Researchers discover algorithm to create shapes that roll down pre-determined paths
In an accompanying article, Elisabetta Matsumoto, post-doctoral fellow at the School of Physics, Georgia Institute of Technology, and Henry Segerman, assistant professor at the Department of Mathematics, Oklahoma State University, said:
"This approach is surprising, and suggests that there should be a precise mathematical statement saying exactly when a two-period trajectoid exists. The authors provide an example curve that doesn’t work, but also show that tiny modifications to that curve make it work. They conjecture that paths that don't work are infinitely rare. It therefore seems likely that any designer wanting to use a trajectoid in a real-world application would not run into problems in constructing one.
"In quantum computing, this representation could be used to control the evolution of a quantum bit – the basic unit of quantum information, which can be encoded in spin," they said. A similar technique could help reduce unwanted noise in medical magnetic resonance imaging."Trajectoids that have been engineered to control the spin dynamics – and therefore the magnetic fields – in these devices could be used to help separate useful signals from noise," the commentators said.
"Whether or not these applications materialize, Sobolev and colleagues' algorithm offers an insightful answer to the problem of how to encode an object's trajectory using its shape alone," they added. ®
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