VectorSTEM • Research & Projects
Research & Projects
This page presents ongoing research initiatives and projects. Scroll to explore all tracks. Supporting materials and attachments are listed on separate project pages.
№1. Radiation from a Curved Contour on a Plane via a Parabolic Equation Approach
Research on radiation from a curved contour using natural coordinates, geometric derivations, Helmholtz-to-parabolic reduction, and numerical verification through a Crank–Nicolson scheme. The project page contains Russian-language derivations, PDFs, code, CSV results, and plots.
Project overview
Theory, derivations, numerical code, exported results, and convergence / runtime plots
for a curved-contour radiation model.
Geometry
Helmholtz
Parabolic
Numerics
Waves
Crank–Nicolson
Geometry
Natural coordinates near a smooth contour, Frenet–Serret formulas, and coefficient interpretation.
Reduction
Helmholtz formulation, variable substitution, and parabolic equation approximation.
Numerics
Crank–Nicolson implementation, benchmark circle test, and reference comparisons.
Output
Theory PDFs, Python code, CSV runs, and relative error / runtime plots.
What’s inside the project
Theory
Natural coordinates, Frenet–Serret formulas, variable substitution, and derivations of key formulas.
Numerics
Crank–Nicolson solver, benchmark circle test, exported CSV results, and verification workflow.
Outputs
Research PDFs, Python code, tables, and plots for error decay and runtime tradeoffs.
№2. From Cello Acoustics to Mathematical Wave Models
Cello acoustics modeled as wave components: spectrum, harmonics, envelope, timbre. Turning sound into mathematical wave models and clean visualizations.
Project overview
Signal analysis and wave-based modeling of cello sound, with explainable visual outputs.
Signal
Fourier
Modeling
Visualization
Physics
Music
Input
Audio recordings (cello tones, dynamics, articulations)
Extraction
Spectrum, harmonics, envelope, timbre descriptors
Math model
Wave components, parameter fitting, structure inference
Output
Readable plots + explanations + reproducible steps
What’s inside the PDF
Method
How the signal is processed step-by-step and why the features matter.
Results
Visual wave models, frequency maps, timbre structure, comparisons.
Roadmap
Next steps: datasets, robustness, publication-ready pipeline.