It would take nearly a century for mathematicians to prove him right. In the early 1930s, Jesse Douglas and Tibor Radó independently showed that the answer to the “Plateau problem” is yes: For any closed curve (your wire frame) in three-dimensional space, you can always find a minimizing two-dimensional surface (your soap film) that has the same boundary. The proof later earned Douglas the first-ever Fields Medal.
Since then, mathematicians have expanded on the Plateau problem in hopes of learning more about minimizing surfaces. These surfaces appear throughout math and science — in proofs of important conjectures in geometry and topology, in the study of cells and black holes, and even in the design of biomolecules. “They’re very beautiful objects to study,” said Otis Chodosh (opens a new tab) of Stanford University. “Very natural, appealing and intriguing.”
Mathematicians now know that Plateau’s prediction is categorically true up through dimension seven. But in higher dimensions, there’s a caveat: The minimizing surfaces that form might not always be nice and smooth, like the disk or hourglass. Instead, they might fold, pinch or intersect themselves in places, forming what are known as singularities. When minimizing surfaces have singularities, it becomes much harder to understand and work with them.
Liftoff of the Sentinel-6B satellite is scheduled for 12:21 a.m. ET on Monday (Nov. 17).
Intel might have been lagging significantly behind in the chip business, but when it comes to advanced packaging, the firm has competitive options.
Ever since high-performance computing became the norm in the industry, the demand for robust compute solutions has increased at a pace that surpasses the improvements brought about by relying solely on Moore’s Law. But, to meet the industry’s demand, manufacturers like AMD and NVIDIA adopted advanced packaging technologies, which essentially brought in ‘multiple chips’ in a single package, boosting chip densities as well as platform performance. Advanced packaging solutions have become an integral part of the supply chain, and TSMC has dominated this segment for several years now, but this could change.
In new job listings by Qualcomm and Apple, it appears that both companies are seeking talent with expertise in Intel’s EMIB advanced packaging technology. The Cupertino giant is hiring a DRAM packaging engineer, requiring experience in “advanced packaging technologies such as CoWoS, EMIB, SoIC, and PoP”. Similarly, Qualcomm is recruiting a Director of Product Management for its Data Center Business Unit, which requires familiarity with Intel’s EMIB as well, indicating that interest is defintely there.
Cascaded nonlinear optics has long enabled advances in short-wavelength generation, but equivalent approaches for long wavelengths remain underdeveloped. Here, the authors demonstrate a chip-based lithium niobate platform that delivers tunable mid-infrared light, opening new possibilities for sensing, spectroscopy, and communications.
Every year, 12 million people worldwide suffer a stroke; many die or are permanently impaired. Currently, drugs are administered to dissolve the thrombus that blocks the blood vessel. These drugs spread throughout the entire body, meaning a high dose must be administered to ensure that the necessary amount reaches the thrombus. This can cause serious side effects, such as internal bleeding.
Since medicines are often only needed in specific areas of the body, medical research has long been searching for a way to use microrobots to deliver pharmaceuticals to where they need to be: in the case of a stroke, directly to the stroke-related thrombus.
Now, a team of researchers at ETH Zurich has made major breakthroughs on several levels. They have published their findings in Science.