Experiments and simulations present the tine transferring alongside the double helix from the clamped finish in direction of the free finish. Credit: Harvard SEAS
As anybody who has ever needed to brush lengthy hair is aware of, knots are a nightmare. But with sufficient expertise, most be taught the methods of detangling with the least quantity of ache—begin on the backside, work your approach as much as the scalp with quick, mild brushes, and apply detangler when essential.
L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics, discovered the mechanics of combing years in the past whereas brushing his younger daughter’s hair.
“I recall that detangling spray appeared to work generally, however I nonetheless needed to be cautious to comb gently, by ranging from the free ends,” mentioned Mahadevan. “But I used to be quickly fired from the job as I used to be not very affected person.”
While Mahadevan misplaced his position as hairdresser, he was nonetheless a scientist and the topology, geometry and mechanics of detangling posed fascinating mathematical questions which can be related to a variety of functions together with textile manufacturing and chemical processes corresponding to polymer processing.
In a brand new paper, printed within the journal Soft Matter, Mahadevan and co-authors Thomas Plumb Reyes and Nicholas Charles, discover the arithmetic of combing and clarify why the brushing approach utilized by so many is the best methodology to detangle a bundle of fibers.
To simplify the issue, the researchers simulated two helically entwined filaments, somewhat than a complete head of hair.
“Using this minimal mannequin, we examine the detangling of the double helix through a single stiff tine that strikes alongside it, leaving two untangled filaments in its wake,” mentioned Plumb-Reyes, a graduate pupil at SEAS. “We measured the forces and deformations related to combing after which simulated it numerically.”
“Short strokes that begin on the free finish and transfer in direction of the clamped finish take away tangles by making a move of a mathematical amount referred to as the ‘hyperlink density’ that characterizes the quantity that hair strands which can be braided with one another, in keeping with simulations of the method,” mentioned Nicholas Charles, a graduate pupil at SEAS.
The researchers additionally recognized the optimum minimal size for every stroke—any smaller and it could take perpetually to comb out all of the tangles and any longer and it could be too painful.
The mathematical rules of brushing developed by Plumb-Reyes, Charles and Mahadevan have been lately utilized by Professor Daniela Rus and her staff at MIT to design algorithms for brushing hair by a robotic.
Next, the staff goals to review the mechanics of brushing curlier hair and the way it responds to humidity and temperature, which can result in a mathematical understanding of a truth each particular person with curly hair is aware of: by no means brush dry hair.
Untangle your hair with assist from robots
More data:
Thomas B. Plumb-Reyes et al, Combing a double helix, Soft Matter (2022). DOI: 10.1039/D1SM01533H
Provided by
Harvard John A. Paulson School of Engineering and Applied Sciences
Citation:
Tear-free brushing? All you want is math (2022, April 13)
retrieved 13 April 2022
from https://phys.org/information/2022-04-tear-free-math.html
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