Overview of Laplacian spherical harmonics, explaining their definition as functions on a sphere intrinsically linked to Laplace's equation and highlighting their mathematical foundations, including orthogonality and completeness. It traces their historical development from celestial mechanics to modern physics.
The sources emphasize their versatility in solving partial differential equations with spherical symmetry and showcase their extensive applications across fields such as quantum mechanics, geophysics, computer graphics, astronomy, acoustics, medical imaging, and materials science.
Finally, the texts touch upon computational aspects, including the challenges of numerical stability and the Gibbs phenomenon, and explore recent research and potential future directions, particularly in synergy with machine learning.
Popular Podcasts
Bookmarked by Reese's Book Club
Welcome to Bookmarked by Reese’s Book Club — the podcast where great stories, bold women, and irresistible conversations collide! Hosted by award-winning journalist Danielle Robay, each week new episodes balance thoughtful literary insight with the fervor of buzzy book trends, pop culture and more. Bookmarked brings together celebrities, tastemakers, influencers and authors from Reese's Book Club and beyond to share stories that transcend the page. Pull up a chair. You’re not just listening — you’re part of the conversation.
Dateline NBC
Current and classic episodes, featuring compelling true-crime mysteries, powerful documentaries and in-depth investigations. Follow now to get the latest episodes of Dateline NBC completely free, or subscribe to Dateline Premium for ad-free listening and exclusive bonus content: DatelinePremium.com
Stuff You Should Know
If you've ever wanted to know about champagne, satanism, the Stonewall Uprising, chaos theory, LSD, El Nino, true crime and Rosa Parks, then look no further. Josh and Chuck have you covered.