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Field work – the physics of sheep, from phase transitions to collective motion

You’re probably familiar with the old joke about a physicist who, when asked to use science to help a dairy farmer, begins by approximating a spherical cow in a vacuum. But maybe it’s time to challenge this satire on how physics-based models can absurdly over-simplify systems as complex as farm animals. Sure, if you want to understand how a cow or a sheep works, approximating those creatures as spheres might not be such a good idea. But if you want to understand a herd or a flock, you can learn a lot by reducing individual animals to mere particles – if not spheres, then at least ovoids (or bovoids; see what I did there?).

By taking that approach, researchers over the past few years have not only shed new insight on the behaviour of sheep flocks but also begun to explain how shepherds do what they do – and might even be able to offer them new tips about controlling their flocks. Welcome to the emerging science of sheep physics.

“Boids” of a feather

Physics-based models of the group dynamics of living organisms go back a long way. In 1987 Craig Reynolds, a software engineer with the California-based computer company Symbolics, wrote an algorithm to try to mimic the flocking of birds. By watching blackbirds flock in a local cemetery, Reynolds intuited that each bird responds to the motions of its immediate neighbours according to some simple rules.

His simulated birds, which he called “boids” (a fusion of bird and droid), would each match their speed and orientation to those of others nearby, and would avoid collisions as if there was a repulsive force between them. Those rules alone were enough to generate group movements resembling the striking flocks or “murmurations” of real-life blackbirds and starlings, that swoop and fly together in seemingly perfect unison. Reynolds’ algorithms were adapted for film animations such as the herd of wildebeest in The Lion King.

Murmuration of starlings — **Aerial display** Physicists have been studying the collective motion of flocks of birds, such as groups of starlings – known as murmurations – that are seemingly governed by rules of physics. (Courtesy: iStock/georgeclerk)

Over the next two or three decades, these models were modified and extended by other researchers, including the future Nobel-prize-winning physicist Giorgio Parisi, to study collective motions of organisms ranging from birds to schooling fish and swarming bacteria. Those studies fed into the emerging science of active matter, in which particles – which could be simple colloids – move under their own propulsion. In the late 1990s physicist Tamás Vicsek and his student Andras Czirók, at Eötvös University in Budapest, revealed analogies between the collective movements of such self-propelled particles and the reorientation of magnetic spins in regular arrays, which also “feel” and respond to what their neighbours are doing (Phys. Rev. Lett. 82 209; J. Phys. A: Math. Gen. 30 1375).

In particular, the group motion can undergo abrupt phase transitions – global shifts in the pattern of behaviour, analogous to how matter can switch to a bulk magnetized state – as the factors governing individual motion, such as average velocity and strength of interactions, are varied. In this way, the collective movements can be summarized in phase diagrams, like those depicting the gaseous, liquid and solid states of matter as variables such as temperature and density are changed.

Models like these have now been used to explore the dynamics not just of animals and bacteria, but also of road traffic and human pedestrians. They can predict the kinds of complex behaviours seen in the real world, such as stop-and-start waves in traffic congestion or the switch to a crowd panic state. And yet the way they represent the individual agents seems – for humans anyway – almost insultingly simple, as if we are nothing but featureless particles propelled by blind forces.

Follow the leader

If these models work for humans, you might imagine they’d be fine for sheep too – which, let’s face it, seem behaviourally and psychologically rather unsophisticated compared with us. But if that’s how you think of sheep, you’ve probably never had to shepherd them. Sheep are decidedly idiosyncratic particles.

“Why should birds, fish or sheep behave like magnetic spins?” asks Fernando Peruani of the University of Cergy Paris. “As physicists we may want that, but animals may have a different opinion.” To understand how flocks of sheep actually behave, Peruani and his colleagues first looked at the available data, and then tried to work out how to describe and explain the behaviours that they saw.

1 Are sheep like magnetic spins?

Sheep walking in a line — (Diagram courtesy: *Nat. Phys.* 18 1402. Photo courtesy: iStock/scottyh)

In a magnetic material, magnetic spins interact to promote their mutual alignment (or anti-alignment, depending on the material). In the model of collective sheep motion devised by Fernando Peruani from the University of Cergy Paris, and colleagues, each sheep is similarly assumed to move in a direction determined by interactions with all the others that depend on their distance apart and their relative angles of orientation. The model predicts the sheep will fall into loose alignment and move in a line, following a leader, that takes a more or less sinuous path over the terrain.

For one thing, says Peruani, “real flocks are not continuously on the move. Animals have to eat, rest, find new feeding areas and so on”. No existing model of collective animal motion could accommodate such intermittent switching between stationary and mobile phases. What’s more, bird murmurations don’t seem to involve any specific individual guiding the collective behaviour, but some animal groups do exhibit a hierarchy of roles.

Elephants, zebras and forest ponies, for example, tend to move in lines such that the animal at the front has a special status. An advantage of such hierarchies is that the groups can respond quickly to decisions made by the leaders, rather than having to come to some consensus within the whole group. On the other hand, it means the group is acting on less information than would be available by pooling that of everyone.

To develop their model of collective sheep behaviour, Peruani and colleagues took a minimalistic approach of watching tiny groups of Merino Arles sheep that consisted of “flocks” of just two to four individuals who were free to move around a large field. They found that the groups spend most of their time grazing but would every so often wander off collectively in a line, following the individual at the front (Nat. Phys. 18 1494).

They also saw that any member of the group is equally likely to take the lead in each of these excursions, selected seemingly at random. In other words, as George Orwell famously suggested for certain pigs, all sheep are equal but some are (temporarily) more equal than others. Peruani and colleagues suspected that this switching of leaders allows some information pooling without forcing the group to be constantly negotiating a decision.

The researchers then devised a simple model of the process in which each individual has some probability of switching from the grazing to the moving state and vice versa – rather like the transition probability for emission of a photon from an excited atom. The empirical data suggested that this probability depends on the group size, with the likelihood getting smaller as the group gets bigger. Once an individual sheep has triggered the onset of the “walking phase”, the others follow to maintain group cohesion.

In their model, each individual feels an attractive, cohesive force towards the others and, when moving, tends to align its orientation and velocity with those of its neighbour(s). Peruani and colleagues showed that the model produces episodic switching between a clustered “grazing mode” and collective motion in a line (figure 1). They could also quantify information exchange between the simulated sheep, and found that probabilistic swapping of the leader role does indeed enable the information available to each individual to be pooled efficiently between all.

Although the group size here was tiny, the team has video footage of a large flocks of sheep adopting the same follow-my-leader formation, albeit in multiple lines at once. They are now conducting a range of experiments to get a better understanding of the behavioural rules – for example, using sirens to look at how sheep respond to external stimuli and studying herds composed of sheep of different ages (and thus proclivities) to probe the effects of variability.

The team is also investigating whether individual sheep trained to move between two points can “seed” that behaviour in an entire flock. But such experiments aren’t easy, Peruani says, because it’s hard to recruit shepherds. In Europe, they tend to live in isolation on low wages, and so aren’t the most forthcoming of scientific collaborators.

The good shepherd

Of course, shepherds don’t traditionally rely on trained sheep to move their flocks. Instead, they use sheepdogs that are trained for many months before being put to work in the field. If you’ve ever watched a sheepdog in action, it’s obvious they do an amazingly complex job – and surely one that physics can’t say much about? Yet mechanical engineer Lakshminarayanan Mahadevan at Harvard University in the US says that the sheepdog’s task is basically an exercise in control theory: finding a trajectory that will guide the flock to a particular destination efficiently and accurately.

Mahadevan and colleagues found that even this phenomenon can be described using a relatively simple model (arXiv:2211.04352). From watching YouTube videos of sheepdogs in action, he figured there were two key factors governing the response of the sheep. “Sheep like to stay together,” he says – the flock has cohesion. And second, sheep don’t like sheepdogs – there is repulsion between sheep and dog. “Is that enough – cohesion plus repulsion?” Mahadevan wondered.

Sheepdogs and a flock of sheep — **Let’s stay together** Harvard University researcher Lakshminarayanan Mahadevan studied the interactions between sheepdogs and a flock of sheep, to develop a model that describes how a flock reacts to different herding tactics employed by the dogs. They found that the size of the flock and how fast it moves between its initial and final positions are two main factors that determine the best herding strategy. (Courtesy: Shutterstock/Danica Chang)

The researchers wrote down differential equations to describe the animals’ trajectories and then applied standard optimization techniques to minimize a quantity that captures the desired outcome: moving the flock to a specific location without losing any sheep. Despite the apparent complexity of the dynamical problem, they found it all boiled down to a simple picture. It turns out there are two key parameters that determine the best herding strategy: the size of the flock and the speed with which it moves between initial and final positions.

Four possible outcomes emerged naturally from their model. One is simply that the herding fails: nothing a dog can do will get the flock coherently from point A to point B. This might be the case, for example, if the flock is just too big, or the dog too slow. But there are three shepherding strategies that do work.

One involves the dog continually running from one side of the flock to the other, channelling the sheep in the desired direction. This is the method known to shepherds as “droving”. If, however, the herd is relatively small and the dog is fast, there can be a better technique that the team called “mustering”. Here the dog propels the flock forward by running in corkscrews around it. In this case, the flock keeps changing its overall shape like a wobbly ellipse, first elongating and then contracting around the two orthogonal axes, as if breathing. Both strategies are observed in the field (figure 2).

But the final strategy the model generated, dubbed “driving”, is not a tactic that sheepdogs have been observed to use. In this case, if the flock is large enough, the dog can run into the middle of it and the sheep retreat but don’t scatter. Then the dog can push the flock forward from within, like a driver in a car. This approach will only work if the flock is very strongly cohesive, and it’s not clear that real flocks ever have such pronounced “stickiness”.

2 Shepherding strategies: the three types of herding

Diagram of herding patterns — (Courtesy: L Mahadevan *et al.*, arXiv:2211.04352)

In the model of interactions between a sheepdog and its flock developed by Lakshminarayanan Mahadevan at Harvard University and coworkers, optimizing a mathematical function that describes how well the dog transports the flock results in three possible shepherding strategies, depending on the precise parameters in the model. In “droving”, the dog runs from side to side to steer the flock towards the target location. In “mustering”, the dog takes a helix-like trajectory, repeatedly encircling the flock. And in “driving”, the dog steers the flock from “inside” by the aversion – modelled as a repulsive force – of the sheep for the dog.

These three regimes, derived from agent-based models (ABM) and models based on ordinary differential equations (ODE), are plotted above. In the left column, the mean path of the flock (blue) over time is shown as it is driven by a shepherd on a separate path (red) towards a target (green square). Columns 2-4 show snapshots from column 1, with trajectories indicated in black, where fading indicates history. From left to right, snapshots represent the flock at later time points.

These herding scenarios can be plotted on a phase diagram, like the temperature–density diagram for states of matter, but with flock size and speed as the two axes. But do sheepdogs, or their trainers, have an implicit awareness of this phase diagram, even if they did not think of it in those terms? Mahadevan suspects that herding techniques are in fact developed by trial and error – if one strategy doesn’t work, they will try another.

Mahadevan admits that he and his colleagues have neglected some potentially important aspects of the problem. In particular, they assumed that the animals can see in every direction around them. Sheep do have a wide field of vision because, like most prey-type animals, they have eyes on the sides of their heads. But dogs, like most predators, have eyes at the front and therefore a more limited field of view. Mahadevan suspects that incorporating these features of the agents’ vision will shift the phase boundaries, but not alter the phase diagram qualitatively.

Another confounding factor is that sheep might alter their behaviour in different circumstances. Chemical engineer Tuhin Chakrabortty of the Georgia Institute of Technology in Atlanta, together with biomolecular engineer Saad Bhamla, have also used physics-based modelling to look at the shepherding problem. They say that sheep behave differently on their own from how they do in a flock. A lone sheep flees from a dog, but in a flock they employ a more “selfish” strategy, with those on the periphery trying to shove their way inside to be sheltered by the others.

3 Heavy and light: how flocks interact with sheepdogs

In the agent-based model of the interaction between sheep and a sheepdog devised by Tuhin Chakrabortty and Saad Bhamla, sheep may respond to a nearby dog by reorienting themselves to face away from or at right angles to it. Different sheep might have different tendencies for this – “heavy” sheep ignore the dog unless they are facing towards it. The task of the dog could be to align the flock facing away from it (herding) or to divide the flock into differently aligned subgroups (shedding).

What’s more, says Chakrabortty, contrary to the stereotype, sheep can show considerable individual variation in how they respond to a dog. Essentially, the sheep have personalities. Some seem terrified and easily panicked by a dog while others might ignore – or even confront – it. Shepherds traditionally call the former sort of sheep “light”, and the latter “heavy” (figure 3).

In the agent-based model used by Chakrabortty and Bhamla, the outcomes differ depending on whether a herd is predominantly light or heavy (arXiv:2406.06912). When a simulated herd is subjected to the “pressure” of a shepherding dog, it might do one of three things: flee in a disorganized way, shedding panicked individuals; flock in a cohesive group; or just carry on grazing while reorienting to face at right angles to the dog, as if turning away from the threat.

Again these behaviours can be summarized in a 2D phase diagram, with axes representing the size of the herd and what the two researchers call the “specificity of the sheepdog stimulus” (figure 4). This factor depends on the ratio of the controlling stimulus (the strength of sheep–dog repulsion) and random noisiness in the sheep’s response. Chakrabortty and Bhamla say that sheepdog trials are conducted for herd sizes where all three possible outcomes are well represented, creating an exacting test of the dog’s ability to get the herd to do its bidding.

4 Fleeing, flocking and grazing: types of sheep movement

Graph showing types of sheep movement — (Courtesy: T Chakrabortty and S Bhamla, arXiv:2406.06912)

The outcomes of the shepherding model of Chakrabortty and Bhamla can be summarized in a phase diagram showing the different behavioural options – uncoordinated fleeing, controlled flocking, or indifferent grazing – as a function of two model parameters: the size of the flock N_s and the “specificity of stimulus”, which measures how strongly the sheep respond to the dog relative to their inherent randomness of action. Sheepdog trials are typically conducted for a flock size that allows for all three phases.

Into the wild

One of the key differences between the movements of sheep and those of fish or birds is that sheep are constrained to two dimensions. As condensed-matter physicists have come to recognize, the dimensionality of a problem can make a big difference to phase behaviour. Mahadevan says that dolphins make use of dimensionality when they are trying to shepherd schools of fish to feed on. To make them easier to catch, dolphins will often push the fish into shallow water first, converting a 3D problem to a 2D problem. Herders like sheepdogs might also exploit confinement effects to their benefit, for example using fences or topographic features to help contain the flock and simplify the control problem. Researchers haven’t yet explored these issues in their models.

Dolphins using herding tactics to drive a school of fish — **Shoal of thought** In nature, dolphins have been observed using a number of herding tactics to drive schools of fish into shallow water or even beach them, to making hunting easier and more efficient. (Courtesy: iStock/atese)

As the case of dolphins shows, herding is a challenge faced by many predators. Mahadevan says he has witnessed such behaviour himself in the wild while observing a pack of wild dogs trying to corral wildebeest. The problem is made more complicated if the prey themselves can deploy group strategies to confound their predator – for example, by breaking the group apart to create confusion or indecision in the attacker, a behaviour seemingly adopted by fish. Then the situation becomes game-theoretic, each side trying to second-guess and outwit the other.

Sheep seem capable of such smart and adaptive responses. Bhamla says they sometimes appear to identify the strategy that a farmer has signalled to the dog and adopt the appropriate behaviour even without much input from the dog itself. And sometimes splitting a flock can be part of the shepherding plan: this is actually a task dogs are set in some sheepdog competitions, and demands considerable skill. Because sheepdogs seem to have an instinct to keep the flock together, they can struggle to overcome that urge and have to be highly trained to split the group intentionally.

Giorgio Parisi: the Nobel-prize winner whose complex interests stretch from spin glasses to starlings

Iain Couzin of the Max Planck Institute of Animal Behavior in Konstanz, Germany, who has worked extensively on agent-based models of collective animal movement, cautions that even if physical models like these seem to reproduce some of the phenomena seen in real life, that doesn’t mean the model’s rules reflect what truly governs the animals’ behaviour. It’s tempting, he says, to get “allured by the beauty of statistical physics” at the expense of the biology. All the same, he adds that whether or not such models truly capture what is going on in the field, they might offer valuable lessons for how to control and guide collectives of agent-like entities.

In particular, the studies of shepherding might reveal strategies that one could program into artificial shepherding agents such as robots or drones. Bhamla and Chakrabortty have in fact suggested how one such swarm control algorithm might be implemented. But it could be harder than it sounds. “Dogs are extremely good at inferring and predicting the idiosyncrasies of individual sheep and of sheep–sheep interactions,” says Chakrabortty. This allows them to adapt their strategy on the fly. “Farmers laugh at the idea of drones or robots,” says Bhamla. “They don’t think the technology is ready yet. The dogs benefit from centuries of directed evolution and training.”

Perhaps the findings could be valuable for another kind of animal herding too. “Maybe this work could be applied to herding kids at a daycare,” Bhamla jokes. “One of us has small kids and recognizes the challenges of herding small toddlers from one room to another, especially at a party. Perhaps there is a lesson here.” As anyone who has ever tried to organize groups of small children might say: good luck with that.

New on-chip laser fills long sought-after green gap

A series of visible-light colours generated by a microring resonator — **Closing the green gap** Series of visible-light colours generated by a microring resonator. (Courtesy: S Kelley/NIST)

On-chip lasers that emit green light are notoriously difficult to make. But researchers at the National Institute of Standards and Technology (NIST) and the NIST/University of Maryland Joint Quantum Institute may now have found a way to do just this, using a modified optical component known as a ring-shaped microresonator. Green lasers are important for applications including quantum sensing and computing, medicine and underwater communications.

In the new work, a research team led by Kartik Srinivasan modified a silicon nitride microresonator such that it was able to convert infrared laser light into yellow and green light. The researchers had already succeeded in using this structure to convert infrared laser light into red, orange and yellow wavelengths, as well as a wavelength of 560 nm, which lies at the edge between yellow and green light. Previously, however, they were not able to produce the full range of yellow and green colours to fill the much sought-after “green gap”.

More than 150 distinct green-gap wavelengths

To overcome this problem, the researchers made two modifications to their resonator. The first was to thicken it by 100 nm so that it could more easily generate green light with wavelengths down to 532 nm. Being able to produce such a short wavelength means that the entire green wavelength range is now covered, they say. In parallel, they modified the cladding surrounding the microresonator by etching away part of the silicon dioxide layer that it was fabricated on. This alteration made the output colours less sensitive to the dimension of the microring.

These changes meant that the team could produce more than 150 distinct green-gap wavelengths and could fine tune these too. “Previously, we could make big changes – red to orange to yellow to green – in the laser colours we could generate with OPO [optical parametric oscillation], but it was hard to make small adjustments within each of these colour bands,” says Srinivasan.

Like the previous microresonator, the new device works thanks to a process known as nonlinear wave mixing. Here, infrared light that is pumped into the ring-shaped structure is confined and guided within it. “This infrared light circulates around the ring hundreds of times due to its low loss, resulting in a build-up of intensity,” explains Srinivasan. “This high intensity enables the conversion of pump light to other wavelengths.”

Third-order optical parametric oscillation

“The purpose of the microring is to enable relatively modest, input continuous-wave laser light to build up in intensity to the point that nonlinear optical effects, which are often thought of as weak, become very significant,” says team member Xiyuan Lu.

The specific nonlinear optical process the researchers use is third-order optical parametric oscillation. “This works by taking light at a pump frequency n_p and creating one beam of light that’s higher in frequency (called the signal, at a frequency n_s) and one beam that’s lower in frequency (called the idler, at a frequency n_i),” explains first author Yi Sun. “There is a basic energy conservation requirement that 2n_p= n_s+ n_i.”

Simply put, this means that for every two pump photons that are used to excite the system, one signal photon and one idler photon are created, he tells Physics World.

Towards higher power and a broader range of colours

The NIST/University of Maryland team has been working on optical parametric oscillation as a way to convert near-infrared laser light to visible laser light for several years now. One of their main objectives was to fill the green gap in laser technology and fabricate frequency-converted lasers for quantum, biology and display applications.

“Some of the major applications we are ultimately targeting are high-end lasers, continuous-wave single-mode lasers covering the green gap or even a wider range of frequencies,” reveals team member Jordan Stone. “Applications include lasers for quantum optics, biology and spectroscopy, and perhaps laser/hologram display technologies.”

For now, the researchers are focusing on achieving higher power and a broader range of colours (perhaps even down to blue wavelengths). They also hope to make devices that can be better controlled and tuned. “We are also interested in laser injection locking with frequency-converted lasers, or using other techniques to further enhance the coherence of our lasers,” says Stone.

The work is detailed in Light: Science & Applications.

Researchers exploit quantum entanglement to create hidden images

**Encoding images in photon correlations** Simplified experimental setup (a). A conventional intensity image (b) reveals no information about the object, while a correlation image acquired using an electron-multiplied CCD camera (c) reveals the hidden object. (Courtesy: *Phys. Rev. Lett.* 10.1103/PhysRevLett.133.093601)

Ever since the double-slit experiment was performed, physicists have known that light can be observed as either a wave or a stream of particles. For everyday imaging applications, it is the wave-like aspect of light that manifests, with receptors (natural or artificial) capturing the information contained within the light waves to “see” the scene being observed.

Now, Chloé Vernière and Hugo Defienne from the Paris Institute of Nanoscience at Sorbonne University have used quantum correlations to encode an image into light such that it only becomes visible when particles of light (photons) are observed by a single-photon sensitive camera – otherwise the image is hidden from view.

Encoding information in quantum correlations

In a study described in Physical Review Letters, Vernière and Defienne managed to hide an image of a cat from conventional light measurement devices by encoding the information in quantum entangled photons, known as a photon-pair correlation. To achieve this, they shaped spatial correlations between entangled photons – in the form of arbitrary amplitude and phase objects – to encode image information within the pair correlation. Once the information is encoded into the photon pairs, it is undetectable by conventional measurements. Instead, a single-photon detector known as an electron-multiplied charge couple device (EMCCD) camera is needed to “show” the hidden image.

“Quantum entanglement is a fascinating phenomenon, central to many quantum applications and a driving concept behind our research,” says Defienne. “In our previous work, we demonstrated that, in certain cases, quantum correlations between photons are more resistant to external disturbances, such as noise or optical scattering, than classical light. Inspired by this, we wondered how this resilience could be leveraged for imaging. We needed to use these correlations as a support – a ‘canvas’ – to imprint our image, which is exactly what we’ve achieved in this work.”

How to hide an image

The researchers used a technique known as spontaneous parametric down-conversion (SPDC), which is used in many quantum optics experiments, to generate the entangled photons. SPDC is a nonlinear process that uses a nonlinear crystal (NLC) to split a single high-energy photon from a pump beam into two lower energy entangled photons. The properties of the lower energy photons are governed by the geometry and type of the NLC and the characteristics of the pump beam.

In this study, the researchers used a continuous-wave laser that produced a collimated beam of horizontally polarized 405 nm light to illuminate a standing cat-shaped mask, which was then Fourier imaged onto an NLC using a lens. The spatially entangled near-infrared (810 nm) photons, produced after passing through the NLC, were then detected using another lens and the EMCCD.

This SPDC process produces an encoded image of a cat. This image does not appear on regular camera film and only becomes visible when the photons are counted one by one using the EMCCD. This allowed the image of the cat to be “hidden” in light and unobservable by traditional cameras.

“It is incredibly intriguing that an object’s image can be completely hidden when observed classically with a conventional camera, but then when you observe it ‘quantumly’ by counting the photons one by one and examining their correlations, you can actually see it,” says Vernière, a PhD student on the project. “For me, it is a completely new way of doing optical imaging, and I am hopeful that many powerful applications will emerge from it.”

What’s next?

This research has extended on previous work and Defienne says that the team’s next goal is to show that this new method of imaging has practical applications and is not just a scientific curiosity. “We know that images encoded in quantum correlations are more resistant to external disturbances – such as noise or scattering – than classical light. We aim to leverage this resilience to improve imaging depth in scattering media.”

When asked about the applications that this development could impact, Defienne tells Physics World: “We hope to reduce sensitivity to scattering and achieve deeper imaging in biological tissues or longer-range communication through the atmosphere than traditional technologies allow. Even though we are still far from it, this could potentially improve medical diagnostics or long-range optical communications in the future.”

Ambipolar electric field helps shape Earth’s ionosphere

A drop in electric potential of just 0.55 V measured at altitudes of between 250–768 km in the Earth’s atmosphere above the North and South poles could be the first direct measurement of our planet’s long-sought after electrostatic field. The measurements, from NASA’s Endurance mission, reveal that this field is important for driving how ions escape into space and shaping the upper layer of the atmosphere, known as the ionosphere.

Researchers first predicted the existence of the ambipolar electric field in the 1960s as the first spacecraft flying over the Earth’s poles detected charged particles (including positively-charged hydrogen and oxygen ions) flowing out from the atmosphere. The theory of a planet-wide electric field was developed to directly explain this “polar wind”, but the effects of this field were thought to be too weak to be detectable. Indeed, if the ambipolar field was the only mechanism driving the electrostatic field of Earth, then the resulting electric potential drop across the exobase transition region (which lies at an altitude of between 200–780 km) could be as low as about 0.4 V.

A team of researchers led by Glyn Collinson at NASA’s Goddard Space Flight Center in Greenbelt, Maryland, has now succeeded in measuring this field for the first time thanks to a new instrument called a photoelectron spectrometer, which they developed. The device was mounted on the Endurance rocket, which was launched from Svalbard in the Norwegian Arctic in May 2022. “Svalbard is the only rocket range in the world where you can fly through the polar wind and make the measurements we needed,” says team member Suzie Imber, who is a space physicist at the University of Leicester, UK.

Just the “right amount”

The spacecraft reached an altitude of 768.03 km, where it remained for 19 min while the onboard spectrometer measured the energies of electrons there every 10 seconds. It measured a drop in electric potential of 0.55 V±0.09 V over an altitude range of 258–769 km. While tiny, this is just the “right amount” to explain the polar wind without any other atmospheric effects, says Collinson.

The researchers showed that the ambipolar field, which is generated exclusively by the outward pressure of ionospheric electrons, increases the “scale height” of the ionosphere by as much as 271% (from a height of 77.0 km to a height of 208.9 km). This part of the atmosphere therefore remains denser to greater heights than it would if the field did not exist. This is because the field increases the supply of cold oxygen ions (O⁺) to the magnetosphere (that is, near the peak at 768 km) by more than 3.8%, so counteracting the effects of other mechanisms (such as wave-particle interactions) that can heat and accelerate these particles to velocities high enough for them to escape into space. The field also probably explains why the magnetosphere is made up primarily of cold hydrogen ions (H⁺).

The ambipolar field could be as fundamental for our planet as its gravity and magnetic fields, says Collinson, and it may even have helped shape how the atmosphere evolved. Similar fields might also exist on other planets in the solar system with an atmosphere, including Venus and Mars. “Understanding the forces that cause Earth’s atmosphere to slowly leak to space may be important for revealing what makes Earth habitable and why we’re all here,” he tells Physics World. “It’s also crucial to accurately forecast the impact of geomagnetic storms and ‘space weather’.”

Looking forward, the scientists say they would like to make further measurements of the Earth’s ambipolar field in the future. Happily, they recently received endorsement for a follow-up rocket – called Resolute – to do just this.

Light-absorbing dye turns skin of a live mouse transparent

One of the difficulties when trying to image biological tissue using optical techniques is that tissue scatters light, which makes it opaque. This scattering occurs because the different components of tissue, such as water and lipids, have different refractive indices, and it limits the depth at which light can penetrate.

A team of researchers at Stanford University in the US has now found that a common water-soluble yellow dye (among several other dye molecules) that strongly absorbs near-ultraviolet and blue light can help make biological tissue transparent in just a few minutes, thus allowing light to penetrate more deeply. In tests on mice skin, muscle and connective tissue, the team used the technique to observe a wide range of deep-seated structures and biological activity.

In their work, the research team – led by Zihao Ou (now at The University of Texas at Dallas), Mark Brongersma and Guosong Hong – rubbed the common food dye tartrazine, which is yellow/red in colour, onto the abdomen, scalp and hindlimbs of live mice. By absorbing light in the blue part of the spectrum, the dye altered the refractive index of the water in the treated areas at red-light wavelengths, such that it more closely matched that of lipids in this part of the spectrum. This effectively reduced the refractive-index contrast between the water and the lipids and allowed the biological tissue to appear more transparent at this wavelength, albeit tinged with red.

In this way, the researchers were able to visualize internal organs, such as the liver, small intestine and bladder, through the skin without requiring any surgery. They were even able to observe fluorescent protein-labelled enteric neurons in the abdomen and monitor the movements of these nerve cells. This enabled them to generate maps showing different movement patterns in the gut during digestion. They were also able to visualize blood flow in the rodents’ brains and the fine structure of muscle sarcomere fibres in their hind limbs.

Reversible effect

The skin becomes transparent in just a few minutes and the effect can be reversed by simply rinsing off the dye.

So far, this “optical clearing” study has only been conducted on animals. But if extended to humans, it could offer a variety of benefits in biology, diagnostics and even cosmetics, says Hong. Indeed, the technique could help make some types of invasive biopsies a thing of the past.

“For example, doctors might be able to diagnose deep-seated tumours by simply examining a person’s tissue without the need for invasive surgical removal. It could potentially make blood draws less painful by helping phlebotomists easily locate veins under the skin and could also enhance procedures like laser tattoo removal by allowing more precise targeting of the pigment beneath the skin,” Hong explains. “If we could just look at what’s going on under the skin instead of cutting into it, or using radiation to get a less than clear look, we could change the way we see the human body.”

Hong tells Physics World that the collaboration originated from a casual conversation he had with Brongersma, at a café on Stanford’s campus during the summer of 2021. “Mark’s lab specializes in nanophotonics while my lab focuses on new strategies for enhancing deep-tissue imaging of neural activity and light delivery for optogenetics. At the time, one of my graduate students, Nick Rommelfanger (third author of the current paper), was working on applying the ‘Kramers-Kronig’ relations to investigate microwave–brain interactions. Meanwhile, my postdoc Zihao Ou (first author of this paper) had been systematically screening a variety of dye molecules to understand their interactions with light.”

Tartrazine emerged as the leading candidate, says Hong. “This dye showed intense absorption in the near-ultraviolet/blue spectrum (and thus strong enhancement of refractive index in the red spectrum), minimal absorption beyond 600 nm, high water solubility and excellent biocompatibility, as it is an FD&C-approved food dye.”

“We realized that the Kramers-Kronig relations could be applied to the resonance absorption of dye molecules, which led me to ask Mark about the feasibility of matching the refractive index in biological tissues, with the aim of reducing light scattering,” Hong explains. “Over the past three years, both our labs have had numerous productive discussions, with exciting results far exceeding our initial expectations.”

The researchers say they are now focusing on identifying other dye molecules with greater efficiency in achieving tissue transparency. “Additionally, we are exploring methods for cells to express intensely absorbing molecules endogenously, enabling genetically encoded tissue transparency in live animals,” reveals Hong.

The study is detailed in Science.

Science thrives on constructive and respectful peer review

It is Peer Review Week and celebrations are well under way at IOP Publishing (IOPP), which brings you the Physics World Weekly podcast.

Reviewer feedback to authors plays a crucial role in the peer-review process, boosting the quality of published papers to the benefit of authors and the wider scientific community. But sometimes authors receive very unhelpful or outright rude feedback about their work. These inappropriate comments can shake the confidence of early career researchers, and even dissuade them from pursuing careers in science.

Our guest in this episode is Laura Feetham-Walker, who is reviewer engagement manager at IOPP. She explains how the publisher is raising awareness of the importance of constructive and respectful peer review feedback and how innovations can help to create a positive peer review culture.

As part of the campaign, IOPP asked some leading physicists to recount the worst reviewer comments that they have received – and Feetham-Walker shares some real shockers in the podcast.

The interview refers to a paper in PeerJ by Nyssa Silbiger and Amber Stubler: “Unprofessional peer reviews disproportionately harm underrepresented groups in STEM“

IOPP has created a video called “Unprofessional peer reviews can harm science” in which leading scientists share inappropriate reviews that they have received.

The publisher also offers a  Peer Review Excellence  training and certification programme, which equips early-career researchers in the physical sciences with the skills to provide constructive feedback.

Convection enhances heat transport in sea ice

The thermal conductivity of sea ice can significantly increase when convective flow is present within the ice. This new result, from researchers at Macquarie University, Australia, and the University of Utah and Dartmouth College, both in the US, could allow for more accurate climate models – especially since current global models only account for temperature and salinity and not convective flow.

Around 15% of the ocean’s surface will be covered with sea ice at some time in a year. Sea ice is a thin layer that separates the atmosphere and the ocean and it is responsible for regulating heat exchange between the two in the polar regions of our planet. The thermal conductivity of sea ice is a key parameter in climate models. It has proved difficult to measure, however, because of its complex structure, made up of ice, air bubbles and brine inclusions, which form as the ice freezes from the surface of the ocean to deeper down. Indeed, sea ice can be thought of as being a porous composite material and is therefore very sensitive to changes in temperature and salinity.

The salty liquid within the brine inclusions is heavier than fresh ocean water. This results in convective flow within the ice, creating channels through which liquid can flow out, explains applied mathematician Noa Kraitzman at Macquarie, who led this new research effort. “Our new framework characterizes enhanced thermal transport in porous sea ice by combining advection-diffusion processes with homogenization theory, which simplifies complex physical properties into an effective bulk coefficient.”

Thermal conductivity of sea ice can increase by a factor of two to three

The new work builds on a 2001 study in which researchers observed an increase in thermal conductivity in sea ice at warmer temperatures. “In our calculations, we had to derive new bounds on the effective thermal conductivity, while also accounting for complex, two-dimensional convective fluid flow and developing a theoretical model that could be directly compared with experimental measurements in the field,” explains Kraitzman. “We employed Padé approximations to obtain the required bounds and parametrized the Péclet number specifically for sea ice, considering it as a saturated rock.”

Padé approximations are routinely used to approximate a function by a rational analysis of given order and the Péclet number is a dimensionless parameter defined as the ratio between the rate of advection to the rate of diffusion.

The results suggest that the effective thermal conductivity of sea ice can increase by a factor of two to three because of conductive flow, especially in the lower, warmer sections of the ice, where temperature and the ice’s permeability favour convection, Kraitzman tells Physics World. “This enhancement is mainly confined to the bottom 10 cm during the freezing season, when convective flows are present within the sea ice. Incorporating these bounds into global climate models could improve their ability to predict thermal transport through sea ice, resulting in more accurate predictions of sea ice melt rates.”

Looking forward, Kraitzman and colleagues say they now hope to acquire additional field measurements to refine and validate their model. They also want to extend their mathematical framework to include more general 3D flows and incorporate the complex fluid exchange processes that exist between ocean and sea ice. “By addressing these different areas, we aim to improve the accuracy and applicability of our model, particularly in ocean-sea ice interaction models, aiming for a better understanding of polar heat exchange processes and their global impacts,” says Kraitzman.

The present work is detailed in Proceedings of the Royal Society A.

Short-range order always appears in new type of alloy

Short-range order plays an important role in defining the properties and performance of “multi-principal element alloys” (MPEAs), but the way in which this order develops is little understood, making it difficult to control. In a surprising new discovery, a US-based research collaboration has have found that this order exists regardless of how MPEAs are processed. The finding will help scientists develop more effective ways to improve the properties of these materials and even tune them for specific applications, especially those with demanding conditions.

MPEAs are a relatively new type of alloy and consist of three or more components in nearly equal proportions. This makes them very different to conventional alloys, which are made from just one or two principal elements with trace elements added to improve their performance.

In recent years, MPEAs have spurred a flurry of interest thanks to their high strength, hardness and toughness over temperature ranges at which traditional alloys, such as steel, can fail. They could also be more resistant to corrosion, making them promising for use in extreme conditions, such as in power plants, or aerospace and automotive technologies, to name but three.

Ubiquitous short-range order

MPEAs were originally thought of as being random solid solutions with the constituent elements being haphazardly dispersed, but recent experiments have shown that this is not the case.

The researchers – from Penn State University, the University of California, Irvine, the University of Massachusetts, Amherst, and Brookhaven National Laboratory – studied the cobalt/chromium/nickel (CoCrNi) alloy, one of the best-known examples of an MPEA. This face-centred cubic (FCC) alloy boasts the highest fracture toughness for an alloy at liquid helium temperatures ever recorded.

Using an improved transmission electron microscopy characterization technique combined with advanced three-dimensional printing and atomistic modelling, the team found that short-range order, which occurs when atoms are arranged in a non-random way over short distances, appears in three CoCrNi-based FCC MPEAs under a variety of processing and thermal treatment conditions.

Their computational modelling calculations also revealed that local chemical order forms in the liquid–solid interface when the alloys are rapidly cooled, even at a rate of 100 billion °C/s. This effect comes from the rapid atomic diffusion in the supercooled liquid, at rates equal to or even greater than the rate of solidification. Short-range order is therefore an inherent characteristic of FCC MPEAs, the researchers say.

The new findings are in contrast to the previous notion that the elements in MPEAs arrange themselves randomly in the crystal lattice if they cool rapidly during solidification. It also refutes the idea that short-range order develops mainly during annealing (a process in which heating and slow cooling are used to improve material properties such as strength, hardness and ductility).

Short-range order can affect MPEA properties, such as strength or resistance to radiation damage. The researchers, who report their work in Nature Communications, say they now plan to explore how corrosion and radiation damage affect the short-range order in MPEAs.

“MPEAs hold promise for structural applications in extreme environments. However, to facilitate their eventual use in industry, we need to have a more fundamental understanding of the structural origins that give rise to their superior properties,” says team co-lead Yang Yang, who works in the engineering science and mechanics department at Penn State.

We should treat our students the same way we would want our own children to be treated

“Thank goodness I don’t have to teach anymore.” These were the words spoken by a senior colleague and former mentor upon hearing about the success of their grant application. They had been someone I had respected. Such comments, however, reflect an attitude that persists across many UK higher-education (HE) science departments. Our departments’ students, our own children even, studying across the UK at HE institutes deserve far better.

It is no secret in university science departments that lecturing, tutoring and lab supervision are perceived by some colleagues to be mere distractions from what they consider their “real” work and purpose to be. These colleagues may evasively try to limit their exposure to teaching, and their commitment to its high-quality delivery. This may involve focusing time and attention solely on research activities or being named on as many research grant applications as possible.

University workload models set time aside for funded research projects, as they should. Research grants provide universities with funding that contributes to their finances and are an undeniably important revenue stream. However, an aversion to – or flagrant avoidance of – teaching by some colleagues is encountered by many who have oversight and responsibility for the organization and provision of education within university science departments.

It is also a behaviour and mindset that is recognized by students, and which negatively impacts their university experience. Avoidance of teaching displayed, and sometimes privately endorsed, by senior or influential colleagues in a department can also shape its culture and compromise the quality of education that is delivered. Such attitudes have been known to diffuse into a department’s environment, negatively impacting students’ experiences and further learning. Students certainly notice and are affected by this.

The quality of physics students’ experiences depends on many factors. One is the likelihood of graduating with skills that make them employable and have successful careers. Others include: the structure, organization and content of their programme; the quality of their modules and the enthusiasm and energy with which they are delivered; the quality of the resources to which they have access; and the extent to which their individual learning needs are supported.

We should always be present and dispense empathy, compassion and a committed enthusiasm to support and enthral our students with our teaching.

In the UK, the quality of departments’ and institutions’ delivery of these and other components has been assessed since 2005 by the National Student Survey (NSS). Although imperfect and continuing to evolve, it is commissioned every year by the Office for Students on behalf of UK funding and regulatory bodies and is delivered independently by Ipsos.

The NSS can be a helpful tool to gather final-year students’ opinions and experiences about their institutions and degree programmes. Publication of the NSS datasets in July each year should, in principle, provide departments and institutions with the information they need to recognize their weaknesses and improve their subsequent students’ experiences. They would normally be motivated to do this because of the direct impact NSS outcomes have on institutions’ league table positions. These league tables can tangibly impact student recruitment and, therefore, an institution’s finances.

My sincerely held contention, however, communicated some years ago to a red-faced finger-wagging senior manager during a fraught meeting, is this. We should ignore NSS outcomes. They don’t, and shouldn’t, matter. This is a bold statement; career-ending, even. I articulated that we and all our colleagues should instead wholeheartedly strive to treat our students as we would want our own children, or our younger selves, to be treated, across every academic aspect and learning-related component of their journey while they are with us. This would be the right and virtuous thing to do. In fact, if we do this, the positive NSS outcomes would take care of themselves.

Academic guardians

I have been on the frontline of university teaching, research, external examining and education leadership for close to 30 years. My heartfelt counsel, formed during this journey, is that our students’ positive experiences matter profoundly. They matter because, in joining our departments and committing three or more years and many tens of thousands of pounds to us, our students have placed their fragile and uncertain futures and aspirations into our hands.

We should feel privileged to hold this position and should respond to and collaborate with them positively, always supportively and with compassion, kindness and empathy. We should never be the traditionally tough and inflexible guardians of a discipline that is academically demanding, and which can, in a professional physics academic career, be competitively unyielding. That is not our job. Our roles, instead, should be as our students’ academic guardians, enthusiastically taking them with us across this astonishing scientific and mathematical world; teaching, supporting and enabling wherever we possibly can.

A narrative such as this sounds fantastical. It seems far removed from the rigours and tensions of day-in, day-out delivery of lecture modules, teaching labs and multiple research targets. But the metaphor it represents has been the beating heart of the most successfully effective, positive and inclusive learning environments I have encountered in UK and international HE departments during my long academic and professional journey.

I urge physics and science colleagues working in my own and other UK HE departments to remember and consider what it can be like to be an anxious or confused student, whose cognitive processes are still developing, whose self-confidence may be low and who may, separately, be facing other challenges to their circumstances. We should then behave appropriately. We should always be present and dispense empathy, compassion and a committed enthusiasm to support and enthral our students with our teaching. Ego has no place. We should show kindness, patience, and a willingness to engage them in a community of learning, framed by supportive and inclusive encouragement. We should treat our students the way we would want our own children to be treated.

Working in quantum tech: where are the opportunities for success?

The quantum industry in booming. An estimated $42bn was invested in the sector in 2023 and is projected to rise to $106 billion by 2040. In this episode of Physics World Stories, two experts from the quantum industry share their experiences, and give advice on how to enter this blossoming sector. Quantum technologies – including computing, communications and sensing – could vastly outperform today’s technology for certain applications, such as efficient and scalable artificial intelligence.

Our first guest is Matthew Hutchings, chief product officer and co-founder of SEEQC. Based in New York and with facilities in Europe, SEEQC is developing a digital quantum computing platform with a broad industrial market due to its combination of classical and quantum technologies. Hutchings speaks about the increasing need for engineering positions in a sector that to date has been dominated by workers with a PhD in quantum information science.

The second guest is Araceli Venegas-Gomez, founder and CEO of QURECA, which helps to train and recruit individuals, while also providing business development services. Venegas-Gomez’s journey into the sector began with her reading about quantum mechanics as a hobby while working in aerospace engineering. In launching QURECA, she realized there was an important gap to be filled between quantum information science and business – two communities that have tended to speak entirely different languages.

Get even more tips and advice in the recent feature article ‘Taking the leap – how to prepare for your future in the quantum workforce’.