Exploring collective interactions of matter and antimatter

STRIP AWAY ELECTRONS FROM THEIR ATOMS and you get a plasma — a collection of negatively charged electrons and positively charged ions. But at high energies around compact cosmic objects such as black holes, quasars and pulsars, curious plasmas may form that, instead of ions, contain positrons, the antimatter counterparts of electrons.

Scientists are searching for ways of distinguishing this type of plasma from others, both in astrophysical environments and in laboratories on Earth. Julia Mikhailova, an assistant professor of mechanical and aerospace engineering, and Matthew Edwards, a graduate student in her lab, together with Professor of Astrophysical Sciences Nathaniel Fisch, found that, contrary to earlier claims, an electron-positron plasma would scatter some wavelengths of light surprisingly intensely via a process called Brillouin scattering.

This fundamental insight into the unusual behavior of matter-antimatter plasmas, published in the journal Physical Review Letters Jan. 8, 2016, may help to find such plasmas in space, or validate methods for creating them in the lab. The work was funded in part by the National Science Foundation and the National Nuclear Security Administration. –By Bennett McIntosh

Researcher probes the secret life of electrons

ELECTRONS DART within and between atoms far too quickly for current imaging techniques to observe their motion. To capture fast-moving objects without a blur, a photographer can use a camera flash to light up a scene for an instant. Julia Mikhailova, an assistant professor of mechanical  and aerospace engineering, hopes to capture electron motion in a similar way, but her camera flash must last only a few attoseconds — just millionths of a trillionth of a second.

Mikhailova and her team use lasers and plasmas, which are collections of charged particles, to create attosecond pulses of light. “With these pulses one can observe the action inside atoms and molecules,” Mikhailova said. These observations could help researchers predict electron behavior, leading to a better understanding of everything from chemical reactions to superconductivity.

Lasers cannot by themselves produce such brief pulses. Instead, scientists scatter high-powered laser light off a stream of gas. Too much energy from the laser, however, can strip the electrons in the gas from their atoms to make a plasma that no longer scatters light in the right way.

Mikhailova and her team, with funding from the National Science Foundation, are taking a different approach. Instead of using a gas target, they aim a much higher-powered laser at a solid glass disc, creating a dense plasma at its surface. The laser light — an oscillating electromagnetic field — accelerates the electrons in the plasma toward nearly the speed of light. At these speeds, Newton’s physics breaks down and relativity takes over, causing the release of light in the form of attosecond pulses.

To improve the technique, Matthew Edwards, a graduate student in Mikhailova’s lab, ran simulations of plasma-laser interactions on Princeton’s TIGRESS high-performance computer cluster. The results, published Sept. 16, 2016, in the journal Physical Review Letters, showed that mixing laser light with light at harmonic frequencies — which are multiples of the original laser’s frequency — increases the efficiency of the process.

In a paper published Feb. 24, 2016, in the journal Physical Review A, the researchers proposed an extremely efficient two-target system: the first target generates light with harmonic frequencies, which hits the second target to generate attosecond pulses. With such powerful pulses, a new domain becomes visible, Mikhailova said. “We may be able to really see what the electron is doing as it ‘orbits’ in the atom.” –By Bennett McIntosh

Bioengineering: Unlocking the secrets of human health

Bioengineering cover imageBy Takim Williams

RED-HOT RIVERS OF MOLTEN COPPER and aluminum alloys streamed from one receptacle to another. As an undergraduate watching the demonstration in a materials science class, Clifford Brangwynne was reminded of cells migrating through the bloodstream. He realized at that moment that he could mold his interest in materials science and engineering into work that might ultimately have implications for human health.

Bioengineering blood vessel imageScientists like Brangwynne, now an assistant professor of chemical and biological engineering at Princeton, recognize the natural connection between engineering and the life sciences. Their research is setting the groundwork for future applications in health and medicine, including curing diseases such as Alzheimer’s, growing replacement organs and preventing developmental abnormalities. Each of these pursuits hinges on the understanding that living matter obeys the same principles as nonliving matter.

Discovering the relevant principles — and using them to manipulate biological systems to meet our needs — is the goal of the growing field of bioengineering. “The thing that we do that’s different from other scientists who are looking at states of matter and their properties is that we are doing it in the context of living cells,” Brangwynne said. “What is the state of matter inside of a cell and how does that enable biological function?”

Brangwynne gestures toward a can of Gillette shaving foam next to a cylinder of silly putty on his desk and explains that the familiar grade school schema of three states of matter — solid, liquid, gas — is not entirely accurate. There are phases in between, and combinations with their own surprising properties.

“A mound of foam is essentially a solid,” Brangwynne said. “You can push on it and it deforms, and when you take your finger away it springs back into shape. You’ve taken something that is 95 percent gas — it’s mostly air — and 5 percent liquid, and you’ve combined those in such a way that you get a solid.”

Correct biological function depends on transitions between these phases of matter. For example, your blood — typically a free-flowing liquid — clots to form a protective scab. However, these transitions can cause problems, for instance when an internal blood clot causes a stroke.

Likewise, the liquid inside each cell — the cytoplasm — regularly goes through local phase transitions, some of which are disruptive. This issue is linked to neurodegenerative diseases, including Alzheimer’s disease and amyotrophic lateral sclerosis (Lou Gehrig’s disease). In these cases, proteins aggregate and spontaneously transition from a liquid phase into a sticky, solid-like state, prohibiting normal function in the brain or nervous system. These phase transitions are also thought to be involved in controlling cell size and growth, and thus diseases such as cancer.

Nucleoli from amphibian egg cells

Researchers in the Brangwynne lab use nucleoli from amphibian egg cells to study the role of gravity in determining the size of living cells. IMAGE COURTESY OF CLIFFORD BRANGWYNNE LAB

Brangwynne’s research focuses on gaining a better understanding of these living states of matter, and how they can be manipulated. Over the past few years, his group has published several studies exploring the molecules that control intracellular phase transitions and how the living matter within a cell affects gene regulation and cell size.

In one particularly exciting study, graduate student Marina Feric discovered that liquid-phase droplets of RNA and protein are biophysically linked to cell size through the force of gravity. Brangwynne, who receives support from the National Science Foundation (NSF) and the National Institutes of Health (NIH), is optimistic that these fundamental studies will lead to medical applications. “We’re certainly hoping to use our findings to perturb these systems and keep cells in a healthier state,” he said.

Swimming upstream

Like Brangwynne, Professor Howard Stone followed the flow of ideas from an area of engineering — fluid mechanics — to biology. “The living world involves flow almost by definition,” said Stone, who is the Donald R. Dixon ’69 and Elizabeth W. Dixon Professor of Mechanical and Aerospace Engineering. “You circulate blood, you breathe streams of air in and out, you sweat to regulate temperature. If you study fluid mechanics, and if you’re somewhat open-minded, it’s easy to stumble across biological problems.”

One of the biological problems that caught Stone’s attention is how bacteria move in a fluid. Moving through water is far more difficult for bacteria than it is for a human. For single-celled creatures a millionth of a meter long, the force of friction dominates their ability to swim in a given direction. Instead, bacteria are usually just carried along for the ride.

Image of lungs

“The living world involves flow almost by definition.” –Howard Stone, the Donald R. Dixon ’69 and Elizabeth W. Dixon Professor of Mechanical and Aerospace Engineering

The dominance of friction led to a discovery in Stone’s lab four years ago by visiting graduate student Yi Shen, who found that P. aeruginosa, a dangerous pathogen sometimes found in hospitals, can move against a current. The bacterium loses its flagellum — a long tail for swimming — when it adheres to a surface, which for many cells dictates the end of mobility. Yet P. aeruginosa can drag itself along a wall of, for example, a branched medical tube, by its small, tentacle-like pili, which are strong enough to resist the force of friction.

After observing this phenomenon, Stone and his collaborators — Professor of Molecular Biology Zemer Gitai; Albert Siryaporn, an associate research scholar in molecular biology; and Kevin Minyoun Kim, a graduate student in chemistry — began researching this behavior in systems mimicking the human body.

“Your blood vessels have branches. Your lungs are branched. We’ve made model branched systems and used a pump — like a heart — to drive fluid through it,” Stone said. “Bacteria inoculated into this flow sometimes end up in places you wouldn’t expect, and that, at this time, a simulation would never predict.” This basic research, which is supported by NSF, may allow us to better anticipate the movements of pathogens — in our bodies or our environments — in order to prevent infection and contamination.

Fluid environment

Bacteria are single-celled organisms that can form colonies, but a more sophisticated arrangement occurs in our own bodies, where huge communities of cells organize into tissues and organs. Celeste Nelson, an associate professor of chemical and biological engineering, studies the fetal development of these organs, which depends on the fluid environment in which they form.

One of the organs that forms in a fluid environment is the lung. A fetus’s lungs are filled with fluid during gestation. Nelson uses tissue cultures — parts of organs grown in laboratory dishes — and manipulates the speed and pressure of tiny streams of liquid that are directed onto the growing lung cells by small tubes.

Nelson has discovered that the higher the pressure of this fluid in the fetal lung, the more quickly the lungs develop, whereas lower pressure leads to slower development. Several congenital disorders can derail lung development, and Nelson’s work — which is supported by NIH, NSF, the David and Lucile Packard Foundation, the Camille and Henry Dreyfus Foundation, the Burroughs Wellcome Fund, the Essig Enright Family Foundation, and Princeton’s Project X, which provides seed funding for unconventional research — may improve our ability to diagnose such problems early.

The lungs, kidneys, mammary glands and other organs develop through a branched structure, which is an efficient space-filling strategy for functions that require maximum surface area. This exponential branching pattern is a highly reproducible selfassembly process, and in Nelson’s opinion, the forest of alveoli in the lungs is the most beautiful example. “The 23 generations of branches means several hundred million paths,” said Nelson. “Every one of those paths is needed for efficient diffusion of oxygen into the infant blood stream immediately after birth. “What’s amazing,” she said, “is that all of the branches in my lungs look exactly like the branches in your lungs.”

Lung image

Lung tissue extracted from a reptile embryo helps the Nelson lab study the effect of the fluid environment on lung development.

Nelson’s lab also studies a behavior in cancer cells called reversion, which — if it could be induced — would turn many cancers into benign, treatable illnesses. She collaborates with Derek Radisky, a researcher at the Mayo Clinic in Jacksonville, Florida. For Nelson, who started studying breast cancer while a postdoctoral fellow, the body’s organ systems have a mechanical elegance.

Timing is everything

Stanislav Shvartsman is as fascinated by the chemical aspects of development as Nelson is by the mechanical aspects. His research focuses on embryogenesis, the very early stages of fetal development.

“When you want to bake a cake, it’s not enough to say that you need eggs and milk and flour,” said Shvartsman, a professor of chemical and biological engineering and the Lewis-Sigler Institute for Integrative Genomics. “Knowing the ingredients, and even knowing the sequence in which you add these ingredients — which is what we know from genetics — is not enough to bake a cake that tastes good.”

When the recipe — the proper quantities of chemicals released by the cells of the embryo at the proper times — isn’t followed exactly, there are consequences for the developing organism. For example, a large class of developmental abnormalities, known as RAS-opathies, is associated with asymmetry in the craniofacial complex, stunted height, congenital heart defects, developmental delays and other issues. Such defects are observed in one in every thousand births and are believed to be caused by mutations in genes of the Ras-MAPK pathway.

Biologists know which genes are mutated, and even where to find these genes on our DNA. What they don’t know is why these particular mutations lead to a distinct set of clinical features. To find out, researchers turn to organisms that macroscopically look very different from us — such as bacteria and worms — but are very similar at the cellular level. Shvartsman’s research group, which is supported by NIH and NSF, uses the fruit fly to study embryogenesis.

Initially, the handful of cells that make up an embryo are all identical. By the time of birth, that homogenous handful will have given rise to brain, nerve, heart, blood and every other kind of cell required for a living, breathing organism. In order to differentiate into the right kind of cell at the right time, and to arrange into the correct three-dimensional shape, the embryonic cells have to communicate. They speak to each other through a language of chemical signals.

The signals are actually protein molecules, Shvartsman said. A protein released by one cell attaches to a receptor protein embedded in the surface of a neighboring cell. That surface protein reacts by changing shape, and in turn changing the internal environment of its cell. In this way cells “hear” each other. At any given time multiple cells are releasing various proteins, and the combination of signals floating through the embryonic environment tells a cell what to become, or when to divide to make more of itself.

To crack the code, Shvartsman is looking at one signal at a time, beginning with a set of proteins that is well understood genetically thanks to the work of such Princeton biologists as Gertrud Schüpbach, the Henry Fairfield Osborn Professor of Biology. By controlling the amount of these proteins released in the fly embryo, Bomyi Lim, a former graduate student in Shvartsman’s lab and now a postdoctoral research associate at the Lewis-Sigler Institute for Integrative Genomics, has discovered the minimum dosage necessary for proper structural development. This is the first step in a long process, but it is a milestone, and Shvartsman is excited about continuing the process. “It’s very exciting to work in a field where there’s no risk of ever saying, ‘This is the end of the times-table. There is no more material to learn,’” he said.

Image of fruit fly embryo structure

The image shows thin slices of a part of fruit fly embryos where stem cells turn into mature eggs. Created by graduate students Yogesh Goyal and Bomyi Lim and postdoctoral researcher Miriam Osterfield in the laboratory of Stanislav Shvartzman, the image was selected for display in Princeton’s 2014 Art of Science competition.

Some assembly required

Brangwynne views embryogenesis as the epitome of self-assembly, the process by which small, disorganized components interact based on simple rules to form complex structures without human intervention. A classic example is the snowflake, a delicate crystalline jewel formed in midair as water molecules freeze. Engineers have been trying to take advantage of self-assembly for some time — often in Brangwynne’s field of materials science — where time and money could be saved if certain synthetic materials would form on their own in a solution, rather than being painstakingly put together atom by atom.

“The embryo of an organism like C. elegans essentially starts out as just a bag of molecules,” Brangwynne said. Once the egg is fertilized, it begins to organize, and the unstructured soup of molecules turns into a wriggling worm. “There’s absolutely nothing that human engineering can do that comes anywhere close to what I just described takes place in embryos all the time,” Brangwynne said.

While Princeton scientists are importing methods and paradigms from engineering disciplines to biology, they see a two-way street, recognizing that biology itself has methods to share.

“We would like to learn how nature, through hundreds of millions of years of evolution, has generated these systems that are just completely unbelievable in their level of sophistication,” Brangwynne said. “It’s as if we’ve been visited by an alien civilization that was millions of years more advanced than us. The first thing we would do would be to take a really close look at that spaceship. We’d try to figure out what it is made of, what are the principles that govern its flight and its control systems. That’s what we are doing with biological systems.”

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Inventions Bridge the Gap between lab and marketplace

Road trip

A road trip offered Mark Zondlo and his team the opportunity to test their new air quality sensors. (Photo by Lei Tao)

The college experience often involves at least one road trip, but most students do not bring along their faculty adviser. But last spring, two graduate students crammed into a rented Chevy Impala with Professor Mark Zondlo and a postdoctoral researcher to drive eight hours a day across California’s Central Valley, testing their new air-quality sensors, which were strapped to a rooftop ski rack.

The sensors are an example of technologies being developed at Princeton that have the potential to improve quality of life as commercial products or services. Although teaching and research are Princeton’s core missions, the campus is home to a vibrant entrepreneurial spirit, one that can be found among faculty members who are making discoveries that could lead to better medicines as well as students working to turn a dorm-room dream into the next big startup.

“Princeton has a number of initiatives aimed at supporting innovation and technology transfer,” said John Ritter, director of Princeton’s Office of Technology Licensing, which works with University researchers to file invention disclosures and patent applications, and with businesses and investment capitalists to find partners for commercialization. “Our goal is to accelerate the transfer and development of Princeton’s basic research so that society can benefit from these innovations,” he said.

Crossing the valley

One of the ways that Princeton supports this transfer is with programs that help bridge the gap between research and commercialization, a gap that some call the Valley of Death because many promising technologies never make it to the product stage. One such program is the Intellectual Property Accelerator Fund, which provides financial resources for building a prototype or conducting additional testing with the goal of attracting corporate interest or investor financing.

Zondlo, an assistant professor of civil and environmental engineering, is one of the researchers using the fund to cross the valley — in this case literally as well as figuratively. Earlier this year, Zondlo and his research team, which consisted of graduate students Kang Sun and David Miller and postdoctoral researcher Lei Tao, tested their air-quality sensor in California’s Central Valley, a major agricultural center that is home to some of the worst air pollution in the nation.

Their goal was to compare the new portable sensors to existing stationary sensors as well as to measurements taken by plane and satellite as part of a larger NASA-funded air-quality monitoring project, DISCOVER-AQ.

One of the new sensors measures nitrous oxide, the worst greenhouse gas after carbon dioxide and methane. Nitrous oxide escapes into the air when fertilizers are spread on farm fields. Currently, to measure this gas, workers must collect samples of air in bottles and then take them to a lab for analysis using equipment the size of refrigerators.

Zondlo’s sensor, which is bundled with two others that measure ammonia and carbon monoxide, is portable and can be held in one hand, or strapped to a car roof. “The portability allows measurements to be taken quickly and frequently, which could greatly expand the understanding of how nitrous oxide and other gases are released and how their release can be controlled,” Zondlo said.

The sensors involve firing a type of battery-powered laser, called a quantum cascade laser, through a sample of air, while a detector measures the light absorption to deduce the amount of gas in the air. The researchers replaced bulky calibration equipment, necessary to ensure accurate measurements in the field, with a finger-sized chamber of reference gas against which the sensor’s accuracy can be routinely tested.

The decision to commercialize the sensor arose from the desire to make the device available to air-quality regulators and researchers, Zondlo said. “Our sensor has precision and stability similar to the best sensors on the market today, but at a fraction of the size and power requirements,” said Zondlo, a member of the Mid-Infrared Technologies for Health and the Environment (MIRTHE) center, a multi-institution center funded by the National Science Foundation (NSF) and headquartered at Princeton. “We are already getting phone calls from people who want to buy it.”

Lighting up the brain — with help from a synthetic liver

Far from the dusty farm roads of California, Princeton faculty member John (Jay) Groves sits in his office in the glass-enclosed Frick Chemistry Laboratory, thinking about the potential uses for a new synthetic enzyme. Modeled on an enzyme isolated from the liver, the synthetic version can carry out reactions that human chemists find difficult to pull off.

One of these reactions involves attaching radioactive fluorine tags to drugs to make them visible using a brain-imaging method known as positron emission tomography (PET) scanning.

PET scans of the radiolabeled drugs could help investigators track experimental medicines in the brain, to see if they are reaching their targets, and could aid in the development of drugs to treat disorders such as Alzheimer’s disease and stroke, according to Groves, Princeton’s Hugh Stott Taylor Chair of Chemistry. The synthetic enzyme adds fluorine tags without the toxic and corrosive agents used with radioactive fluorine today.

Groves’ initial work was supported by the NSF, but to develop the technology for use in pharmaceutical research, the Groves team, which includes graduate students Wei Liu and Xiongyi Huang, is receiving funding from a Princeton program aimed at supporting concepts that are risky but have potential for broad impact. The Eric and Wendy Schmidt Transformative Technology Fund was created with a $25 million endowment from Google executive chairman Eric Schmidt, a 1976 alumnus and former trustee, and his wife, Wendy.

“The Schmidt funding is enabling us to explore ways to optimize the chemical reaction and create a prototype of an automated system,” Groves said. “This will allow us to create a rapid and noninvasive way to evaluate drug candidates and observe important metabolites within the human brain.”

Aiding the search for planets

Tyler Groff

Postdoctoral researcher Tyler Groff is creating an improved system for adjusting the blurry images seen through telescopes due to atmospheric turbulence, heat and vibrations. (Photo by Denise Applewhite)

Inspired by the search for planets outside our solar system, Princeton postdoctoral researcher Tyler Groff conceived of a technology that could enhance the quality of images from telescopes. Groff received Schmidt funding to develop a device for controlling the mirrors that telescopes use to correct blurring and distortion caused by atmospheric turbulence, heat and vibrations.

This technology, known as adaptive optics, involves measuring disturbances in the light coming into the telescope and making small deformations to the surface of a mirror in precise ways to correct the image. These deformations are made using an array of mechanical devices, known as actuators, each capable of moving a small area of the flexible reflective surface up or down. But existing actuators are limited in the amount of correction they can provide, and the spaces between the actuators create dimples in the mirror, producing a visible pattern in the resulting images that astronomers call “quilting.”

Groff envisioned replacing the array of rigidly attached actuators with flexible ones made from packets containing iron particles suspended in a liquid, or ferrofluid. Just as iron filings can be moved by waving a magnet over them, applying varying magnetic fields to the ferrofluid changes the shape of the fluid in ways that deform the mirror.

The ferrofluid mirror enables highquality images while being more resistant to vibrations and potentially more power efficient, which will be important for future satellite-based telescopes, said Groff, who works in the laboratory of Jeremy Kasdin, professor of mechanical and aerospace engineering. A ferrofluid mirror can also achieve something that a rigid actuator mirror cannot: it can assume a concave or bowl-like shape that aids the focusing of the telescope on objects in space. “A telescope that uses ferrofluid mirrors would be able to see dim objects better,” Groff said, “which would greatly enhance our ability to probe other solar systems.”

From drug discovery to space exploration, Princeton’s dedication to supporting technology transfer and potentially disruptive but high-risk research ideas is yielding tremendous benefits for the advancement of science and the improvement of people’s lives.

Box: From student project to startup

Carlee Joe-Wong (Photo by Steve Schultz)

Carlee Joe-Wong (Photo by Steve Schultz)

In 2009 when Princeton undergraduate Carlee Joe-Wong started working on the technology that would become the DataMi company, she didn’t even own a smartphone. Today, the startup company co-founded by Joe-Wong provides mobile traffic management solutions to wireless Internet providers, and also helps consumers manage their data usage through an app, DataWiz, that has been downloaded by more than 200,000 Apple and Android users.

Joe-Wong became involved in the study of mobile data usage in the spring of her junior year when Professor Mung Chiang challenged her to explore ways that wireless providers could reduce congestion by adjusting their prices based on the variations in network supply and demand. “I mostly just worked on the project in my dorm room,” Joe-Wong said. “I thought it would be cool if it was adopted but I didn’t think that I would be the one helping to make that happen.” After graduation, Joe-Wong became a graduate student working with Chiang on mathematical algorithms that predict the most effective methods for balancing network use across “peak” minutes and “valley” minutes.

“With companies charging $10 per gigabyte, mobile consumers today need to intelligently manage their data,” said Chiang, the Arthur LeGrand Doty Professor of Electrical Engineering. “What the DataWiz app does is tell you when, where and what app used how much of your quota.”

In May 2013 the team, under the engineering leadership of associate research scholar Sangtae Ha, opened an office for DataMi one block off campus. Needless to say, Joe-Wong now has a smartphone.

Taking it to the streets with help from Princeton’s eLab

ELab students

From left: Nathan Haley, Christine Odabashian, Luke Amber and Leif Amber. (Photo by Denise Applewhite)

A love of motorcycles brought them together: three Princeton undergraduates decided to explore building and marketing an electric motorcycle to provide a superior riding experience at significantly lower emissions than gasoline powered models.

The team was one of nine groups selected to participate in the 10-week eLab Summer Accelerator Program, an initiative of the Keller Center in the School of Engineering and Applied Science, which teaches entrepreneurship by offering resources, mentoring and working space.

Throughout the summer, the team members worked on ways to market the bike while simultaneously building a prototype. “We geared the product toward people who enjoy taking weekend trips,” said Nathan Haley, Class of 2014, an economics major.

Haley was joined by Luke Amber, Class of 2015, and Christine Odabashian, Class of 2014, both majors in mechanical and aerospace engineering. The team also included Luke’s older brother, Leif Amber, a graduate student in electrical engineering at Clarkson University.

-By Catherine Zandonella

American Mathematical Society awards Steele Prizes to Yakov Sinai, Philip Holmes

Yakov Sinai

Yakov Sinai (Photo courtesy of the Princeton University Department of Mathematics)

Professor of Mathematics Yakov Sinai was awarded the American Mathematical Society (AMS)’s Leroy P. Steele Prize for Lifetime Achievement, one of the highest distinctions in mathematics. Sinai was honored for his “pivotal role in shaping the theory of dynamical systems and for his groundbreaking contributions to ergodic theory, probability theory, statistical mechanics and mathematical physics,” according to the AMS. The prize recognizes the breadth and depth of the recipient’s mathematical work as well as the recipient’s influence on mathematics through Ph.D. student supervision.

Philip Holmes

Philip Holmes (Photo by James Phillips)

Philip Holmes, the Eugene Higgins Professor of Mechanical and Aerospace Engineering, was the co-winner of the Leroy P. Steele Prize for Mathematical Exposition along with John Guckenheimer for the book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. The publication helped bridge the various developments of different mathematicians working with dynamical systems in the 1960s and 1970s. According to the official citation for the prize, “Thirty years later this book remains in wide use as a standard text for graduate-level courses in mathematics departments and throughout the sciences and engineering, and Chinese and Russian translations have appeared.”