Burgers shock · 3d retro graphics

{"slug":"burgers","number":"31","title":"Burgers shock","era":"Hopf · 1950 · 2026 illustration","section":"modern","provenance":"documented","reference":{"label":"E. Hopf, \"The partial differential equation u_t + uu_x = μu_xx\", Communications on Pure and Applied Mathematics 3, 1950","url":"https://doi.org/10.1002/cpa.3160030302"},"summary":"Inviscid Burgers. Characteristics cross at a predicted T*.","description":"u_t + u u_x = 0 with u₀ = −amp sin(x). The most negative slope is −amp, so the classical solution ends at T* = 1/amp. Each particle keeps its speed; the x–t plot is those lines, and they cross at T*. ‖∂x u‖∞ = 1/(T*−t) until it leaves the top of the chart. After T* the parametric wave is multi-valued; the vertical mark is the entropy shock. This one actually blows up. Pointer sets the phase.","apis":["Canvas 2D","Pointer Events","requestAnimationFrame","matchMedia"],"tags":["pde","shock"],"hasGlsl":false,"interaction":"Move the pointer left or right to shift the phase of the sine.","url":"https://3d-retro.com/experiments/burgers","example_url":"https://3d-retro.com/examples/burgers.html","api_url":"https://3d-retro.com/api/v1/experiments/burgers","html":"\n\n\n \n \n \n \n Burgers shock · 3d retro graphics\n \n\n\n

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