Unique 3D printed shapes shook Kelvin’s 150 years of mathematical theory

Researchers at Wesleyan University used3D printingTechnology reassessed a long-standing theory put forward by the British mathematician Lord Kelvin 150 years ago. Essentially, Kelvin predicts that a spherical shape with blades is called an “isotropic helix”. If immersed in a fluid, it will behave very unusually and look the same from any angle. At the same time” Naturally “rotate.” Until recently, the professor’s ideas were difficult to evaluate, but using Form 2 3D printingmachine, The team at Wesleyan College has now produced an ultra-accurate sample, which may prove that it needs to be modified after all.

“We treat him[开尔文]Of the design3D printingThe realization was found to have no detectable translation-rotation coupling in experiments, although the point group symmetry of the particles allows coupling,” the team said in their paper. “The isotropic spiral body predicted by Kelvin[因此]Exist, but only as a weak breakthrough in the symmetry of the non-interacting blades. ”

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Kelvin’s “Isotropic Spirograph” Theory

As early as 1871, the pioneer Lord Kelvin, who was famous for the temperature scale named after him, proposed that if created properly, an isotropic spiral body would spin like a propeller when immersed in a viscous fluid. Therefore, in practice, this shape is like a sphere, regardless of its direction, it has the same resistance, but it will also rotate due to its built-in fins, some of which have an angle of 45° and some of which have an angle of 90°.

In theory, this spiral behavior contradicts the isotropic principle that supports the idea of ​​continuous rotational symmetry, but Kelvin has always insisted that fins of this shape can offset this effect. As far as they are concerned, the Wesleyan team believes that this theory has been discussed in textbooks for decades, but they could not find any evidence for new research, which means that previous research was limited by existing equipment.

“You have to guess that someone else has tried this in 150 years-in Kelvin’s original paper, it even sounds like he did,” Greg Voss of Wesleyan University explained to The New Scientist. “I suspect that people have tried to make these particles, but they are limited by the defects in the manufacturing process, so they have not published at all, so the hypothesis of this behavior has always been with us.”

Scientists’ 3D models of spirochetes and experimental results. The picture comes from Greg Voth of Wesleyan University.

Revised 150-year-old papers

To test Kelvin’s suggestion, researchers at Wesleyan University decided3D printingFive slightly different isotropic spirals, and then throw them into a silicone oil tank. Interestingly, all five prototypes sank directly into the bottom of the fuel tank and did not exhibit the expected “translation-rotation coupling” spiral motion, even though they had the same discrete symmetry suggested by Kelvin.

In order to assess what went wrong, the team then performed a hydrodynamic analysis of their test devices and found that the non-interactive blades of these devices caused the rotation effect to “disappear”. Although the scientists managed to determine the connection between the movement and rotation of the particle and proved this element of Kelvin’s theory is correct, any coupling effect is actually too small to be seen with the naked eye.

“Our small-scale discovery of chiral coupling helps explain why the measurement results of isotropic spirochetes are not published.” Therefore, the researchers concluded that the weak effect of this force may be the reason for the lack of public research in this field. Their research provides “deep insights into quantum physics.” Looking to the future, scientists say, “The work of quantifying and optimizing isotropic spirochetes may also be fruitful.” They are now considering how the reformed shape can help to clearly prove Kelvin’s theory.

“We did not find any translation-rotation coupling in the experiment. This raises the question of whether Lord Kelvin’s original argument is flawed,” the team concluded in their paper. “But considering the hydrodynamic interaction between the blades, it shows a non-zero translation-rotation coupling. The coupling is tiny, but it still exists.”

AM and the laws of physics

Surprisingly, the experiments conducted at Wesleyan University do not represent3D printingIt was used to test established physics principles for the first time. Earlier this month, Youtuber’Integza’3D printingA copy of the wind car that “breaks the laws of physics” was created to help clarify the long-standing debate of “downwind is faster than the wind” or “DWFTTW”. This decade-long controversy can be traced back to 2010, when researchers discovered that a wind car was driving on the runway nearly three times faster than the wind that pushed it. Although Derek Mueller, the host of the popular Veritasium Youtube channel, insisted that it was indeed possible, Professor Alex Kusenko of UCLA disagreed, so the two bet $10,000 that they could Prove that the other party is wrong.

In the end, with the help of Xyla Foxlin, who is also a Youtuber, Muller was able to fully explain his reason for DWFTTW and won the bet, which Integza did later. Use Elegoo Mars Pro 2 3D printingIntegza has been able to produce a replica of the 2010 car design and deploy it on a treadmill to show how the relative speed of the wind striking its blades effectively makes it “faster than the wind.”

This Youtuber kindly provided his model that clearly violates physics to everyone through Thingiverse for freedownload.

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