Duke Research Blog

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Category: Mathematics Page 1 of 6

Leaving the Louvre: Duke Team Shows How to Get out Fast

Students finish among top 1% in 100-hour math modeling contest against 11,000 teams worldwide


Imagine trying to move the 26,000 tourists who visit the Louvre each day through the maze of galleries and out of harm’s way. One Duke team spent 100 straight hours doing just that, and took home a prize.

If you’ve ever visited the Louvre in Paris, you may have been too focused on snapping a selfie in front of the Mona Lisa to think about the nearest exit.

But one Duke team knows how to get out fast when it matters most, thanks to a computer simulation they developed for the Interdisciplinary Contest in Modeling, an international contest in which thousands of student teams participate each year.

Their results, published in the Journal of Undergraduate Mathematics and Its Applications, placed them in the top 1% against more than 11,000 teams worldwide.

With a record 10.2 million visitors flooding through its doors last year, the Louvre is one of the most popular museums in the world. Just walking through a single wing in one of its five floors can mean schlepping the equivalent of four and a half football fields.

For the contest, Duke undergraduates Vinit Ranjan, Junmo Ryang and Albert Xue had four days to figure out how long it would take to clear out the whole building if the museum really had to evacuate — if the fire alarm went off, for instance, or a bomb threat or a terror attack sent people pouring out of the building.

It might sound like a grim premise. But with a rise in terrorist activity in Europe in recent years, facilities are trying to plan ahead to get people to safety.

The team used a computer program called NetLogo to create a small simulated Louvre populated by 26,000 visitors, the average number of people to wander through the maze of galleries each day. They split each floor of the Louvre into five sections, and assigned people to follow the shortest path to the nearest exit unless directed otherwise.

Computer simulation of a mob of tourists as they rush to the nearest exit in a section of the Louvre.

Their model uses simple flow rates — the number of people that can “flow” through an exit per second — and average walking speeds to calculate evacuation times. It also lets users see what happens to evacuation times if some evacuees are disabled, or can’t push through the throngs and start to panic.

If their predictions are right, the team says it should be possible to clear everyone out in just over 24 minutes.

Their results show that the exit at the Passage Richelieu is critical to evacuation — if that exit is blocked, the main exit through the Pyramid would start to gridlock and evacuating would take a whopping 15 minutes longer.

The students also identified several narrow corridors and sharp turns in the museum’s ground floor that could contribute to traffic jams. Their analyses suggest that widening some of these bottlenecks, or redirecting people around them, or adding another exit door where evacuees start to pile up, could reduce the time it takes to evacuate by 15%.

For the contest, each team of three had to choose a problem, build a model to solve it, and write a 20-page paper describing their approach, all in less than 100 hours.

“It’s a slog fest,” Ranjan said. “In the final 48 hours I think I slept a total of 90 minutes.”

Duke professor emeritus David Kraines, who advised the team, says the students were the first Duke team in over 10 years to be ranked “outstanding,” one of only 19 out of the more than 11,200 competing teams to do so this year. The team was also awarded the Euler Award, which comes with a $9000 scholarship to be split among the team members.

Robin Smith – University Communications

Science in haiku: // Interdisciplinary // Student poetry

On Friday, August 2, ten weeks of research by Data+ and Code+ students wrapped up with a poster session in Gross Hall where they flaunted their newly created posters, websites and apps. But they weren’t expecting to flaunt their poetry skills, too! 

Data+ is one of the Rhodes Information Initiative programs at Duke. This summer, 83 students addressed 27 projects addressing issues in health, public policy, environment and energy, history, culture, and more. The Duke Research Blog thought we ought to test these interdisciplinary students’ mettle with a challenge: Transforming research into haiku.

Which haiku is your
favorite? See all of their
finished work below!

Eric Zhang (group members Xiaoqiao Xing and Micalyn Struble not pictured) in “Neuroscience in the Courtroom”
Maria Henriquez and Jake Sumner on “Using Machine Learning to Predict Lower Extremity Musculoskeletal Injury Risk for Student Athletes”
Samantha Miezio, Ellis Ackerman, and Rodrigo Aruajo in “Durham Evictions: A snapshot of costs, locations, and impacts”
Nikhil Kaul, Elise Xia, and Mikaela Johnson on “Invisible Adaptations”
Karen Jin, Katherine Cottrell, and Vincent Wang in “Data-driven approaches to illuminate the responses of lakes to multiple stressors”.

By Vanessa Moss

Overdiagnosis and the Future of Cancer Medicine

For many years, the standard strategy for fighting against cancer has been to find it early with screening when the person is still healthy, then hit it with a merciless treatment regimen to make it go away.

But not all tumors will become life-threatening cancers. Many, in fact, would have caused no issues for the rest of the patients’ lives had they not been found by screening. These cases belong to the category of overdiagnosis, one of the chief complaints against population-level screening programs.

Scientists are reconsidering the way to treat tumors because the traditional hit-it-hard approach has often caused the cancer to seemingly go away, only to have a few cells survive and the entire tumor roar back later with resistance to previously effective medicine.

Dr. Marc Ryser, the professor who gave this meaty talk

In his May 23 talk to Duke Population Health, “Cancer Overdiagnosis: A Discourse on Population Health, Biologic Mechanism and Statistics,” Marc Ryser, an assistant professor at Duke’s Departments of Population Health Sciences and Mathematics, walked us through how parallel developments across different disciplines have been reshaping our cancer battle plan. He said the effort to understand the true prevalence of overdiagnosis is a point of focus in this shift.

Past to Future: the changing cancer battle plan
Credit: Marc Ryser, edit: Brian Du

Ryser started with the longstanding biological theory behind how tumors develop. Under the theory of clonal sweeps, a relatively linear progression of successive key mutations sweeps through the tumor, giving it increasing versatility until it is clinically diagnosed by a doctor as cancer.

Clonal sweeps model, each shade is a new clone that introduces a mutation credit: Sievers et al. 2016

With this as the underpinning model, the battle plan of screen early, treat hard (point A) makes sense because it would be better to break the chain of progression early rather than later when the disease is more developed and much more aggressive. So employing screening extensively across the population for the various types of cancer is the sure choice, right?

But the data at the population level for many different categories of cancers doesn’t support this view (point B). Excluding the cases of cervical cancer and colorectal cancer, which have benefited greatly from screening interventions, the incidence of advanced cases of breast cancer and other cancers have stayed at similar levels or actually continued to increase during the years of screening interventions. This has raised the question of when screening is truly the best option.

Scientists are thinking now in terms of a “benefit-harm balance” when mass-screening public health interventions are carried out. Overdiagnosis would pile up on the harms side, because it introduces unnecessary procedures that are associated with adverse effects.

Thinking this way would be a major adjustment, and it has brought with it major confusion.

Paralleling this recent development on the population level, new biological understanding of how tumors develop has also introduced confusion. Scientists have discovered that tumors are more heterogeneous than the clonal sweeps model would make it appear. Within one tumor, there may be many different subpopulations of cancer cells, of varying characteristics and dangerousness, competing and coexisting.

Additional research has since suggested a more complex, evolutionary and ecological based model known as the Big Bang-mutual evolution model. Instead of the “stepwise progression from normal to increasingly malignant cells with the acquisition of successive driver mutations, some cancers appear to evolve more like a Big Bang, where the malignant ability is already concentrated in the founder cell,” Ryser said.

As the first cell starts to replicate, its descendants evolve in parallel into different subpopulations expressing different characteristics. While more research has been published in favor of this model, some scientists remain skeptical.

Ryser’s research contributes to this ongoing discussion. In comparing the patterns by which mutations are present or absent in cancerous and benign tumors, he obtained results favoring the Big Bang-mutual evolution model. Rather than seeing a neat region of mutation within the tumor, which would align with the clonal sweeps model, he saw mutations dispersed throughout the tumor, like the spreading of newborn stars in the wake of the Big Bang.

How to think about mutations within a tumor
credit: NASA

The more-complicated Big Bang-mutual evolution model justifies an increasingly nuanced approach to cancer treatment that has been developing in the past few years. Known as precision medicine (point C), its goal is to provide the best treatment available to a person based on their unique set of characteristics: genetics, lifestyle, and environment. As cancer medicine evolves with this new paradigm, when to screen will remain a key question, as will the benefit-harm balance.

There’s another problem, though: Overdiagnosis is incredibly hard to quantify. In fact, it’s by nature not possible to directly measure it. That’s where another area of Ryser’s research seeks to find the answers. He is working to accurately model overdiagnosis to estimate its extent and impact.

Going forward, his research goal is to try to understand how to bring together different scales to best understand overdiagnosis. Considering it in the context of the multiscale developments he mentioned in his talk may be the key to better understand it.

Post by Brian Du

Kicking Off a Summer of Research With Data+

If the May 28 kickoff meeting was any indication, it’s going to be a busy summer for the more than 80 students participating in Duke’s summer research program, Data+.

Offered through the Rhodes Information Initiative at Duke  (iiD), Data+ is a 10-week summer program with a focus on data-driven research. Participants come from varied backgrounds in terms of majors and experience. Project themes range  from health, public policy, energy and environment, and interdisciplinary inquiry.

“It’s like a language immersion camp, but for data science,” said Ariel Dawn, Rhodes iiD Events & Communication Specialist. “The kids are going to have to learn some of those [programming] languages like Java or Python to have their projects completed,” Dawn said.

Dawn, who previously worked for the Office of the Vice Provost for Research, arrived during the program’s humble beginnings in 2015. Data+ began in 2014 as a small summer project in Duke’s math department funded by a grant from the National Science Foundation. The following year the program grew to 40 students, and it has grown every year since.

Today, the program also collaborates with the Code+ and CS+ summer programs, with  more than 100 students participating. Sponsors have grown to include major corporations such as Exxonmobil, which will fund two Data+ projects on oil research within the Gulf of Mexico and the United Kingdom in 2019.

“It’s different than an internship, because an internship you’re kind of told what to do,” said Kathy Peterson, Rhodes iiD Business Manager. “This is where the students have to work through different things and make discoveries along the way,” Peterson said.

From late May to July, undergraduates work on a research project under the supervision of a graduate student or faculty advisor. This year, Data+ chose more than 80 eager students out of a pool of over 350 applicants. There are 27 projects being featured in the program.

Over the summer, students are given a crash course in data science, how to conduct their study and present their work in front of peers. Data+ prioritizes collaboration as students are split into teams while working in a communal environment.

“Data is collected on you every day in so many different ways, sometimes we can do a lot of interesting things with that,” Dawn said.  “You can collect all this information that’s really granular and relates to you as an individual, but in a large group it shows trends and what the big picture is.”

Data+ students also delve into real world issues. Since 2013, Duke professor Jonathan Mattingly has led a student-run investigation on gerrymandering in political redistricting plans through Data+ and Bass Connections. Their analysis became part of a 205-page Supreme Court ruling.

The program has also made strides to connect with the Durham community. In collaboration with local company DataWorks NC, students will examine Durham’s eviction data to help identify policy changes that could help residents stay in their homes.

“It [Data+] gives students an edge when they go look for a job,” Dawn said. “We hear from so many students who’ve gotten jobs, and [at] some point during their interview employers said, ‘Please tell us about your Data+ experience.’”

From finding better sustainable energy to examining story adaptations within books and films, the projects cover many topics.

A project entitled “Invisible Adaptations: From Hamlet to the Avengers,” blends algorithms with storytelling. Led by UNC-Chapel Hill grad student Grant Class, students will make comparisons between Shakespeare’s work and today’s “Avengers” franchise.

“It’s a much different vibe,” said computer science major Katherine Cottrell. “I feel during the school year there’s a lot of pressure and now we’re focusing on productivity which feels really good.”

Cottrell and her group are examining the responses to lakes affected by multiple stressors.

Data+ concludes with a final poster session on Friday, August 2, from 2 p.m. to 4 p.m. in the Gross Hall Energy Hub. Everyone in the Duke Community and beyond is invited to attend. Students will present their findings along with sister programs Code+ and the summer Computer Science Program.

Writing by Deja Finch (left)
Art by Maya O’Neal (right)

Biology by the Numbers

Michael C. Reed was trained as a pure mathematician, but from the start, he was, as he explained to me, a “closet physiologist.” He’s a professor of mathematics at Duke, but he’s always wondered how the body works.

Michael Reed in his office

Reed explains an example to me: women have elbows that are bent when their arms are straightened, but men do not. He rationalized his own explanation: women have wide hips and narrow shoulders; their bodies are designed so their arms don’t knock into their sides when they walk. (That basically ended up being the answer.)

Still, Reed never really explored his interest in physiology until he was 40 years old, when he realized that if he wanted to explore something, he should just do it. Why not? He had tenure by that point, so it didn’t really matter what his colleagues thought. He was interested in physiology, but was a mathematician. The obvious answer was mathematical biology.

Now he uses mathematics to find out how various physiological systems work.

In order to decide on a research project, he works with a biologist, Professor Fred Nijhout. They meet for two hours every day and work together. They have lots of projects, but they also just talk science sometimes. That’s how they get their ideas, mainly focusing on things in cell metabolism that have to do with important public health questions.

Reed has been investigating dopamine and serotonin metabolism in the brain, in a collaborative project with Nijhout and Dr. Janet Best, a mathematician at The Ohio State University.

Maybe better math is going to help us understand the human brain

As he explained to me, the brain isn’t like a computer; you don’t know how it works and there are a lot of systems in play. Serotonin is one of them. Low serotonin concentration is thought to be one of the causes of depression. There’s a biochemical network that synthesizes, packages, and transfers serotonin in the brain.

He told me that his work consists of making mathematical models for systems like this that consist of differential equations for concentrations of different chemicals. He then experiments with the system of differential equations to understand how the system works together. It’s not really something you can learn by having it explained to you, he told me. You have to learn through practice.

In a way, biology doesn’t seem like it would be the most compatible science, especially with math. But as Reed explained to me, “Math is easy because it’s very orderly and organized. If you work hard enough, you can understand it.” Biology, on the other hand, “is a mess.”

Everything in biology is linked to everything else in a system of connectedness that ends up all tangled together, and it can be hard to identify how something happens in the human body. But Reed applies math – an organized construct – to understand biological systems.

In the end, Reed does what he does because it’s how we — as human beings — work. He has no regrets about the choices he’s made at all.Mathematical biology seems to be his calling — he’s more interested in understanding how things work, and that’s what he does when he works.

Or rather, he doesn’t really work; because, as he told me,“try to find something to do that you really like, and are passionate about,because if you do, it won’t seem like work.” Reed doesn’t see coming into work as a struggle. He’s excited about it every single day and “it’s because you want to do it, it’s fun.”

Guest Post by Rachel Qu, NCSSM 2019

Artificial Intelligence Knows How You Feel

Ever wondered how Siri works? Afraid that super smart robots might take over the world soon?

On April 3rd researchers from Duke, NCSU and UNC came together for Triangle Machine Learning Day to provoke everyone’s curiosities about the complex field that is Artificial Intelligence. A.I. is an overarching term for smart technologies, ranging from self-driving cars to targeted advertising. We can arrive at artificial intelligence through what’s known as “machine learning.” Instead of explicitly programming a machine with the basic capabilities we want it to have, we can make it so that its code is flexible and adapts based on information it’s presented with. Its knowledge grows as a result of training it. In other words, we’re teaching a computer to learn.

Matthew Philips is working with Kitware to get computers to “see,” also known as “machine vision.” By providing thousands and thousands of images, a computer with the right coding can learn to actually make sense of what an image is beyond different colored pixels.

Machine vision has numerous applications. An effective way to search satellite imagery for arbitrary objects could be huge in the advancement of space technology – a satellite could potentially identify obscure objects or potential lifeforms that stick out in those images. This is something we as humans can’t do ourselves just because of the sheer amount of data there is to go through. Similarly, we could teach a machine to identify cancerous or malignant cells in an image, thus giving us a quick diagnosis if someone is at risk of developing a disease.

The problem is, how do you teach a computer to see? Machines don’t easily understand things like similarity, depth or orientation — things that we as humans do automatically without even thinking about. That’s exactly the type of problem Kitware has been tackling.

One hugely successful piece of Artificial Intelligence you may be familiar with is IBM’s Watson. Labeled as “A.I. for professionals,” Watson was featured on Sixty Minutes and even played Jeopardy on live television. Watson has visual recognition capabilities, can work as a translator, and can even understand things like tone, personality or emotional state. And obviously it can answer crazy hard questions. What’s even cooler is that it doesn’t matter how you ask the question – Watson will know what you mean. Watson is basically Siri on steroids, and the world got a taste of its power after watching it smoke its competitors on Jeopardy. However, Watson is not to be thought of as a physical supercomputer. It is a collection of technologies that can be used in many different ways, depending on how you train it. This is what makes Watson so astounding – through machine learning, its knowledge can adapt to the context it’s being used in.

Source: CBS News.

IBM has been able to develop such a powerful tool thanks to data. Stacy Joines from IBM noted, “Data has transformed every industry, profession, and domain.” From our smart phones to fitness devices, data is being collected about us as we speak (see: digital footprint). While it’s definitely pretty scary, the point is that a lot of data is out there. The more data you feed Watson, the smarter it is. IBM has utilized this abundance of data combined with machine learning to produce some of the most sophisticated AI out there.

Sure, it’s a little creepy how much data is being collected on us. Sure, there are tons of movies and theories out there about how intelligent robots in the future will outsmart humans and take over. But A.I. isn’t a thing to be scared of. It’s a beautiful creation that surpasses all capabilities even the most advanced purely programmable model has. It’s joining the health care system to save lives, advising businesses and could potentially find a new inhabitable planet. What we choose to do with A.I. is entirely up to us.

Post by Will Sheehan

Will Sheehan

Jonathan Mattingly: Mathematics and Maps to Define Democracy

Jonathan Mattingly is the chair of mathematics at Duke and an alumnus of the NC School of Science and Math

What began as an undergraduate project looking at how to create a “typical” map of congressional districts expanded to a national investigation for Duke mathematics chair Jonathan Mattingly. He was generous enough to speak to me about some of his recent work in mathematically investigating gerrymandering and the communication which followed between lawmakers and statisticians.

By strategically manipulating certain lines, it is possible to ensure a certain number of seats for one party even if that party does not win the majority vote. What “Team Gerrymandering” set out to do was to create an algorithm which would create the least biased map possible. The use of the term “fair” is complex in this instance, as politics and geography are very rarely simple enough to be split fairly.

An example of a mathematical model of precincts and districts.

In Wisconsin, the algorithm which “Team Gerrymandering” developed was used to prove that the voting districts were being disproportionately drawn in favor of the Republican votes, a trend which had was also been seen after the 2015 elections in North Carolina districts.

By strategically manipulating certain lines, it is possible to ensure a certain number of seats for one party even if that party does not win the majority vote. What “Team Gerrymandering” set out to do was to create an algorithm which would create the least biased map possible. The use of the term “fair” is complex in this instance, as politics and geography are very rarely simple enough to be split fairly.

The algorithm developed was then submitted as an brief amicus curae brief and used (it was used as a piece of appellate evidence) in the Wisconsin case Whitford vs. Bill. case. The mathematicians hoped to , in an attempt to prove that the districting of Wisconsin is an outlier in comparison to thousands of other mapping simulations run under their algorithm, which provide statistically sound data.

A problem such as this is a prime example of the bridge between the Humanities and STEM fields, which become increasingly separate as the level of expertise rises. as this truly bridges the humanities and STEM fields:, a solution has been found, but effectively communicating it was not as simple.

When asked about explaining and publishing this work in order to submit it as evidence, Mattingly admitted that it was, at times difficult, but it only further proved how important the effort is.

“It starts with a conversation. I’m willing to explain it, but you have to be willing to listen.”

A team full of lawyers looking to win a case is arguably a highly motivated audience, but this is not always the case. Mattingly, who is a 1988 graduate of the NC School of Science and Math which I attend, mentioned being at parties and hearing people state, “Oh, I’m no good at math, it’s just numbers and letters to me,” but he could never recount anyone saying “Oh, I don’t see the point in using language, or reading a dictionary.” These may seem like harmless comments, but a subconscious form of selective ignorance is still selective ignorance.

In light of the gerrymandering case, and “Team Gerrymandering’s” involvement in it, we are called to think again about the importance of fields we are not necessarily involved in, especially the STEM fields. What other patterns aren’t we noticing because we failed to look? Where else could we be improving if we were willing to listen? If we both don’t try, then we aren’t getting anywhere.”

The results of the Whitman vs Gill case are expected in June of 2018, and until then, the conversation must continue.

UPDATE: On Jan. 9, a federal court panel struck down North Carolina’s Congressional district maps on the grounds that they had been gerrymandered to favor Republicans. Mattingly commented.

Guest post by Paris Geolas, a senior at the North Carolina School of Science and Math

Anita Layton: A Model of STEM Versatility

Using mathematics to model the kidney and its biological systems is a field of study located at the intersection of two disciplines.

Anita Layton is a math professor at Duke. (Photo by Chris Hildreth, Duke Photography)

But for Duke’s Anita Layton, PhD, the Robert R. and Katherine B. Penn Professor of Mathematics and a professor of biomedical engineering, that just adds to the fun of it.

Growing up, with her father as the head of mathematics at her school, she was always told she was going to be a mathematician just like him. So she knew that was the last thing she wanted to do.

When Layton arrived as an undergraduate at Duke, she began a major in physics, but she seemed rather cursed when it came to getting correct results from her experiments. She settled for a BA in physics, but her academic journey was far from over. She had also taken a computer science course at Duke and fallen in love with it. If an experiment went wrong “things didn’t smell or blow up” and you could fix your mistake and move on, she said.

While pursuing her PhD in computer science at the University of Toronto, Layton was performing very math-oriented computer science, working with and analyzing numbers. However, it would be a while before biology entered the mix

While she was never good at dissections, she told me she was always good at understanding things that ‘flow’ and she came to the realization that blood is something that flows. She thought, “Hey, I can do that.

Anita Layton, Duke

Anita Layton, Ph.D.

Layton began creating programs that could solve the equations that model blood flow quickly, using her background in computer science. She then started learning about physiology, focusing on the renal system, and making models

It was a journey that took her to many different places, with pit stops and U-turns throughout many different fields. Had Layton stuck with just physics or computer science or math, she never would have ventured out and found this field that she is an expert in now.

It’s her interest in many different fields that has set Layton apart from many other people in the STEM field. In learning a wide variety of things, she has gotten better at computer science, mathematics, biology, physics, and more

When asked about what advice she would give her younger self, or any young person going into college, it would be to do just that: “Learn more things that you’re not good at.” She encouraged just taking a chemistry or biology class once in a while, or a philosophy course that makes you think in ways that you don’t normally. It’s often in those classes that you unearth things that can truly set your life in a completely different direction, Layton said, and she’s living proof of that.

Cecilia Poston, NCSSM

Cecilia Poston

Guest Post by Cecilia Poston, a senior at North Carolina School of Science and Math

Morphogenesis: All Guts and Morning Glories

What is morphogenesis? Morphogenesis examines the development of the living organisms’ forms.

It also is an area of research for Lakshminarayanan Mahadevan, Professor of Applied Mathematics, Organismic and Evolutionary Biology and Physics at Harvard University. On his presentation in the Public Lectures Unveiling Math (PLUM) series here at Duke, he credited the beginnings of morphogenesis to D’Arcy Wentworth Thompson, author of the book On Growth and Form.

Mathematically, morphogenesis focuses on how different rates of growth change the shapes of organisms as they develop. Cell number, cell size, cell shape, and cell position comprise the primary cellular factors of multicellular morphogenesis, which studies larger structures than individual cells and is Mahadevan’s focus.

Effects on tissues appear through changes in sizes, connectivities, and shapes, altering the phenotype, or the outward physical appearance. All these variables change in space and time. Professor Mahadevan presented on morphogenesis studies that have been conducted on plant shoots, guts, and brains.

Research on plant shoots often concentrates on the question, “Why do plant shoots grow in such a wide variety of directions and what determines their shapes?” The picture below shows the different postures appearances of plant shoots from completely straight to leaning to hanging.

Can morphogenesis make sense of these differences? Through mathematical modeling, two stimuli for shoots’ shapes was determined: gravity and itself. Additionally, elasticity as a function of the shoots’ weight plays a role in the mathematical models of plant shoots’ shapes which appear in Mahadevan’s paper co-written with a fellow professor, Raghunath Chelakkot. Mahadevan also explored the formation of flower and leaf shapes with these morphogenesis studies. 

Over twenty feet of guts are coiled up inside you. In order to fit these intestines inside the mammals, they must coil and loop. But what variables determine how these guts loop around? To discover the answer to this question, Mahadevan and other researchers examined chick embryos which increase their gut lengths by a factor greater than twenty over a twelve-day span. They were able to create a physical model using a rubber tube sewn to a sheet that followed the same patterns as the chicks’ guts. Through their observation of not only chicks but also quail and mice, Mahadevan determined that the morphogenesis of the guts has no dependence on genetics or any other microscopic factors.

Mahadevan’s study of how the brain folds occurs through MRI images of human fetal development. Initially, barely any folding exists on fetal brains but eventually the geometry of the surrounding along with local stress forms folds on the brain. By creating a template with gel and treating it to mimic the relationship between the brain’s gray matter and white matter, Mahadevan along with other researchers discovered that they could reproduce the brain’s folds. Because they were able to recreate the folds through only global geometry and local stress, they concluded that morphogenesis evolution does not depend on microscopic factors such as genetics. Further, by examining if folding regions correlate with the activity regions of the brain, questions about the effect of physical form on abilities and the inner functions of the brain.

  

     

Cheating Time to Watch Liquids do the Slow Dance

Colorful spheres simulating liquid molecules shift around inside a cube shape

The team’s new algorithm is able to simulate molecular configurations of supercooled liquids below the glass transition. The properties of these configurations are helping to solve a 70-year paradox about the entropy of glasses. Credit: Misaki Ozawa and Andrea Ninarello, Université de Montpellier.

If you could put on a pair of swimming goggles, shrink yourself down like a character from The Magic School Bus and take a deep dive inside a liquid, you would see a crowd of molecules all partying like it’s 1999.

All this frenetic wiggling makes it easy for molecules to rearrange themselves and for the liquid as a whole to change shape. But for supercooled liquids — liquids like honey that are cooled below their freezing point without crystallizing – the lower temperature slows down the dancing like Etta James’ “At Last.” Lower the temperature enough, and the slow-down can be so dramatic that it takes centuries or even millennia for the molecules to rearrange and the liquid to move.

Scientists can’t study processes that last longer than their careers. But Duke chemists and their Simons Foundation collaborators have found a way to cheat time, simulating the slow dance of deeply supercooled liquids. Along the way, they have found new physical properties of “aged” supercooled liquids and glasses.

A droplet rises above a surface of water

Credit: Ruben Alexander via Flickr.

To understand just how slow deeply supercooled liquids move, consider the world’s longest-running experiment, the University of Queensland’s Pitch Drop Experiment. A single drop of pitch forms every eight to thirteen years — and this pitch is moving faster than deeply supercooled liquids.

“Experimentally there is a limit to what you can observe, because even if you managed to do it over your entire career, that is still a maximum of 50 years,” said Patrick Charbonneau, an associate professor of chemistry and physics at Duke. “For many people that was considered a hard glass ceiling, beyond which you couldn’t study the behavior of supercooled liquids.”

Charbonneau, who is an expert on numerical simulations, said that using computers to simulate the behavior of supercooled liquids has even steeper time limitations. He estimates that, given the current rate of computer advancement, it would take 50 to 100 years before computers would be powerful enough for simulations to exceed experimental capabilities – and even then the simulations would take months.

To break this glass ceiling, the Charbonneau group collaborated with Ludovic Berthier and his team, who were developing an algorithm to bypass these time constraints. Rather than taking months or years to simulate how each molecule in a supercooled liquids jiggles around until the molecules rearrange, the algorithm picks individual molecules to swap places with each other, creating new molecular configurations.

This allows the team to explore new configurations that could take millennia to form naturally. These “deeply supercooled liquids and ultra-aged glasses” liquids are at a lower energy, and more stable, than any observed before.

“We were cheating time in the sense that we didn’t have to follow the dynamics of the system,” Charbonneau said. “We were able to simulate deeply supercooled liquids well beyond is possible in experiments, and it opened up a lot of possibilities.”

Two columns of blue and red spheres represent simulations of vapor-deposited glasses.

Glasses that are grown one layer at a time have a much different structure than bulk glasses. The team used their new algorithm to study how molecules in these glasses rearrange, and found that at low temperatures (right), only the molecules at the surface are mobile. The results may be used to design better types of glass for drug delivery or protective coatings. Credit: Elijah Flenner.

Last summer, the team used this technique to discover a new phase transition in low-temperature glasses. They recently published two additional studies, one of which sheds light on the “Kauzmann paradox,” a 70-year question about the entropy of supercooled liquids below the glass transition. The second explores the formation of vapor-deposited glasses, which have applications in drug delivery and protective coatings.

“Nature has only one way to equilibrate, by just following the molecular dynamics,” said Sho Yaida, a postdoctoral fellow in Charbonneau’s lab. “But the great thing about numerical simulations is you can tweak the algorithm to accelerate your experiment.”

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling.” Ludovic Berthier, Patrick Charbonneau, Daniele Coslovich, Andrea Ninarello, Misaki Ozawa and Sho Yaida. PNAS, Oct. 24, 2017. DOI: 10.1073/pnas.1706860114

The origin of ultrastability in vapor-deposited glasses.” Ludovic Berthier, Patrick Charbonneau, Elijah Flenner and Francesco Zamponi. PRL, Nov. 1, 2017. DOI: 10.1103/PhysRevLett.119.188002

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