Scientific Computing Demo

Gravitational Lensing Simulator

A visual toy model for exploring how mass, distance, alignment, and observing frequency influence light bending, Einstein rings, magnification, and relative time delay.

Interactive optics model

Geometric Optics ↔ Wave Optics

Switch between ray-path intuition and interference-style structure to see why coherent signals can carry more information than a brightness-only view.

View the paper

Lens mass 45 solar masses Source distance 6.0 kpc Observer distance 4.0 kpc Alignment 0.32 arcsec Observing frequency 1.4 GHz

Einstein radius 0.74 arcsec

Magnification 2.4x

Relative delay 18.2 ms

Image split 1.7 arcsec

Paper observables

Frequency-Domain Signature

Open source paper

Channel width

Delta t grav --

Delta phi --

Fringe spacing --

Optics regime --

Channel test --

Plasma distinction Achromatic delay

Core claim sensitivity

Δφ = 2π ν Δt_grav , Δν ≈ 1 / Δt_grav

Δt_grav ∝ M × θ_split( D_s , D_o , β ) × G( D_o ) ; W_chan samples Δν

Heat shows which current parameter changes most affect the paper observable.

Gravitational delay is achromatic; phase grows linearly with observing frequency. Plasma dispersion has a different frequency dependence.

3D Web Viewer

Rotatable Lensing Geometry

Orbit the source, lens, observer, curved light paths, and wavefronts as a true 3D scene.

Lens mass 45 solar masses Source distance 6.0 kpc Observer distance 4.0 kpc Alignment 0.32 arcsec Observing frequency 1.4 GHz

dominant path secondary path lens plane

Alignment Matters

Near-perfect alignment produces ring-like symmetry. Offset sources split into brighter and dimmer apparent images.

Mass Changes Curvature

Higher lens mass increases bending strength, magnification, apparent separation, and relative path delay.

Wave View Adds Texture

The wave optics mode emphasizes interference-style structure useful for thinking about coherent signals.