Discovering New Underwater Force

This image shows a time series, a through d, of self assembly of collection of neutrally buoyant spheres suspended within a sharply salt-stratified fluid viewed from above. Spheres radii and densities are 0.025–0.05cm and 1.05 g cc⁻¹, top fluid is fresh water, 0.997 g ^cc−1, bottom is NaCl water solution of density 1.1 g ^cc−1. e Shows schematic experimental setup, f the initial cluster – different trial. FInally g shows the final cluster.

An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems.

In a study, published in Nature Communications, researchers from the Department of Mathematics at the University of North Carolina at Chapel Hill, in collaboration with colleagues from the School of Engineering at Brown University, and the Department of Physics and Center for Biological Physics at the Arizona State University, observe and model mathematically an unexpected fundamental mechanism by which particles suspended within stratification may self-assemble and form large aggregates without adhesion. This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and aggregate geometry, which produces toroidal flows.

The Team members show that these flows yield attractive horizontal forces between particles at the same heights. They further observe that many particles demonstrate a collective motion revealing a system which appears to solve jigsaw-like puzzles on its way to organizing into a large-scale disc-like shape, with the effective force increasing as the collective disc radius grows.

Control experiments isolate the individual dynamics, which are quantitatively predicted by simulations. Numerical force calculations with two spheres are used to build many-body simulations which capture observed features of self-assembly.

New Revelations in Nepal

The Carolina research group with their guides celebrating the Nepali national holiday, Dashain, on the second day of the trek. The red mark on their foreheads, the tika, is from a blessing ritual. From left, Harvey Seim, Lauren Leve, Rich McLaughlin, guide Deep Rai, Roberto Camassa, Emily Eidam and guide Daman Rai. – Photo courtesy of Emily Eidam

An interdisciplinary team of Carolina researchers recently returned to the Himalayas to continue studying the effects of climate change on Buddhist holy lakes. A major goal: To retrieve data from instruments they installed 15 months ago.

Windy. Cold. Wet. Those were the conditions one October day as a team of Carolina researchers tried to retrieve instruments left behind 15 months earlier in a remote lake in Sagarmatha National Park, the region of Nepal dominated by Mount Everest. The thermistors were supposed to measure lake temperature and pressure at different depths every 15 minutes, for more than a year, but whether they had survived monsoons and freezing temperatures was an unknown.

Day one was not a success. The afternoon winds were too strong.

Climate change is impacting the Gokyo Lakes, there are six in total – and these holy lakes are very important to Himalayan Buddhists. They lie next to the Ngozumba glacier, the largest glacier in Nepal. The team of interdisciplinary explorers who made the first trip to study the lakes included mathematics professor and chair Rich McLaughlin, Kenan Distinguished Professor of Mathematics Roberto Camassa, associate professor of religious studies and anthropologist Lauren Leve and marine sciences professor and chair Harvey Seim. Joining the same crew for the return trip was new team member Emily Eidam, an assistant professor and marine geologist.

Seim, who was battling an intestinal illness, had guided Eidam, Camassa and McLaughlin on locating the instruments on lake 4, relying on notes and GPS coordinates from when they were first deployed. But it turned out it would take multiple tries.

Day two dawned clear and calm, but the winds began to pick up in the 15 minutes it took to load the boat. This time Camassa and Eidam, joined by porters who also acted as paddlers and pullers, managed to snag the line 50 meters below with a grapple hook and pull up all 15 thermistors, along with three very heavy bags of rocks that helped to anchor the instruments. The haul was, in McLaughlin’s words, a “beautiful data set that shows over a year’s time what has been happening in the lake.”

“Getting more than a year of data at multiple elevations in a remote lake is the type of thing that makes science extremely rewarding, both from a logistical perspective and what we’re learning about seasonal lake dynamics,” Eidam said.

After collecting the data, the team redeployed all 15 thermistors. They will leave them there for about two years.

“We recognize that studying just one season doesn’t necessarily give the complete picture,” Eidam added. “So being able to redeploy them means that we have a chance to do a much more comprehensive study of how the lake responds to changing snow and meltwater inputs, variable air temperatures, et cetera.”

The team also measured the depth of lake 4 again. A Kathmandu University colleague had measured its depth at 62 meters in 2009; the Carolina crew measured it at 45 meters in spring 2018. It rose to 57 meters in fall 2019, likely due to monsoon rain and the fact that the lake does not have an outflow river source, McLaughlin said. It undergoes cycles of draining and filling. The mathematicians will be working on modeling what’s happening with the depth fluctuations.

“We’d love to create a permanent way to keep measuring these lakes,” McLaughlin said. “Our feeling is these are critical lakes for assessing climate change and it’s happening here faster than in other parts of the world.”

Challenges and Opportunities
A required permit that didn’t come through until the last minute. Possible food poisoning. A broken tooth. Garbled data and a faulty piece of equipment. Spotty communication access. A longer-than-normal monsoon season. Surviving below-freezing night-time temperatures. A yak stampede. Hours of backed-up traffic at Ramechhap Airport for the journey to Lukla. It’s about a six-day hike from Lukla to the lakes. –Welcome to the world of the field scientist.

Despite the expedition challenges, Leve, who is an expert on Himalayan Buddhism and has been traveling to Nepal for nearly thirty years, said she thought the journey went smoother the second time.

“In my experience with the way things work in Nepal, I expect not to have complete control,” she said. “And our communication with the local community far exceeded my expectations this time.”

“I was pleasantly surprised to get as much done as we did,” Seim added, noting that Eidam was a brilliant addition to the group.

“Emily’s expertise aligned nicely with what we were interested in doing; she is much more familiar with glaciology and geology so she added another strength to our interdisciplinary team,” Seim said. “She brought some lightweight sensors with her that we didn’t have last time that measured turbidity, cloudiness of the water, and chlorophyll.”

Eidam added that she benefited from working with seasoned scientists. “Working with mathematicians and physicists helps me expand my way of thinking about fluid motions, in an out-of-the-box way for a geologist. And teaming up with experienced faculty, including an expert on cultural matters in Nepal, is always educational for navigating field studies in international locations,” she said.

The team continued their earlier research on lakes 2, 3 and 4. They had a new opportunity to explore lake 5, even though the instrument they were using on the new lake bungled the data.

“Lake 5 had not been studied that much,” Camassa said. “The quality of the water there was also moderately different than the murky color of lake 4; it was much more transparent and blue like lake 3.”

The team also collected water samples from the lakes that will be analyzed for isotope concentrations to try to determine the source of water to the lakes — is it primarily surface water or groundwater?

In addition, Camassa and McLaughlin made connections with scientists who work at The Pyramid International Laboratory/Observatory, a research station in the Khumbu Valley, which could prove useful in gathering weather and atmospheric data to correlate with the lake water data.

And sometimes, despite the obstacles, you just have to stop and enjoy the beauty of Nepal. “One night the stars were magnificent and the view of the Milky Way was incredible,” McLaughlin said.

Communicating Science, Developing Best Practices
For Leve, one of her key goals has been to work with community leaders and the national park service in Nepal to help them develop helpful information for future researchers — and to find a way to share the scientific data the Carolina team is collecting.

Before heading to Gokyo, the team members gave a presentation in Namche Bazaar that was attended by key stakeholders – from government, nonprofits, the national park and more. They shared details about the first trip and fielded questions. Leve then stayed behind for a few days to attend a meeting with local elected representatives. She is working with the parties to develop a best practices guide for scientists seeking to do research in the national park.

“While various parties may have conflicting ideas about how to best show respect for an environment that is locally perceived as living and sacred, in the end we are all invested in understanding this land that means many different things to different individuals,” she said. “We share the same concerns about what it means to protect this world. We have to figure out how to do it together.”

After returning home, Leve led a panel at the American Anthropological Association conference in Vancouver, presenting on “Climate Contradictions: Sacred/Sentient Mountains, Science and the Anthropocene in the Andes and the Himalayas.”

What the Nepali people want is a partnership with future researchers, an opportunity to be a part of the conversation, Leve said.

“UNC is modeling best practices, but it’s a work in progress; this is just the beginning,” she said. “They have a great interest in seeing science happen and in building these collaborative relationships. At a certain point it will be in their hands entirely, and that’s the goal.”

Philanthropic support from Cosby George ’83 and the College of Arts & Sciences helped to fund the return research expedition.

Story by Kim Spurr, College of Arts & Sciences

Hobson wins first prize

Congratulations to undergraduate student Gabrielle Hobson, who won first prize in the student poster contest at the American Physical Society Division of Fluid Dynamics annual meeting. The prize recognized her work last summer at the University of California, Merced. She is currently doing her honors undergraduate thesis in the UNC fluids lab.

McCombs in The Daily Tarheel

Mark McCombs, an exhibiting artist and professor in the Department of Mathematics, combines math, fractals and origami to create unique paper sculptures and 2D images. McCombs is restructuring the first-year seminar he teaches to reflect what he learned while exhibiting his art in Stockholm, Sweden last summer.

Staff writer Mary Mac Porter talked to McCombs about the similarities between literature and mathematics and how he’s combining numbers and art in unique ways to attract math-adverse students to the subject.

DTH: How would you describe the first-year seminar that you’re restructuring and the art you’re creating in the process?

MM: The art projects grew out of the first-year seminar I was asked to teach, I think, maybe 10 years ago now. The first few semesters I taught it, I knew how to talk about, math, topics, but I didn’t create art because I felt like I’m one of those people that doesn’t have any art in me. I appreciate art and enjoy it and everything, but I was always intimidated by trying to make my own art.

Then one semester, after a couple years, the first day of class… a student came up and asked, ‘Are we going to do origami?’ I said, ‘Well, I don’t know how to do that.’ He said, ‘I really like origami,’ and I said, ‘Tell you what, how about if you teach the class for two class meetings?’ So, he did. I really liked what he showed us how to do.

Then in 2015, my younger brother – who was an amazing guitarist – died unexpectedly from a heart attack. I brought home all his music, so I could archive it for his son who also plays guitar. So, as I’m transferring all this music, I’ve got the headphones on, and I’m folding paper, and then all of the sudden, the origami started coming out of me. I feel like in some ways it’s a gift to me from my brother.

What this discovery has inspired me to do is redesign my first-year seminar, so that it’s now focused on making origami and making fractal tessellations.

DTH: How does your artwork challenge preconceived notions about math?

MM: I’ve been teaching here for thirty years, and I’ve been teaching this math art class for around ten. But for thirty years, whenever someone asks what I do, and I tell them I teach math, they kind of back away from me or they’ll say, ‘I hate math. I’m not good at it.’

So part of what I hope to do in this particular class – because it’s not the traditional solve the equations, draw the graphs, do the calculus kind of thing – is maybe help persuade people who are coming in intimidated that they don’t have to be intimidated. I’m not trying to force them to become a math major or something like that.

My hope for the students in this first-year seminar is that when the semester ends, they’re not so quick to say, ‘I can’t think mathematically.’ I think another thing that has been an unexpected moment of insight for me is, I guess, my version of that is when someone would say, ‘Hey, I make art,’ and I would go, ‘Well, I can’t do that.’ Now I don’t feel as intimidated.

I guess if you find the medium you connect with, we can all express ourselves. And that’s what art really is, and I think that’s what math is too: you try to express how you understand the world through relationships of objects and ideas.

DTH: What is your favorite part of all of the work you do here at UNC?

MM: It’s always gratifying to me when, at the end of the semester, I get my course reviews back, and a student writes, ‘I never thought I’d say this, but my favorite class was my math class this semester.’ That’s not because of me – I mean, I was part of it – but when that happens for that student, it’s what my younger brother would always describe as moments of grace. In his music, he saw moments of grace that happened because of experiencing harmony — whether it’s musical harmony or harmony with a person or whatever.

DTH: Do you have anything else you’d like to add about your work in math, at UNC or in art?

MM: I did undergrad and grad here. I was an English major through my junior year. I took math all along because I liked it, but I wanted to write. Then when I went home over Christmas my junior year, I started to panic because if I graduate with a degree in English, I thought, ‘I’m going to end up being a teacher.’ It’s not that I thought that was a bad job. I just never imagined I could do that.

So I switched my major to math, and some practical joker somewhere said, ‘Okay, well guess what? You’re going to be a teacher.’ But that’s another moment of grace for me.

When I tell people that I was an English major before I switched to math, lots of times their response is ‘Wow! That’s a big change.’ For me, it doesn’t feel like a big switch because the parts of me that allow me to respond to literature are the parts of me that allow me to respond to the beauty of the way mathematical objects and ideas relate together.

Story by Mary Mac Porter, The Daily Tar Heel

Mastering the Art of Math

When you take a look at Mark McCombs’ artwork, be sure to consider the mathematical equations behind them. The swirling pieces of paper and repeating designs in this mathematics teaching professor’s art is a study in mathematical symmetry. Math and art may appear to be at different ends of the educational spectrum, but to McCombs and his students, they couldn’t be more connected.

“I want to try to help people believe that math isn’t just numbers. Math is a way of interacting with your environment,” McCombs said.

McCombs works mainly in modular origami, which consists of smaller paper shapes that can be combined to create one complete sculpture. He also uses the Ultra Fractal software application to produce fractal images, geometric shapes that contain infinitely many copies of themselves no matter how many times you zoom in.

Sculpture in Sweden
McCombs’ art is spread all over the state and the world. Last July, two of McCombs’ pieces, a sculpture and a fractal print, were presented at the Bridges Conference in Stockholm, Sweden. The sculpture was purchased by a curator at the Swedish Museum of Science and Technology. McCombs was also a featured artist at the Liquidambar Gallery in Pittsboro from June 2 to July 28. You can view his art at his website

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However, it was because of McCombs’ younger brother, Doug McCombs, that he was able to find the courage to submit his pieces to these galleries. In 2015, McCombs’ brother passed away from an unexpected heart attack. It was through his brother’s passion that McCombs said he began to understand what it meant to create art.

“He was just an amazing guitarist. And he inspired me in so many ways, but one of the ways that he inspired me is in my teaching. It’s just such a joy for me to share him with my students,” McCombs said.

“Doug always told me that tone is what allows us to experience grace through harmony. And that’s what I feel like I started to experience as I’m making the sculpture and fractal images. I really believe that Doug is part of it, too. It’s a gift to me from him.”

Perspectives on Math and Art
For the past ten years, McCombs has taught the first-year seminar Math, Art and the Human Experience, designed to give students different perspectives on what math and art can be.

This interdisciplinary outlook, McCombs said, is essential to create an approachable and humanities-focused curriculum for math. He has always thought this way; he received his undergraduate and master’s degrees in math at Carolina, but he also minored in English.

In the seminar, students look at different artists and evaluate their work based on its different planes of symmetry, angles and perspective. Students also design origami and fractal art using the Adobe Suite and the BeAM Makerspace.

Last spring, McCombs submitted a redesigned proposal for the seminar. For the first time this fall, the course will be completely focused on origami and fractals. Before 2016, McCombs himself hadn’t created art, but he said he’s ready to expand the course even more.

“I’m most gratified by the times at the end of the semester when I get my course reviews back and someone will have written, ‘I never thought I’d ever say, my favorite class was my math class.’”

Story by Kyra Miles, University Gazette

Mucha and Hinton Gilliam Fellowship

The Howard Hughes Medical Institute has awarded grants to 44 doctoral adviser-student pairs to improve faculty mentoring skills, support new scientific leaders, and foster diversity and inclusion in science.

A good scientific mentor can help students navigate different career paths and plug them into new networks. A mentor can be a sounding board and an advocate – and they can also make the experience of being a scientist more fun. Each fellow submitted a career statement describing how their personal experiences and training inform their science, and how they plan to make scientific culture more inclusive.

David Asai, HHMI’s Senior Director for science education, says the fellows all show promise as scientists. “The Gilliam program is aimed at people who will become leaders in science,” he says. “We’re trying to change the face of university faculty, so students see leaders of all different backgrounds.”

Peter Mucha and Andrew Hinton were selected for the Gilliam Fellowship. Along with a $50,000 annual award for up to three years for each adviser-student pair, advisers will participate in a year of mentor training focused on cultural awareness. Over the past four years, more than 130 advisers have taken part; activities include online training and two in-person workshops at HHMI headquarters in Chevy Chase, Maryland.

Congratulations Peter and Andrew!

Metcalfe Award of Excellence

Professor Jason Metcalfe has received the 2019 Faculty Award for Excellence in Doctoral Mentoring.

With this annual award, The Graduate School recognizes a faculty member who, “encourages students to establish their own record of scholarly activity or performance, provides a supportive environment that facilitates the development of best performance and talents from individual graduate students, and achieves a successful record of graduate degree completion among the students they have advised.”

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Graduate School Dean Steve Matson presented the award to Metcalfe at the University’s May 11 Doctoral Hooding Ceremony.

“Mentoring is an act of patience and support – both of which Dr. Metcalfe has demonstrated in multiple ways,” Matson said, in presenting the award.

The nomination letters highlighted numerous examples of Metcalfe’s expertise and “steadfast encouragement” of the students he advises, including, as one letter said, his “uncanny ability to illuminate difficult ideas and help students develop the tools to answer their own questions, rather than just providing a quick answer.”

Metcalfe joined UNC-Chapel Hill in 2007 as an assistant professor, was appointed to associate professor in 2012 and was appointed to professor in 2017. At Carolina, he has advised five doctoral students, two master’s degree students and five undergraduate students.

In 2018, he received the University of North Carolina Board of Governors Award for Excellence in Teaching. Metcalfe also received the mathematics department’s inaugural Sue Goodman Award for Excellence in Undergraduate Education in 2017.

Jason “embodies the best of academic advising – providing the expertise to conduct important research, the support and mentorship needed to succeed in graduate school, and the independence needed to move forward in an academic career,” wrote one nominator.

Metcalfe said that he had been remarkably fortunate to have caring and dedicated mentors at every point of his career and was humbled by the award.

“It is difficult to imagine that I am living up to the standards that these role models have set. It has been an honor and a joy to work with the students at UNC. Their achievements are due to their scholarly courage, dedication, and talent, and I have been a lucky witness to their growth as mathematicians.”

Morgan wins Boka Hadzija Award

Katrina Morgan, a doctoral student in mathematics at the University of North Carolina at Chapel Hill, has received the 2019 Boka W. Hadzija Award for Distinguished University Service.

The annual award recognizes one graduate or professional student for outstanding character, scholarship, leadership and service to UNC-Chapel Hill. The Graduate School presented the award during the 21st Annual Graduate Student Recognition Celebration, held April 4. Morgan and other students were recognized for their outstanding leadership at the Chancellor’s Awards Ceremony on April 16, 2019.

In announcing Morgan’s award, Graduate School Dean Steve Matson commended her for providing “a tremendous amount of outreach to encourage girls’ interest in STEM fields.” One of these initiatives is Girls Talk Math, a two-week summer day camp for high school girls. Morgan and Francesca Bernardi, a recent doctoral alumna, co-founded the annual camp in 2016, and it has now expanded to the University of Maryland.

In July 2017, Girls Talk Math was honored with the Association for Women in Mathematics’ first Student Chapter Award for Community Outreach. Morgan and Bernardi received the 2018 University Award for the Advancement of Women for their work.

Additionally, Morgan frequently volunteers at outreach events such as the UNC Science Expo, the InspiHER Student Club at East Chapel Hill High School and conferences for undergraduate women in mathematics. She has served as president of the UNC-Chapel Hill Graduate Mathematics Association and is currently president of the campus student chapter of the Association for Women in Mathematics.

The nomination letter provided examples of her excellence in service to UNC-Chapel Hill and beyond, in research and in teaching. Morgan holds both a Dissertation Completion Fellowship within The Graduate School and a Thomas S. Kenan III Graduate Fellowship within the College of Arts and Sciences.

“She is excelling in all aspects of academic life, including independently procuring funding for many of these activities. It has been a privilege to work with her,” Katrina’s nominator wrote.

Jason Metcalfe, a professor of mathematics, is Morgan’s doctoral adviser.

Boka W. Hadzija was an award-winning professor in the Eshelman School of Pharmacy; she established the award in 2000 in honor of her students. Hadzija, who died in 2013, is remembered by students and faculty for her strong mentorship, her generous support of students and her outstanding leadership.

Students Earn NSF Fellowships

We are excited to announce that three students in the Department of Mathematics have earned prestigious National Science Foundation funded Graduate Research Fellowships. We congratulate second year graduate student Samantha Moore, first year graduate student Maddie Brown, and undergraduate Keshav Patel on this remarkable achievement.

The NSF GRFP recognizes and supports outstanding graduate students in NSF-supported STEM disciplines who are pursuing research-based master’s and doctoral degrees at accredited US institutions. The five-year fellowship includes three years of financial support including an annual stipend of $34,000 and a cost of education allowance of $12,000 to the institution.

Strayer and Morgan FPG Honor Society

Department of Mathematics graduate students Katrina Morgan and Michael Strayer have been inducted into the Frank Porter Graham Graduate and Professional Student Honor Society.

This honor recognizes outstanding service to the university and to the community. Katrina and Michael are the first inductees from the Department of Mathematics since 1994. Both have served as officers of the Graduate Student Association for Mathematics, for the local chapter of the Association for Women in Mathematics, AWM, and for the local Graduate Student Chapter for the American Mathematical Society, AMS.

Both have been mentors through the AWM chapter and through the new Directed Reading Program, which pairs interested undergraduate and graduate students for intensive one on one study. Moreover, Katrina’s work as a co-founder and co-director of the Girls Talk Math, summer program and Michael’s work as the founder and first president of the Graduate Student Chapter of the AMS, which first brought the TAGMAC Conference to UNC, have been particularly influential.

We are very proud of Katrina and Michael’s achievements. Congratulations both!