Research offers insight into how snakes move by bending and twisting out of the plane, into the third dimension.

Coordinated behaviors like swarming – from ant colonies to schools of fish – are found everywhere in nature. Researchers at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have given a nod to nature with a next-generation robot system that’s capable of movement, exploration, transport and cooperation.

The concept of constructing a self-supporting structure made of rods — without the use of nails, ropes, or glue — dates back to Leonardo da Vinci. In the Codex Atlanticus, da Vinci illustrated a design for a self-supporting bridge across a river, which can be easily demonstrated using toothpicks, matches, or chopsticks. However, this design is fragile — pulling one of the rods or pushing the bridge from below can cause it to collapse.

Researchers show how changes in cellular activity can drive changes in embryonic development.

Researchers combine physics and machine learning to use Pollock’s drip paint technique for quick and accurate 3D printing.

A scientist who has studied falling playing cards, coiling rope and other phenomena has now analyzed what transforms a carpenter’s tool into a sonorous instrument.

The Harvard professor formed a team to solve a riddle stumping many exasperated parents: What’s the most painless way to brush tangled hair?

Insights on centuries-old folk instrument is underpinned by a mathematical principle that may pave the way for high-quality resonators for sensing, electronics and more.

Researchers develop a mathematical understanding of detangling that could be used for textile manufacturing, robotic hairdressers

Researchers from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have developed a shape-shifting material that can take and hold any possible shape, paving the way for a new type of multifunctional material that could be used in a range of applications, from robotics and biotechnology to architecture.

Researchers in the US have used the physics of singularities to study the recess, or cusp, that forms around the stalk of an apple.

Researchers develop a mathematical model to explain the complex architecture of termite mounds

Platform could be used for self-cleaning surfaces and other applications

From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

Researchers use geometry and dynamics to better understand tissue organization.

Research sheds light on the underlying mechanics of soft filaments

Complex lattices that change in response to stimuli open a range of applications in electronics, robotics, medicin

A mathematical model created to more effectively prevent protein clumping, widely thought to underlie diseases like Parkinson’s, found that different potential treatments work best at different disease stages

Mechanical cues play critical role in shaping form and function

Mathematical framework turns any sheet of material into any shape using kirigami cuts

Insights into treatments for protein aggregation diseases from control theory and chemical kinetics

Researchers develop method to control the rigidity of structures through origami folds

Shedding light on the principles of termite mound size and shape with a model coupling insect behavior and environmental remodeling

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Researchers explore how bees collaborate to stabilize swarm clusters

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Researchers engineered a cell-like structure that harnesses photosynthesis to perform designer reactions

Researchers develop simple device to recreate complex birdsong

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The distinctive troughs and crests of the human brain are actually not present in most animal brains; highly folded brains are seen only in a handful of species, including some primates, dolphins, elephants and pigs. In humans, folding begins in fetal brains around the 20th week of gestation and is completed only when the child is about a year and a half.

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​Simple origami fold may hold the key to designing pop-up furniture, medical devices and scientific tools

Of the diversity of living form, Charles Darwin said, “It is enough to drive the sanest man mad.” A century and a half later, how can we quantify, understand and predict this variety? How might we control it? Motivated by biological observations on scales ranging from molecular to histological, L. Mahadevan will explain how a combination of biological and physical experiments, together with mathematical models and computations, begin to unravel the physical basis for morphogenesis. He will go on to explore how these pan-disciplinary problems enrich the origins of this topic, creating new questions in mathematics, physics and biology.

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Planning to have roast turkey at Christmas? You’ll be glad to hear that physicists have revealed exactly how to carve it – using jelly and a fishing line.

Biological movements are brought about in various ways, and not all of these involve the action of motor proteins. Apart from motor proteins, biological movements can be brought about by components that act like springs and ratchets. Biological springs store potential energy in various protein filament conformations, while biological ratchets act by biasing random Brownian motion and turning it into directional polymerization.

From a mismatch in growth, a flower blooms

Physicists reveal forces at work in the blossoming of a lily.

Folds on the surface of soft materials are shown to be a consequence of a nonlinear instability

Cause behind the characteristic shape of a long leaf revealed

What the ruck?—The physics of a bump in a rug
Not one, but two papers that examine the physics of a bump in a rug have …

Applied Mathematician | Class of 2009

Investigating principles underlying the behavior of complex systems to address such accessible, but vexing, questions as how flags flutter, how skin wrinkles, how Venus flytraps snap closed.

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Simple curiosities compel scientist - 2008-10-27 22:25:10

L. Mahadevan smiled at the question, which was: “What, exactly, do you do?” It is, on the surface, a simple question, but for Mahadevan the answer could lead many places. Or, maybe, that’s the answer, that Mahadevan, a 43-year-old professor at Harvard, studies seemingly simple, everyday questions,  “I am a wanderer, … and too curious about too many things, …. “

How paint dries, the way flags flutter, how Nature discovered origami, and other marvels of the physical world.

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The wrinkling in an elephant’s trunk and in billionth-of-a-meter nanotubes proceed from the same physical principles. The oscillations and flutters that agitate a piece of paper when you blow on it operate by mechanisms similar to those that caused an improperly designed bridge to tragically, and famously, collapse. Watch demonstrations by applied mathematician Lakshminarayanan Mahadevan, whose curiosity and analytical prowess combine to identify and then explain phenomena such as the vexing problem of folding up a map (to which nature has invented a brilliant solution).

Finding Physics in Everyday Objects from Harvard Magazine on Vimeo.

Here’s a seasonal news story I just wrote for Nature, which will appear (in edited form) in the last issue of the year. I gather, incidentally, that the original text of the ‘Arabian Nights’ doesn’t specify that the carpet flies as such, but only that anyone who sits on it is transported instantly to other lands.

A theoretical study of the way skin, apple peel, and bedsheets wrinkle won Mahadevan “a share” of this year’s Ig Nobel Prize in Physics. He “celebrated” this with a ditty and an essay-let:

The Ignobility of Wrinkles

Wrinkle, wrinkle on my skin

How, I wonder, did you begin ?

By sagging, and swelling and shrinking too

While stretching and bending were mixed into a brew

Till ahah, a formula that fits on a pin

How infinitely familiar and yet how far from being understood our immediate environment is!   No one reminds us of this everyday more than children- and so I thank them all, and in particular, our own two, Kausalya and Aditya.

Wrinkle, wrinkle on my skin

Where, I wonder,  did I sin ?

Celebrated in art and drapery

Until ahah, pruned by  surgery

And then, just a has-been !

I am glad that this little piece of work has amused you, as it did us. I started looking at the problem of wrinkling a few years ago, noticing as you have, that these nuisances appear everywhere –  indeed you too will see more of them as you grow older, so you had better get used to them! I had obtained a simple mathematical formula for the size of wrinkles in various situations, and on talking with my former postdoctoral fellow, Enrique Cerda, found that he had independently obtained some of the same results. So we wrote a paper that is one of those cited generalizing these ideas. Later, with others, I explained how wrinkles appear in nanotubes, elephant trunks, and even the lithosphere, the skin of our planet – of course then we call them mountains.

This little problem serves, I think, to teach us how infinitely familiar and yet how far from being understood, our immediate environment is. No one reminds us of this everyday more than children – and so I thank them all, young and old!

Curiosity is what underlies science which is now even part of our culture as this part parody, part revue that is the Ignobel proves!  And like any other cultural activity, such as art and music, it can be and indeed it should be, unapologetically fun.  It is fun to figure out how things work, at any and all levels,  ignoring the artificial hierarchy on the supposed importance of the questions we ask – after all, Nature never imposes one!   A quote by the English lexicographer and man of letters, Samuel Johnson (1709-84) may be apt: “Vulgar and inactive minds confound familiarity with knowledge, and conceive themselves informed of the whole nature of things when they are shown their form or told their use.”

May we long continue the tradition of celebrating da mental fun in the mundane!

L. Mahadevan

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Physicists make ripples with their “magic carpet” - 2007-08-19 19:00:01

Cereal Science: Why Floating Objects Stick Together

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• Scientists Create ‘Dry’ Water Droplets, Scientific American, 21 June 2001

Self organized Origami - 2005-08-19 19:00:01

Origami May Be an Art, but Nature Got There First

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• Naturkunde: Biologie des Origami, June 15, 2005

Flutter of a flag - 2005-02-19 19:00:02

The flutter of a flag in a gentle breeze, or the flapping of a sail in a rough wind are commonplace and familiar observations of a rich class of problems involving the interaction of fluids and structures, of wide interest and importance in science and engineering. In a recent study, we studied the mechanism that leads to this instability using a combination of analysis and scaling that lead us to a relatively simple theory for the critical velocity for the onset of flutter and the frequency of flapping.

Image courtesy of M. Argentina

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• “What it takes to get in a flap”, The Guardian, 3 February 2005
• “Kármánsche Wirbelstraßen bringen Fahnen in Schwung”, Die Welt, 14 February 2005

The rapid closure of the carnivorous plant Venus flytrap (Dionaea muscipula) is one of the fastest motions (typically 100 ms) in the plant kingdom and led Darwin to describe the plant as “one of the most wonderful in the world.”

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• “Researchers explore mystery, and say gotcha”, Boston Globe, 27 January 2005
• “How a Venus flytrap snaps up its victims”, New Scientist, 29 January 2005
• “Sharing secrets of the Venus flytrap”, Harvard Gazette, 26 January 2005
• Venus flytrap plants use a built-in snap, MSNBC, 26 January 2005
• Venus Flytrap’s Speed Secret Revealed, Live Science, 26 January 2005
• Secret of the Venus Fly Trap Revealed, 27 January 2005
• Scientists discover secret of venus flytrap’s snap, ABC News Online, 27 January 2005
• Harvard scientists discover how the venus flytrap snaps, Eureka Alert, 26 January 2005
• How a Venus flytrap plant catches bugs, Scripps Howard News Service, 26 January 2005
• In a Snap: Leaf geometry drives Venus flytrap’s bite, Science News, 29 January 2005
• Why, Boston.com, 2 February 2005
• “What it takes to get in a flap”, The Guardian, 3 February 2005
• Let’s Keep Asking Why, The Boston Globe, 3 February 2005
• Venus Flytrap – Leader in Biometrics? Newswatch 50
• Plants teach big lessons about how to get going, 16 June 2005

Next time you are trapped inside a neon-lit changing room trying on a possible clothes purchase, you might think of calling a mathematician, rather than a sales assistant, to help work out why those trousers aren’t hanging just right. Researchers from Harvard University and the University of Santiago in Chile have begun to solve the equations governing the way in which fabric drapes, and hope that their work will help make shopping a little easier in the future.

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• https://plus.maths.org/content/os/latestnews/jan-apr04/draping/index

Researchers from the University of Cambridge in England and Lehigh University have shown that it is possible to make a strip of hydrogel mimic the movements of a snail, inchworm, and snake.

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• RANDOM SAMPLES, Science Magazine, 2 January 2004

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• Physik des Faltenwurfs. Altbekannter Lebensretter, Die Zeit, 27 February 2003
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Aphids Marbles - 2002-07-19 19:33:40

Insects provide examples of many cunning stratagems to cope with the challenges of living in a world dominated by surface forces. Despite being the current masters of the land environment, they are at constant risk of being entrapped in liquids, which they prevent by having waxy and hairy surfaces. The problem is particularly acute in an enclosed space, such as a plant gall. Using secreted wax to efficiently parcel and transport their own excrement, aphids were able to solve this problem 200 Myr ago. Here, we report on the physical and physiological significance of this ingenious solution. The secreted powdery wax has three distinct roles: (i) it is hydrophobic, (ii) it creates a microscopically rough inner gall surface made of weakly compacted wax needles making the gall ultra-hydrophobic, and (iii) it coats the honeydew droplets converting them into liquid marbles, that can be rapidly and efficiently moved.

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• Aphids with attitude: an army of real-life adolescent clones, Science News 6 July 2002

When a bubble of air rises to the top of a highly viscous liquid, it forms a dome-shaped protuberance on the free surface. Unlike a soap bubble, it bursts so slowly as to collapse under its own weight simultaneously, and folds into a wavy structure. This rippling effect occurs for both elastic and viscous sheets, and a theory for its onset is formulated. The growth of the corrugation is governed by the competition between gravitational and bending (shearing) forces and is exhibited for a range of densities, stiffnesses (viscosities), and sizes—a result that arises less from dynamics than from geometry, suggesting a wide validity. A quantitative expression for the number of ripples is presented, together with experimental results that support the theoretical predictions.

What do mountains, wrinkled slacks and a crushed soda can have in common? The answer: all have been crumpled

When a stiff rectangular card is dropped in still air with its long axis horizontal, it often settles into a regular mode of motion; while revolving around its long axis it descends along a path that is inclined to the vertical at a nearly constant angle. We show experimentally that the tumbling frequency ΩΩ of a card of length l,l, width w and thickness d (l≫w≫d)(l≫w≫d) scales as Ω∼d1/2w−1,Ω∼d1/2w−1, consistent with a simple dimensional argument that balances the drag against gravity.

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Physicists Study the Honeybee For Clues to Complex Problems