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A computer-implemented method for accurately estimating plasma velocities on the photosphere based on magnetic field data from vector magnetograms. Spatial and temporal derivatives of the magnetic field components are computed and a structure tensor containing terms that specifically include the horizontal magnetic field components is constructed. The structure tensor is convolved with a window function and a least-squares solution based on the convolved structure tensor is found. The solution includes the plasma velocities in the horizontal and vertical directions at the center of the window.