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Home » Page 1076

3D display exploits twisted light

A 3D display that exploits the orbital angular momentum (OAM) of “twisted” light has been proposed by scientists at the University of Cambridge and Disney Research. The team says that its nine-by-nine pixel display demonstrates a new and powerful technique for organizing and transmitting the massive amounts of data required for displaying 3D images – and eventually video.

Using their new technique, Cambridge’s Daping Chu and colleagues were able to display three different images that were projected in different directions. Their prototype display showed pixels lit in the shape of three different letters, “P”, “S” and “G”, with each projected at a different angle (see figure). Depending on where viewers positioned themselves, they would see a different letter.

The technique to create the images involved several steps. First, each letter was recorded as a pattern of pixels. Then that pattern was encoded into a signal that could be transmitted to the display. Finally, the display received and decoded the signal to show the image.

Twisting wavefronts

The technique’s innovation, Chu says, lies in its method of encoding and decoding the signal. This allows the display to organize and transmit a large amount of image data in an efficient way. This comes courtesy of a quirk of quantum mechanics: that photons of specific OAM can easily be sorted from each other. A photon’s OAM is separate from its intrinsic angular momentum (or spin). OAM involves the wavefront of the photon twisting around the direction of propagation, creating a vortex in the middle of the light beam.

This rotation occurs at discrete values of OAM called modes. Chu’s group combined the pixel values of the three images with three different modes, essentially using each mode to “categorize” the pixels by image. The next step in the development of the technique will be to bundle all of the information into a single signal. This signal would then be transmitted to the display, which would then sort the pixels into the appropriate images. Then, the display would project the sorted pixels – three separate images – in three different directions.

This use of just one signal contrasts with some other 3D display techniques, in which different perspectives must be transmitted in multiple signals. Because light can have an infinite number of OAM modes, one signal could in principle bundle together an infinite number of perspectives, each encoded using a different mode. This could be used to weave together a seamless 360° image of an object. “You can add in as many perspectives as you like,” Chu says. “We just did three to show that we could beat two.” Three is important because commercial “3D” movies – technically known as stereoscopic movies – only overlay two perspectives to achieve the illusion of depth.

Not true 3D

Strictly speaking, the prototype that Chu and his colleagues created does not display true 3D images. A true 3D image, better known as a hologram, allows a viewer to look at the image from any angle and focus at any depth – swapping the foreground for background at will. When capturing an object’s image, a hologram must record the complete set of properties of light waves that bounce off the object: not only its intensity and colour, but also a timing property of the light known as its phase. Thus, the necessary data for a holographic movie adds up quickly. To create a true 3D holographic display with the size and clarity of a high-definition television, Chu estimates that you would need to be able to transmit 1000 times more data per second than a current 2D HDTV signal. “No hardware can deliver that at this moment,” he says. Their display inhabits the data-moderate middle ground between a true 3D holographic display and the contemporary cinema stereoscopic display.

Although the use of photon OAM is creative, the commercial viability of the technique may be limited, says Pierre-Alexandre Blanche, a holography expert at the University of Arizona, who was not involved in the work. He says that while in principle the technique can bundle an infinite number of images categorized with an infinite number of modes, it is experimentally challenging to actually produce those modes. Chu’s group could produce 30 modes, and Blanche says: “It is still quite an achievement, don’t get me wrong. It’s a nice scientific paper and nice demonstration, but it’s far from having something commercial in the next five years, or even decade.”

Chu acknowledges that the prototype is still far from commercialization. “It’s in the early stages, and it’s more fundamental,” he says. But his goal is to use this work as jumping-off point for a commercial 3D product. Next, his team plans to create multicoloured 3D images using this technique, in addition to using more modes to bundle more images.

The research is published in the Journal of Optics.

‘Radiation friction’ could make huge magnetic fields with lasers

Huge magnetic fields can be created by firing intense, circularly polarized laser pulses at a target, according to calculations by physicists in Italy, Germany and Russia. Their research suggests that the mysterious phenomenon of “radiation friction” plays a crucial role in generating the field. Measuring such magnetic fields could offer physicists a new way of studying this poorly understood effect, which is believed to play a crucial role in the physics underlying astrophysical objects such as gamma-ray flares.

Physicists have long known that a charged particle, such as an electron, emits electromagnetic radiation when it is accelerated – a phenomenon that makes synchrotron radiation facilities and free-electron lasers possible. As energy is conserved, the charged particle loses energy as it radiates and this can be thought of as radiation friction (RF). As well as playing a key role in gamma-ray flares, RF also affects how energy is dissipated in laser-plasma experiments whereby laser pulses are fired at a solid target to create a plasma in which electrons are accelerated to high energies.

Poor models

While experimental studies of RF have provided some information about the phenomenon, physicists do not have good models for calculating its effects. This is why Andrea Macchi at the University of Pisa, Tatyana Liseykina of the University of Rostock and Sergey Popruzhenko at the Moscow Engineering Physics Institute have come up with a new proposal for an experiment that could help to nail down RF.

Calculations and simulations done by the trio show that intense light pulses produced by next-generation, multi-petawatt or exawatt lasers could create short-lived multi-gigagauss magnetic fields in a plasma. Such fields are billions of times stronger than the Earth’s magnetic field and are created when charged particles in the plasma are accelerated into circular orbits. Crucially, the trio’s work shows that RF is the dominant mechanism whereby the charged particles absorb angular momentum from the pulse. Measuring the magnetic fields would therefore provide a direct probe of RF.

Persistent field

This magnetic field is expected to persist for much longer than the duration of the laser pulse that created it, meaning that the field could be detected using optical polarimetry. This involves sending a much weaker pulse of polarized laser light through the plasma and measuring the rotation of the polarization of the transmitted light, which is caused by the presence of the magnetic field. Macchi told physicsworld.com that “this technique has been previously used successfully with sub-picosecond resolution in laser-produced plasmas.”

Although there have been other proposals for measuring RF, Macchi says that in his team’s case, “the RF signature is robust because without RF there would be no strong magnetic field, so that discriminating RF effects may be less prone to experimental uncertainties.”

Macchi says that a better understanding of RF would be useful to astrophysicists who are trying to recreate in the lab the extreme conditions that occur near astronomical objects such as pulsars. Vast amounts of radiation are created in such regions, which comprise strongly magnetized and radiation-dominated plasmas. A better understanding of the behaviour of charged particles in such regions could also shed further light on how extremely high-energy cosmic rays are created in these environments.

Next-generation limit

Astrophysicists will probably have to wait for the next generation of pulsed lasers to be built, however. “Our calculations suggest that at least a power of several petawatts is needed, which is at the limit of the expected performance for forthcoming lasers such as APOLLON, ELI or XCELS,” says Macchi. However, he is not yet ruling out experiments at existing facilities: “We have not explored yet all the possible range of laser and plasma parameters, thus it might be that more accessible conditions are found.”

The research is described in the New Journal of Physics.

What is the maximum number of layers in a human pyramid?

Creating pyramids from people standing on top of each other is a fun gymnastic challenge that is also a cultural spectacle in various parts of the world. In this video, Roger Leyser from the University of Leicester, UK, approaches the challenge from a physics perspective by calculating the maximum number of layers in such a structure. He addresses the limited case in which each person in the human pyramid is balancing on both of their arms and legs. So what’s the answer? Watch the video to find out.

This is one of a collection of videos based on student projects from the University of Leicester’s “Physics Special Topics” course, in which students use their physics knowledge to define and answer a quirky or unusual research question. The videos are part of our 100 Second Science series.

Nearby supernovae could have affected life on Earth

The surface of the Earth was bathed in life-damaging radiation from nearby supernovae on several different occasions over the past nine million years. That is the claim of an international team of astronomers, which has created a computer model that suggests that high-energy particles from the supernovae created ionizing radiation in Earth’s atmosphere that reached ground level. This influx of radiation, the astronomers say, potentially changed the course of the Earth’s climate and the evolution of life.

Earlier this year, two independent teams of astronomers published evidence that several supernovae had exploded some 330 light-years from Earth. Each event showered the solar system in iron-60, an overabundance of which has been found in core samples from the bottom of the Atlantic, Pacific and Indian oceans – and also in deposits on the Moon.

Iron-60 isn’t all that supernovae produce. The exploding stars produce lots of light, as well as cosmic rays, which are composed of high-energy electrons and atomic nuclei. Previous work, in particular by Neil Gehrels of NASA’s Goddard Space Flight Center, indicated that a supernova would have to explode within 25 light-years of Earth to give our planet a radiation dose strong enough to cause a major mass extinction. In contrast, supernovae several hundred light years away were not thought to be capable of affecting either life or Earth’s atmosphere.

Piercing cosmic rays

Now, a team led by Brian Thomas of Washburn University in the US argues that this conclusion is incorrect. The researchers looked at what would happen if a supernova exploded at a distance of 325 light-years and worked-out how its radiation would affect Earth. They found that, other than disrupting circadian rhythms in terrestrial life forms, the blue and ultraviolet light would have no significant effect. However, the cosmic rays accelerated towards Earth by the supernova are a different story. These have energies in the teraelectronvolt (TeV) region and are able to “pass right through the solar wind and Earth’s magnetic field and propagate much further into the atmosphere than cosmic rays normally do”, says Adrian Melott of the University of Kansas, who is part of the team.

It is not the cosmic rays themselves that do the damage to life, but the radiation they create when they interact with the atmosphere. When a cosmic ray strikes an air molecule, it produces a shower of secondary particles that is filled with the likes of protons, neutrons and a strong flux of muons.

Ordinarily this takes place in the upper atmosphere and can be responsible for ionizing and destroying ozone in the stratosphere. However, the supernova cosmic rays are so energetic that they will pass straight through the stratosphere, instead penetrating the lower atmosphere known as the troposphere. There they create showers, which then ionize atoms on or near the ground and up to a kilometre deep into the ocean.

High-energy focus

“Earlier work on supernova damage hadn’t focused on the high-energy regime of the cosmic-ray spectrum,” says Brian Fields, a professor of astronomy and physics at the University of Illinois, who is not part of Thomas’s team. “Adrian, Brian and colleagues have shown that these cosmic rays are important, even though they are less numerous than the ‘garden variety’ cosmic rays at lower energies.”

Today, muons contribute a sixth of our annual radiation dose, but Thomas’s team calculate that a supernova would result in a 20-fold increase in the muon flux that would triple the annual radiation dose of life forms on the planet over the course of several thousand years. This, the team says, is akin to every life form on Earth having a medical CT scan every year. Although this would not wipe out life on Earth, statistically it may have caused some “minor” mass extinctions, as well as cell mutations that potentially sparked a burst in evolution.

There is evidence for a minor mass extinction around 2.59 million years ago, but it is too early to say how strongly it was linked to a nearby supernova that is believed to have occurred around that time. Nevertheless, the team suggests that the range at which supernovae can do damage perhaps needs to be widened. “The cosmic rays increase the ‘kill radius’ for serious biological damage,” says Fields.

Climate change

The cosmic rays may have also changed Earth’s climate. The most recent batch of supernovae came just before Earth entered a series of ice ages, at the end of which paved the way for humans to emerge. One possible link between the supernovae and climate is that muons in the lower atmosphere affected cloud cover, thereby cooling the planet.

“When ionization takes place down in the troposphere, where all our weather occurs, what will that do to our weather and climate?” asks Melott. “I’m not going to claim it causes ice ages, but it’s a possibility that needs to be investigated.”

The next step, says Melott, is to scour the geological record, searching for any evidence that supernovae really did have an effect, while further refining the models describing the propagation of cosmic rays from supernovae through space.

The research is described in The Astrophysical Journal Letters.

In flight around the world's brightest laser and the inverse Cheerio effect

 

By Tushna Commissariat

If you have never been one of the lucky few to have wandered the tunnels of a particle accelerator, but have always wondered what lies within, take a look at the video above. The European X-ray Free Electron Laser (European XFEL) – which is currently under construction in Germany and will come online next year – will provide ultrashort (27,000 X-ray flashes per second) and ultrabright X-ray laser flashes that are needed to study chemical reactions in situ or to study extreme states of matter (you can read more about the kind of research that will be done there in the September issue of Physics World magazine). The XFEL tunnel is 3.4 km long and you can zoom across all of it in the 5 minute long video. I particularly enjoyed watching particular locations where engineers could be seen carrying out tests, as well as watching folks on bicycles wobble out of the camera’s way.

On a slightly related note, if, like me, you occasionally get a bit muddled when it comes to certain details of different particle accelerators – for example which came first, the synchrotron or the cyclotron – take a look at this excellent “primer” over at Symmetry magazine.

(more…)

Dark-energy study maps 1.2 million galaxies in the early universe

Astronomers working on the Baryon Oscillation Spectroscopic Survey (BOSS) have analysed data from 1.2 million distant galaxies to gain further insights into the evolution of the universe. Acquired by the Sloan Digital Sky Survey III (SDSS-III) telescope in New Mexico, the data have been used to create the best map yet of baryon acoustic oscillations (BAOs). These are the relics of the early universe that chart-out how it has expanded over the past 13 billion years.

The BAO map is consistent with the current “Lambda-CDM” model of the universe, which incorporates dark energy and dark matter. Analysis of the data also shows that Einstein’s general theory of relativity is correct at cosmological length scales.

BAOs were created when the universe was just 400,000 years old and the first atoms were forming. Light and matter in the universe decoupled in this epoch, with the light forming the cosmic microwave background (CMB) that is still visible today. When the matter decoupled, its spatial distribution was defined by the peaks and troughs of pressure waves that had existed throughout the universe. This distinct pattern of matter density – the BAOs – then began to evolve into a universe of stars and galaxies. Thanks to theoretical calculations and information gleaned from the CMB, astronomers have a very good idea of what the BAOs looked like in the early universe.

Galaxies and voids

As the universe expanded over the next 13 billion years, gravity pulled matter into regions of higher density to form galaxies, while regions of lower density became voids in space. This pattern of galaxies and voids resembles the early BAOs, with one crucial exception – the characteristic distances between galaxies and voids have increased greatly as the universe expanded. So by mapping the BAOs as a function of cosmic time, astronomers can chart the expansion of the universe over billions of years.

In this latest development, BOSS astronomers have mapped out the BAOs in great detail from 7 billion to 2 billion years ago. They did this by observing 1.2 million galaxies over one quarter of the sky. The distance to each galaxy – and hence the time at which its light began the journey to Earth – was worked out by observing the redshift of characteristic atomic emission and absorption lines in the spectrum of light from that galaxy.

The standard model of cosmology is called “Lambda-CDM”, and it suggests that the expansion of the universe is governed by two competing agents. The gravitational tug of dark matter – which is about 85% of the matter in the universe – acts as a restoring force that tends to work against the expansion. On the other hand, dark energy – which appears to account for 70% of the energy in the universe – pushes in the opposite direction and is currently accelerating the expansion of the universe.

“Clean cosmological picture”

Dark energy does not appear to have played a role in the early universe, and seems to have kicked-in about 5 billion years ago, which is why BOSS was designed to study the BAOs over that time period. This latest study provides further evidence for Lambda-CDM, with an error of only 5% between the measured and theoretical value of the cosmological constant that describes dark energy. “Our latest results tie into a clean cosmological picture, giving strength to the standard cosmological model that has emerged over the last 18 years,” says BOSS team-member Jose Vazquez of Brookhaven National Laboratory.

To create an accurate map, the team had to contend with the “peculiar motions” of galaxies, which refers to the movement of a galaxy that is not related to the expansion of the universe. This appears in the BAO map as an anisotropy that must be corrected for. This peculiar motion is caused by gravity working over huge distances in the universe and analysis of the anisotropy allowed the BOSS team to show that Einstein’s theory of gravity – his general theory of relativity – is correct over very large distances.

The research is described in a series of papers in the Monthly Notices of the Royal Astronomical Society.

Blue is the colour of the universe’s first supernovae

Astronomers hoping to spot “first-generation” supernovae explosions from the oldest and most distant stars in our universe should look out for the colour blue. So says an international team of researchers, which has discovered that the colour of the light from a supernova during a specific phase of its evolution is an indicator of its progenitor star’s elemental content. The work will help astronomers to directly detect the oldest stars, and their eventual supernovae explosions, in our universe.

Early days

Following the Big Bang, the universe mainly consisted of light elements such as hydrogen, helium and trace amounts of lithium. It was only 200 million years later, after the formation of the first massive stars, that heavier elements such as oxygen, nitrogen, carbon and iron – which astronomers all call “metals” – were forged in their extremely high-pressure centres. The first stars – called “population III” – are thought to have been so massive and unstable that they would have quickly burnt out and exploded in supernovae, which would have scattered the metals across the cosmos. Indeed, these first explosions will most likely have sown the seeds to form the next-generation “population II” stars, which are still “metal poor” compared with “population I” stars like the Sun.

Unfortunately, astronomers have yet to detect a true first population-III star or spot a first-generation supernova. Astronomers have been hunting for old stars, and the best evidence for them was found last year in an extremely bright and distant galaxy in the early universe. There are also some candidate stars in our own galaxy.

Old timers

The constituents and properties of the first-generation of stars and their supernova explosions are still a mystery, thanks to the lack of actual observations, especially when it comes to the supernovae. Studying first-generation supernovae would provide rare insights into the early universe, but astronomers have struggled to distinguish these early explosions from the ordinary supernovae we detect today.

Now though, Alexey Tolstov and Ken’ichi Nomoto from the Kavli Institute for the Physics and Mathematics of the Universe, together with colleagues, have identified characteristic differences between new and old supernovae, after experimenting with supernovae models based on stars with virtually no metals. Such stars make good candidates because they preserve their chemical abundance at the time of their formation.

“The explosions of first-generation stars have a great impact on subsequent star and galaxy formation. But first, we need a better understanding of how these explosions look like to discover this phenomenon in the near future,” says Tolstov, adding that the “most difficult thing here is the construction of reliable models based on our current studies and observations. Finding the photometric characteristics of metal-poor supernovae, I am very happy to make one more step to our understanding of the early universe.”

Blue hue

Just like ordinary supernovae, the light or luminosity of a first-generation supernova should also show the characteristic rise to a peak in brightness, followed by a steady decline – which astronomers call a “light curve”. Indeed, a bright flash would signal the shock waves that emerge from the star’s surface as its core collapses. This “shock breakout” is followed by a several-month-long “plateau” phase, where the luminosity remains relatively constant, before the slow exponential decay.

Nomoto’s team calculated the light curves of metal-poor supernovae, produced by blue supergiant stars, and “metal-rich” red supergiant stars. They found that both the shock-breakout and plateau phases are shorter, bluer and fainter for metal-poor supernovae in comparison to the metal-rich ones. The researchers conclude the blue light-curve could be used as an indicator of a low-metallicity star.

Unfortunately, the expansion of our universe makes it difficult to detect first star and supernova radiation, which is redshifted into the near-infrared wavelength. But the team says that upcoming large telescopes such as the James Webb Space Telescope, currently scheduled for launch in 2018, should be able to detect the distant light from first supernovae, and their method could be used to identify them. Their findings could also help to pick out low-metallicity supernovae in the nearby universe.

The work is published in the Astrophysical Journal.

See like a solar system

Many years ago I read a news item in which a scientist said that a sodium cloud issuing from a volcano on Jupiter’s moon Io was “the largest permanently visible feature in the solar system” (Science News 137 359).

That remark stopped me cold. What does it mean to “see” a sodium cloud? More generally, what do scientists mean when saying they see dark matter or black holes? Are they speaking precisely or metaphorically? What is perception? Questions like these were a big factor in attracting me to the philosophy of science. Perception, I decided, isn’t as easy as it looks. To be a scientist is to develop an extended ability to perceive – and the science of the planets in our solar system is replete with examples.

Seeing like a rover

When scientists say they see things like sodium clouds, they speak rigorously. To perceive is not just to grasp something somewhere from a single perspective. It is also to have a sense, however rudimentary, of how that thing looks from other perspectives. Whenever I see a cup, I see only one profile of it. But thanks to our earlier experiences with cups, to see something as a real cup – rather than as a cutout or hallucination – means to anticipate other profiles; how it’ll appear if I walk around it, pick it up and so on. Sometimes these profiles surprise us, or we turn out to be deceived or wrong, but to perceive is always to grasp a profile of something and have a set of expectations about other anticipated profiles. Perception, in short, has a deep structure.

The same is true for a space scientist’s perception, except that it is technologically mediated. In philosophical language, scientists sometimes “embody” their instruments, seeing the world through them relatively directly, just as a blind person sees the world through a cane. When we perceive a planet or comet through an optical telescope, for instance, our previous experiences make us expect the object to be visible at other times in other locations – and that when observed through stronger telescopes it will have profiles that we might not know but that we can guess. At other times, scientists don’t embody but “interpret” their instruments. Just as we say “it’s cold outside” by looking at a thermometer, so a space scientist “sees” a sodium cloud with filters and spectrometers if these belong to expected profiles.

Astronomical perception involves a complex combination of these two concepts of embodiment and interpretation. An interesting case study is found in the 2013 article “Mediating Mars: perceptual experience and scientific imaging technologies” (Foundations Sci. 18 75) by the philosopher Robert Rosenberger from the Georgia Institute of Technology, US. In it, he describes a debate about a rock formation imaged by NASA’s Mars Global Surveyor in a Martian crater known as Eberswalde. Some scientists argued they were looking at the remains of a river delta, others an alluvial fan, still others that they were seeing the product of mudslide-like events.

Rosenberger shows that the scientists went about resolving the controversy, not by evaluating competing theories or explanations about the rock formation itself, but by appraising the different strategies that they were using to produce the images. They asked themselves, Rosenberger writes, “How does the process of transforming this object of study (i.e. a rock formation on Mars) into a specific form we are able to perceive here on Earth (i.e. images) leave these images open to interpretation in particular ways?” Without being able to move freely around the formation as they would on Earth, the scientists had to sharpen their perception of the rock formation by understanding the profiles better, and by analysing other profiles provided by shadows, laser altimeter data and so on.

Another analysis of scientific perception is found in Seeing Like a Rover: How Robots, Teams, and Images Craft Knowledge of Mars (2014 Princeton University Press) by the Princeton University sociologist Janet Vertesi. She based her book on two years spent as an ethnographer studying scientists in NASA’s Mars Exploration Rover mission. Vertesi found the researchers’ workspaces, computer screens and Powerpoints were saturated with images: filtered, false-colour, 3D, fish-eye, panoramic and more.

Taken by the two rovers Spirit and Opportunity, these images let the researchers “see” on Mars, but not with a human eye. One researcher told Vertesi that the two rovers’ view of the world was like “trying to make your way through a dark cluttered room with nothing but a flashbulb”. Yet the researchers became skilled at it, seeing and manipulating phenomena on the Martian surface. “When you work with the team for a while,” another researcher told her, “you kind of learn to see like a rover.”

Vertesi’s book shows that seeing like a rover is not just a matter of grasping profiles and horizons, but also involves ways of speaking and gesturing, emotional connections, habits and even the research group’s social and organizational structure. Seeing like a rover, she writes, “is…a question of seeing from somewhere, not adopting a view from nowhere” – with the “somewhere” referring not just to the rover’s cameras but to the entire research team and its activity.

The critical point

The curse of current-day philosophy of science is the lingering but fraudulent idea among philosophers that science involves the quest to see phenomena from nowhere. Instead, it’s done by people with inherited concepts using particular equipment to study topics that seem important. To perceive a scientific phenomenon involves grasping how all of the profiles you can see of it – and how others that you don’t yet or never will see – hang together. Not only that, but mediated scientific perception deepens and extends our notion of what it is to perceive at all.

Could we generate useful energy from earthquakes?

In terms of their impact on humans, earthquakes are rightly considered to be threatening and destructive events. In principle, however, something useful could come out of the Earth’s shaking – the generation of electricity using a magnet inside a coil. As the coil flexes with the shaking of tectonic plates, it is subjected to a changing magnetic field, which generates a current in the coil.

In this video, Elliott Spender, a research assistant at the University of Leicester, calculates how much energy could have been generated in this way during the Kobe earthquake of 1995, which measured 7.2 on the Richter scale (or 6.9 on the moment magnitude scale). He then speculates how this energy could be put to use in a city such as San Francisco.

This is one of a collection of videos based on student projects from the University of Leicester’s “Physics Special Topics” course, in which students use their physics knowledge to define and answer a quirky or unusual research question. The videos are part of our 100 Second Science series.

Neural networks provide deep insights into the mysteries of water

Artificial neural networks have been used to simulate interactions between water molecules and provide important clues about the remarkable properties of this live-giving substance. The study has been carried out by physicists in Germany and Austria, who used the networks to perform simulations 100,000 times faster than possible with conventional computers. Their work offers explanations for two key properties of water – its maximum density at 4 °C and its melting temperature – but the technique could be expanded to include other aspects of this ubiquitous substance.

Physicists and chemists have long found water’s unusual properties difficult to explain. Its density, for example, peaks at around 4 °C, which means that frozen water floats on liquid water – a property that is vital for aquatic creatures that have to survive in cold climates. Massive computer simulations have shown that hydrogen bonds between water molecules play a key role, but these simulations do not tell the whole story.

One key challenge is understanding the role of van der Waals interactions, which arise from quantum fluctuations in the electrical polarizations of water and other molecules. Van der Waals interactions have traditionally been hard to include in computer simulations, but Tobias Morawietz and colleagues at the Ruhr-Universität Bochum and the University of Vienna have now used artificial neural networks (ANNs) to model them in water. ANNs are computer algorithms that “learn” how to perform a specific task by being fed data related to that task. An ANN could, for example, learn how to recognize an individual’s face by being fed photographs of people and being told which images are of the target person.

Computationally expensive

In this latest research, Morawietz and his team fed the ANNs data from density functional theory (DFT) calculations of the interactions between water molecules. DFT is widely used to calculate the properties of molecules, but for interactions between water molecules, it can only provide an approximate result that must then be corrected to account for van der Waals interactions. Such calculations are also computationally expensive and so are normally done at just a few temperatures and pressures.

The problem is that to understand the density maximum of water, researchers need to do lots of calculations at different temperatures, which is too computationally intensive to be practical. The team therefore taught their ANNs using data from both van der Waals-corrected and uncorrected DFT calculations, which let the ANNs learn how van der Waals interactions affect the interactions between water molecules.

The ANNs were then used to calculate the properties of water in the temperature range from –100 to 90 °C, which they could do about 100,000 times faster than possible using DFT. Morawietz and colleagues were therefore able to determine the molecular structure of water over a range of temperatures and, then, infer the density of liquid water and ice.

Competing effects

The results reproduced the density maximum at 4 °C, which Morawietz says can be understood in terms of how van der Waals interactions affect the hydrogen bonding of water molecules. As liquid-water cools, the hydrogen bonds between a water molecule and its four nearest neighbours become stronger, pulling them together and making the water denser.

However, as the bonds strengthen, Morawietz says that this group of five molecules becomes more rigid – and so it becomes less likely that a surrounding water molecule can penetrate this tightly knit group. This has the opposite effect on density: as the temperature decreases, the hydrogen bonds become more rigid, allowing fewer water molecules to penetrate the group and so decreasing the density upon cooling.

According to Morawietz and colleagues, the ANN calculations show that van der Waals interactions moderate the rigidity of the hydrogen bonds, with these two competing density effects creating a maximum density at 4 °C. “van der Waals interactions crucially modify the hydrogen-bond network in water and give hydrogen bonds the right flexibility to exhibit a density maximum,” explains Morawietz.

He adds that the ANN calculations also show that van der Waals interactions make liquid water denser than ice at 4 °C, explaining why ice floats when it is formed. The calculations were also able to predict the melting temperature of ice.

Other approaches

Alan Soper of the Rutherford Appleton Laboratory in the UK told physicsworld.com that this research demonstrates clear progress in addressing the inability of DFT to simulate van der Waals interactions. However, he points out that several alternative computational approaches have been used and have delivered results that are comparable to those of Morawietz and colleagues.

Soper also points out that the discrepancy between the measured density of water and the calculated result is either 5 or 10% – depending on which DFT scheme the team used. While the team’s predictions for pressure and structure are much closer to experimental values, he says that a density discrepancy of less than 1% is needed to validate the model.

Morawietz says that the team is now adapting its technique to study proton transfer in water – an effect that is currently difficult to simulate but plays an important role in acid-base chemistry.

The simulations are described in Proceedings of the National Academies of Science.

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