The brush without tears? All you need is math

The brush without tears?  All you need is math

Experiments and comparisons show the movement of the tin in the double helix from the fixed end to the free end. Found: Harvard SEAS

As many people in search of long hair know, knots are a dream come true. But with great foresight, and most tricks work with minimal pain – start at the bottom, work your way up to the head with short, slow strokes, and install a detangler if necessary. .

L. Mahadevan, Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics, has studied the mechanics of combining in recent years while brushing hair. his young daughter.

“I remember doing the detangling spray sometimes, but I had to be careful to mix it slowly, starting from the free effects,” Mahadevan said. “But I was immediately fired because I was not very patient.”

Although Mahadevan lost his career as a hairdresser, he was a scientist and the topology, geometry and mechanics of detangling raised interesting mathematical questions about the nature of the applications. relating to textile processing and chemical processes such as polymer processing.

On a new paper, published in a journal Soft, Mahadevan and co -authors Thomas Plumb Reyes and Nicholas Charles explore the mathematics of joining and explain why the brushing method used by many people is the most effective way to remove it. to a fiber group.

To solve the problem, the researchers compared two helically entwined filaments, rather than the entire head of hair.

“Using this kind of small model, we learn how to open a double helix by a single rigid tin moving over it, leaving two unopened filaments in its path. ”said Plumb-Reyes, a graduate student at SEAS. “We measured the strengths and deformations associated with the joint and then compared it numerically.”

“The short keys that start at the free end and move to the fixed end open the elbows by creating a flow of mathematical mass called the‘ link density ’that represents the many of the hair strands are woven into each other, according to simulations of the process, ”said Nicholas Charles, a graduate student at SEAS.

The researchers also found the best minimum length for each stroke – the smaller and longer the joint length of each stroke the more painful it was.

The mathematical principles of dyeing were used by Plumb-Reyes, Charles and Mahadevan by Professor Daniela Rus and his team at MIT to develop algorithms for dyeing hair by a robot.

Next, the team hopes to learn the mechanics of curling hair and how it responds to humidity and heat, which can lead to a mathematical understanding of the reality that everyone with curly hair: do not brush dry hair.


Remove your hair with the help of robots


More information:
Thomas B. Plumb-Reyes et al. Soft material (2022). DOI: 10.1039 / D1SM01533H

Presented by Harvard John A. Paulson School of Engineering and Applied Sciences

Directions: Brush without tears? Just the math you want (2022, April 13) downloaded on 13 April 2022 from https://phys.org/news/2022-04-tear-free-math.html

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