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Fourier Transform 🤝 Spherical Harmonics = Viral Budding Geometry Viral Budding of an Infected Cell

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Mathelirium

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11,817 görüntüleme • 4 ay önce •via X (Twitter)

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Spherical Harmonics 🤝 Fourier Transform I’m modeling the cell surface as a time-varying field u(θ,φ). Budding is energy shifting into higher angular frequencies. Decompose u into spherical harmonics (the Fourier basis on a sphere), evolve the coefficients aₗₘ(t) where growth/smoothing is clean, then inverse-transform back into a breathing, budding 3D surface. #SphericalHarmonics #FourierTransform #HarmonicAnalysis #SpectralMethods #SignalProcessing #AppliedMath #MathAnimation #ScientificVisualization #Biophysics
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Spherical Harmonics 🤝 Fourier Transform I’m modeling the cell surface as a time-varying field u(θ,φ). Budding is energy shifting into higher angular frequencies. Decompose u into spherical harmonics (the Fourier basis on a sphere), evolve the coefficients aₗₘ(t) where growth/smoothing is clean, then inverse-transform back into a breathing, budding 3D surface. #SphericalHarmonics #FourierTransform #HarmonicAnalysis #SpectralMethods #SignalProcessing #AppliedMath #MathAnimation #ScientificVisualization #Biophysics

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This video presents a recent breakthrough called the Sparse Fourier Transform (SFT). This algorithm yields an exponential speed-up over the celebrated Fast Fourier Transform (FFT) when asked to extract a small number of dominant Fourier coefficients.
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This video presents a recent breakthrough called the Sparse Fourier Transform (SFT). This algorithm yields an exponential speed-up over the celebrated Fast Fourier Transform (FFT) when asked to extract a small number of dominant Fourier coefficients.

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