.

Year 1

Year 1 Mathematical and Physical Foundations

Foundational mathematics and physics courses: Analysis 1, Algebra, Mathematical Methods, astronomy, waves, thermal physics, and classical mechanics.

Year 2

Year 2 Methods and Modelling

Methods-heavy second-year work across complex analysis, fluid mechanics, mathematical methods, electromagnetism, quantum physics, atomic physics, and statistical physics.

Year 3

Year 3 Specialisation and Independent Work

Planned third-year specialisation in general relativity, optimisation, numerical methods, stochastic methods, electromagnetism, nuclear and particle physics, solid state physics, and quantum mechanics.
View full learning route

Projects & outputs

Selected projects, reports, and computing work

Each project is designed to become more than a link: it should explain the question, model, implementation, validation, limits, and next steps.

Generated cover image for Gray-Scott Reaction-Diffusion HPC Summer School Project

Computational Reproductions

Gray-Scott Reaction-Diffusion HPC Summer School Project

Jul 2026 · in progress · Core computational

An in-progress summer-school scientific-computing project on Gray-Scott reaction-diffusion simulation, pattern formation, and HPC-oriented implementation practice.

  • PDEs
  • pattern formation
  • numerical simulation
GitHub repo
Generated cover image for Numerical Solution of the 1-D Schrodinger Equation

Independent Projects

Numerical Solution of the 1-D Schrodinger Equation

Jun 2026 · in progress · Core computational

An in-progress computational quantum mechanics project on numerical solutions to the one-dimensional Schrodinger equation and quantum oscillator models.

  • quantum mechanics
  • numerical methods
  • scientific computing
  • eigenvalue problems
GitHub repo
Generated cover image for Multiphase Tumour Growth 1-Dimensional Slab Model

Summer / Department Projects

Multiphase Tumour Growth 1-Dimensional Slab Model

Jun 2026 · completed · Core computational

A Year 2 summer mathematics department project on a two-phase tumour-growth model with nutrient transport, mechanical stresses, stability analysis, and numerical solutions.

  • mathematical modelling
  • tumour growth
  • PDEs
  • numerical solutions
  • stability analysis
GitHub repoReport PDF
Generated cover image for Lagrangian Mechanics Project

Summer / Department Projects

Lagrangian Mechanics Project

May 2026 · completed · Mathematical report

A Year 1 summer mathematics department project on Lagrangian mechanics, variational calculus, the Euler-Lagrange equation, and classical extremal-path examples.

  • analytical mechanics
  • numerical integration
  • physics
GitHub repoGenerated report PDFLaTeX source

Notes & writing

Notes that turn coursework and seminars into reusable understanding

This section is for polished notes, reading reflections, talks, and technical tutorials rather than an unfiltered list of every class.

Technical Tutorials

Scientific Python and Computing Toolkit

Jun 2026

A learning map for NumPy, SciPy, Matplotlib, Pandas, PyTorch, MATLAB, and LaTeX as tools for reproducible mathematical and physical modelling.

  • scientific computing
  • Python
  • MATLAB
  • LaTeX

Academic Notes

Scientific Computing Learning Map

Jun 2026

A living map for connecting numerical methods, computational physics, modelling projects, and reproducible code.

  • scientific computing
  • learning notes
  • reproducibility

Reports & artifacts

Reports and artifacts with honest labels

Reports, PDFs, and source files are kept visible, but formal publication status is labelled conservatively.

Research Reports

Multiphase Tumour Growth 1-Dimensional Slab Model

Jun 2026 · archived

A summer mathematics department project report on a two-phase tumour-growth model with nutrient transport, mechanical stresses, one-dimensional slab simplification, stability analysis, numerical solutions, and critique.

  • mathematical modelling
  • tumour growth
  • PDEs
  • numerical analysis
Report PDF

Research Reports

Lagrangian Mechanics and Variational Calculus

Jun 2025 · archived

A rewritten LaTeX report based on a Year 1 summer mathematics department project about ordinary extrema, functionals, the Euler-Lagrange equation, shortest paths, the Beltrami identity, and the brachistochrone problem.

  • variational calculus
  • Lagrangian mechanics
  • Euler-Lagrange equation
Report PDFLaTeX source
View reports archive

Music

Trumpet performance as a serious second identity

Selected performances and repertoire document ensemble work, venue experience, style range, and teaching background.

UCL Concert Band and UCL Mezzo Orchestra

UCL Concert Band and UCL Mezzo Orchestra Trumpet Leadership

Jun 2026 · UCL

Trumpet leadership across UCL Concert Band and UCL Mezzo Orchestra, complementing symphony orchestra work with wind-band and flexible ensemble settings.

  • Concert band repertoire
  • Mezzo orchestra programmes
  • Ensemble leadership contexts