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Home » Page 977

Quantum superposition still adds up in three-slit experiment

A group of physicists in Austria has directed a beam of large molecules at a series of extremely narrow slits to search for a phenomenon known as “multipath interference”. Although, as expected, they found nothing, they say that the search is well worth the effort given the potential prize on offer – disproving the principle of superposition and with it quantum mechanics as we know it.

According to the superposition principle, any two quantum states can always be added together to create a third, valid state. Conversely, it is always possible to split an existing quantum state into two sub-states. The latter characteristic is exploited in many quantum technologies, be it the superposition of a 0 and a 1 in a quantum bit or the splitting and interference of a laser beam to measure tiny variations in position or acceleration.

To investigate whether superposition really occurs in nature, the latest research relies on a particular characteristic of a quantum object: that no matter how many paths it could take to go from one state to another, the mathematical expression describing the probability of it yielding a certain measured outcome can always be split into a series of terms, each of which involves the object following no more than two paths at the same time. The existence of irreducible three- or more-path interference would require the (linear) Schrödinger equation to be replaced by a more general, nonlinear alternative.

Massive particles

Other groups have recently looked for evidence of this multipath interference using, among other things, beams of laser light and microwaves. But the new work, carried out by Joseph Cotter of the University of Vienna in Austria and colleagues, is the first to have done so using massive particles. As Cotter explains, the existence of a mass-dependent term in a nonlinear extension to the Schrödinger equation might explain why quantum effects disappear at macroscopic scales.

In its study, the team considers what happens when a beam of massive particles passes through a set of three slits. Thanks to wave-particle duality, the beam will generate a set of interference fringes on a screen placed some distance behind the slits. This pattern will be formed even when only one particle passes through the slits at any one time. If superposition holds true, the wave function describing the beam passing through all three slits will be equal to the sum of the wave functions associated with each individual slit.

In this case, with a total of three slits, the probability of a particle arriving at any point on the screen can be written in terms of six sub-probabilities – three of which specify the odds associated with the particle passing through just each single slit and the other three the chances linked to it instead passing through a given pair of slits. This means superposition can be tested by comparing the probabilities measured in a three-slit experiment with those obtained in one- and two-slit experiments: if the appropriate combination of results from the latter do not match the result of the former then the Schrödinger equation has been found wanting.

Simultaneous patterns

The group used a laser to generate a thermal beam comprising molecules of a dye known as phthalocyanine that they directed at a diffraction mask made by scientists in Israel. The mask contained slits just 80 nm wide arranged into four groups – a single slit, two double slits and a triple slit – that yield simultaneous interference patterns on a screen positioned behind.

The researchers found, as Schrödinger’s equation dictates, that by subtracting the suitably summed intensities of the single and double slits from that of the triple slit they were left with intensities very close to zero. In fact, they observed that the position of less than one particle in every 100 recorded on the screen was at odds with the predictions of quantum mechanics. This result held true for particles across the width of the diffraction pattern and for the full range (2.5–5 pm) of De Broglie wavelengths tested.

Angelo Bassi of the University of Trieste in Italy praises the “novel” experiment, describing it as “further confirmation that quantum mechanics holds true at a higher level than can be explored using ‘standard’ double-slit experiments”. The eventual discovery of multipath interference, according to Raymond Laflamme of the University of Waterloo in Canada, would lead to a “revolution in our understanding of the world”. Indeed, he maintains, “trying to find where quantum mechanics would fail is as interesting as trying to build quantum computers.”

Lighter and heavier

Carrying out more sensitive probes of multipath interference using massive particles could potentially be done in a couple of different ways, says Cotter. One is to replace the relatively heavy, thermal – and therefore short-wavelength – molecules used in the current experiment with cold, low-mass atoms such as helium or lithium with longer wavelengths. This is because if multipath interference occurs, it is expected to scale as the 3/2 power of wavelength. However, if mass does modify the Schrödinger equation, then more massive particles could be tried. Doing so, says Cotter, would require brighter molecular sources to up the rate of data-taking as well as more advanced masks, perhaps created optically.

The research is described in Science Advances.

Eccentric orbit affects solar wind on Mars

Mars has a relatively large eccentricity as it orbits the Sun and this has a significant effect on how the solar wind is deflected by the Red Planet, according to an international team of astronomers. Benjamin Hall of Lancaster University in the UK and colleagues have discovered that the distance between the planet’s bow shock and Mars itself varies by 11% and suggest it is linked to the solar extreme ultraviolet (EUV) irradiation.

Like a boat

When a boat travels across water, its bow (the front) slows and diverts water around the vessel, creating a wave. On a much larger scale, a similar phenomenon occurs as a planet’s magnetosphere diverts highly energetic particles carried in the interplanetary solar wind. The interaction creates a curved wave – dubbed a bow shock – upstream of the planet as it travels through space.

Measurements of Mars’ bow shock have been reported since missions began to the Red Planet in the 1960s. As Mars is unmagnetized but has an atmosphere, the main obstacle for the solar wind is the ionosphere and induced magnetosphere. The planet also has an extended exosphere due to its relatively small size, mass and therefore gravity, which interacts with the solar wind.

Five Martian years

While previous studies have shown that the bow-shock’s location changes during the Martian year, Hall and colleagues have investigated how and why this variation occurs. The team analysed five Martian-years’ worth of data from the European Space Agency’s Mars Express orbiter to identify 11,861 bow-shock crossings. This is the longest period to be analysed and approximately covers a full solar cycle. Each crossing was mapped to the terminator plane (the day–night boundary) to allow direct comparisons.

The team discovered the bow shock is, on average, closer to Mars (minimum 8102 km) when the planet is furthest from the Sun – at aphelion – and further away (maximum 8984 km) when the planet is at its closest point to the Sun – at perihelion. The variation also correlates with the annual changes in atmospheric dust as Martian dust-storm season occurs around perihelion when the solar radiation is higher and the planet is warmer.

Slowing the solar wind

As the bow-shock distance from Mars increases linearly with solar EUV irradiation, while reducing via a power-law relationship with solar-wind dynamic pressure, the former is likely the major driving factor. Hall and colleagues suggest that when closer to the Sun, the enhanced solar EUV increases the number of exospheric ions. This can then act to slow the solar wind and hence raise the bow-shock location. The EUV may also enhance the total electron content and pressure within the ionosphere to form a more effective barrier to the solar wind.

Presenting their work in the Journal of Geophysical Research: Space Physics, the researchers highlight the need for further investigations by the Mars Express Orbiter and NASA’s MAVEN mission.

Meanwhile, another Martian study has been published in Nature Geoscience. Using numerical simulations, researchers from France suggest Mars experiences localized snowstorms during the night.

Dynamical quantum phase transitions seen in ultracold ions and atoms

A type of quantum phase transition first predicted in 2013 has been seen by three independent teams of physicists. All three experiments involved systems of interacting ultracold atoms or ions and the observations could lead to a better understanding of the collective behaviour of quantum matter.

Phase transitions occur when matter transforms spontaneously from one state to another – from solid to liquid at the melting point of water, for example. Classical phase transitions are associated with thermal fluctuations in a system such as the random motion of water molecules. In contrast, quantum phase transitions involve fluctuations that arise from short-term changes in energy as described by Heisenberg’s uncertainty principle. As a result, quantum phase transitions tend to occur at absolute zero or very low temperatures, where quantum fluctuations dominate over thermal fluctuations.

Time passages

Phase transitions are usually studied when a system is at or near thermal equilibrium, but in 2013, Markus Heyl, Anatoli Polkovnikov and Stefan Kehrein pointed out a similarity between the mathematical operator describing the time evolution of a non-equilibrium quantum system and the partition function of a system in thermodynamic equilibrium. Furthermore, the theorists calculated that the quantum system should undergo changes of state that are reminiscent of phase transitions. The difference being that instead of being driven by a change in an external factor such as temperature, the quantum transitions occur as time progresses.

In one of the three independent experiments, Rainer Blatt of the University of Innsbruck and colleagues in Austria and Germany observed dynamical quantum phase transitions in strings of up to 10 ions trapped in an ultracold environment. The system is described by the transverse-field Ising model, whereby an interaction between neighbouring ions can be adjusted so that the ions align their spins along one direction (say x). There is also a magnetic field applied in a transverse direction (such as z), which exerts a torque on the spins.

Random directions

Beginning in an ordered state with all spins pointing in the same direction, the team then changed the interactions between the spins so that they align in random directions – driving the system away from equilibrium. The system is then allowed to evolve with time and the team measured the probability that the spins point in the same direction (a quantity called the rate function). As predicted by Heyl and colleagues, the researchers found that this occurred at two specific times – much like how conventional phase transitions occur at specific temperatures, for example. Writing in Physical Review Letters, they also explain how systems containing six, eight and 10 ions had the same behaviour.

Meanwhile Nick Fläschner of the University of Hamburg and colleagues spotted dynamical quantum phase transitions in a 2D optical lattice of ultracold atoms and describe their work on arXiv. Also on arXiv is a preprint by Christopher Monroe of the University of Maryland and colleagues describing dynamical quantum phase transitions in a string of 53 ions.

Squishy-sphere splashes could lead to better speedboats

High-speed camera image of a silicone rubber sphere plunging into a tank of water. (Courtesy: Splash Lab)

A study of how deformable spheres impact on water surfaces could lead to better inflatable speedboats. The research was done by Randy Hurd, Tadd Truscott and colleagues at Utah State University, Brown University and the Naval Undersea Warfare Center Division Newport – all in the US.

The team dropped balls made of silicone rubber from three different heights (0.53, 1.53 and 2.27 m) into a tank of water. The balls had two different diameters (5.1 and 10 cm) and had three different degrees of stiffness.

Significant oscillations

The team says that this is the first study of the differences in how rigid and non-rigid materials behave when they impact water. “Rigid and elastic materials interact with the water surface quite differently,” says Hurd. “When an elastic body impacts the surface, the material deforms and oscillates significantly, which changes the water-impact physics compared to a rigid body.”

The researchers used high-speed cameras operating at 2000 frames per second to measure the position and deformation of the spheres as they enter the water (see figure). This allowed them to work out how the impact energy is absorbed by the material. They then devised a model of the deformation and vibration based the object’s stiffness and the speed of the impact.

Smoother ride

“Being able to predict water interaction from a materials perspective is an important first step in understanding which material types would be best for developing an inflatable watercraft capable of providing a smoother ride over a choppy surface,” says Hurd.

“While our work focused on answering more fundamental questions, the results could be used in the design of various structures made from deformable materials that interact with the water,” says Hurd. In addition to inflatable boats, “future applications could range from capsules to enable the deployment of sensitive equipment at sea to fly fishing.”

The study is described in the Journal of Fluid Mechanics.

Engineered needles promise direct diagnosis of muscle conditions

Electrodes used to measure the electrical impedance of muscles in neuromuscular diseases can provide more accurate information if they are placed in the shaft of a short needle inserted into the patient’s skin. Now, researchers at Harvard University in the US have exploited numerical modelling to design and fabricate a four-electrode needle that minimizes unwanted interference from subcutaneous fat tissues, increasing the contribution from the muscles and opening up new possibilities in electrodiagnostic medicine (Physiol. Meas. 38 1748).

Neuromuscular disorders (NMD) such as amyotrophic lateral sclerosis affect muscle health, which in turn affects its electrical impedance. The traditional technique for recording skeletal muscle impedance and providing diagnostic information, known as surface Electrical Impedance Myography (EIM), involves placing two pairs of surface electrodes on the skin over the muscle of interest: the outer pair of electrodes sends an electrical current signal that travels through the muscle, and the inner one collects the resulting voltage. However, this surface EIM approach can only measure the most superficial muscles and is prone to measurement errors induced by the thickness of the subcutaneous fat tissue between the skin and the muscle at the measurement site.

To overcome these limitations, recent investigations have focused on developing minimally-invasive unipolar and bipolar needles, containing respectively one and two electrodes, to record the impedance. However, the polarization and dimensions of the electrodes in these configurations can have a major impact on measurements of muscle impedance.

A team led by Benjamin Sanchez from Harvard University therefore turned to theory and modelling to design a tetrapolar needle that would solve these problems. The needle was subsequently manufactured and tested in vivo by recording the muscle impedance in rats, and the results showed a good agreement with reference muscles values previously reported in the literature.

Combining theory, modelling and experiments

The researchers considered many different parameters to design the needle with one major objective in mind: to minimize the contribution of skin and subcutaneous fat tissues that usually distort surface EIM. Different depths and angles of penetrations, changing the distance between the electrodes, and different sampling frequencies were all tested in 3D finite element model simulations to obtain the optimal set of needle parameters.

Exploiting theory and modelling to design the needle and optimize its recordings is a novel approach, since previous needle-based studies have only judged their results qualitatively. And the results speak for themselves: while the contribution to the electrical impedance from muscle is typically ranging between 8 and 32% for surface EIM, the engineered tetrapolar needle increased this contribution to more than 97%.

Although this experiment has been performed on a small sample of rats and needs further testing in both healthy and diseased muscles, the results of this study are promising. Compared to surface EIM, needle EIM offsets the contributions from both skin and subcutaneous fat tissues, thus providing more accurate readings in overweight patients. They are also unaffected by changes in muscle size or shape and consequently generate more robust data, plus they can provide a local assessment of diseased muscle with higher spatial resolution. Taken together, these results show that needle EIM has the potential of becoming a powerful biomarker for the neurology community to assess muscle condition and therapy effect.

Rare gravitational lens caused by mysterious source

A new type of gravitational lens could allow astronomers to probe dark matter as well as matter a million times the mass of the Sun. Harish Vedantham of Caltech’s Owens Valley Radio Observatory in the US and colleagues identified the lens at radio wavelengths, and they suggest it is magnifying light from clumps of matter racing relativistically along jets that are blasting from a galaxy’s central supermassive black hole.

Vedantham and team discovered the lens within a survey of 1800 active galaxies, which has been ongoing since 2008. The team focused on an active galaxy called PKS 1413+135, located about three billion light-years away and which mysteriously brightened, first in 2009 and then again in 2014. Something between us and the galaxy, with a mass equivalent to 10,000 suns, is warping space into a cosmic magnifying glass.

A new approach to finding lenses

Gravitational lensing occurs when the large mass of an object bends space to such a degree that it magnifies the light of more distant objects, and even creates multiple distorted images of those background objects. On large scales, galaxy clusters regularly act as lenses for more distant galaxies. On much smaller scales, exoplanets have been spotted briefly magnifying the light of background stars in cases of gravitational “micro-lenses”.

On the other hand, gravitational “milli-lensing” falls between the two extremes, where objects smaller than galaxies but more massive than individual stars or planets form the lenses, but they are so hard to spot that none had been found until now.

The multiple images a milli-lens creates are spaced so narrowly that they are at the limit of our current telescopic sensitivity. Instead Vedantham’s team has adopted what he describes as “a new approach to finding and studying milli-lenses”. Instead of looking for multiply lensed images, they searched for signs of what they call “symmetric achromatic variability” – the symmetrical brightening and fading of radio emission from an object that is passing precisely behind the lens for about a year. Vedantham’s team suggest that the milli-lens magnified the light from two clumps of searingly hot plasma – one in 2009, the other in 2014 – that were moving along jets blasting out from PKS 1413+135’s central black hole.

Mystery magnifier

The real mystery is the identity of the object acting as the lens. A large star cluster could do the trick, although there are no obvious intervening foreground galaxies where such a cluster could reside, meaning it would have to be within a faint dwarf galaxy that has yet to be discovered. Alternatively, it could be an intermediate mass black hole, perhaps one that was made just after the Big Bang.

“A black hole always fits the bill,” says Vedantham. If it is a black hole, then it is possible it is a member of a large population of primordial black holes that wander alone through space and could account for a significant fraction of dark matter (see our earlier story).

Even if the lensing object is something more mundane like a star cluster, it could still be used to probe dark matter. “Different dark-matter theories make different predictions about structure formation in the universe,” says Vedantham. Therefore, the nature of dark matter can have repercussions for the relative numbers of clumps of matter at different scales, from galaxy clusters to individual galaxies to star clusters and giant molecular clouds. “By observing the abundance of galaxies of different mass we have put these theories to the test, but the lower mass range has always been out of reach,” he says.

To Vedantham’s mind, gravitational milli-lensing is the only “realistic” way of probing matter in this lower mass range, and if more milli-lenses can be discovered they could help define our models of dark matter. Already Vedantham believes his team has identified a second milli-lens, seen by the University of Michigan Radio Astronomy Observatory in the active galaxy AO 0235+164, which displayed variability in 1994 and 1999 across a wide range of wavelengths (hence the phenomenon being described as achromatic). It is hoped that sophisticated “very-long-baseline interferometry” (VLBI) techniques could soon have the resolution to detect the multiple images of milli-lenses and provide another way of discovering them.

The research is published in The Astrophysical Journal.

Row threatens Chinese telescope

Construction is expected to begin in 2018 on the ¥2bn Large Optical/Infrared Telescope, which will dwarf China’s previous largest general-purpose telescope, the 2.4 m Yunnan Observatory shown in this photograph. (Courtesy: SCHOTT)

China’s proposal to build a 12 m-aperture telescope in the west of the country has stalled due to a dispute over how many mirrors the telescope should have. The ¥2bn ($300m) Large Optical/Infrared Telescope (LOT) will be one of the world’s largest upon completion and is expected to let Chinese astronomers explore the early universe and exoplanets. However, optical engineers and scientists hold seemingly irreconcilable differences on the best optical design.

The largest general-purpose telescope in China is currently a 2.4 m facility in Lijiang, Yunnan province. The lack of a large-aperture, general-user optical telescope has seriously hampered the development of Chinese astronomy. Astronomers first submitted a proposal for LOT in 2015 and in December last year it came second on a list of 10 research infrastructures compiled by the National Development and Reform Commission for the current national five-year plan, which runs from 2016 to 2020. Construction is due to begin by the end of 2018 with the telescope’s first light in 2023.

The original optical design for LOT called for a four-mirror system featuring a primary and secondary mirror as well as a so-called “SYZ relay mirror” and a flat-fold mirror. According to its designers from the Nanjing Institute of Astronomical Optics and Technology (NIAOT), which is part of the National Astronomical Observatories of the Chinese Academy of Sciences, the biggest advantage of such a scheme is that it can produce high-quality images.

Complicated and risky

However, the design is complicated and risky as many of the techniques used in a four-mirror system are still at an experimental stage. That is why some researchers – backed by a group at Huazhong University of Science and Technology in Wuhan – have expressed concern about the design. They instead want a three-mirror system that would be based on a Ritchey–Chrétien (RC) design that is widely adopted by existing telescopes such as the twin Keck Telescopes atop Mauna Kea in Hawaii.

“We have little prior technical experience, so we need to minimize the risk, cost and complexity by adopting as simple as a design as possible, and use available, proven technology to satisfy the scientific requirements,” says astrophysicist Luis Ho who is director of the Kavli Institute for Astronomy and Astrophysics at Peking University.

In April a panel of nine international experts from nearly all existing and planned 8–30 m-class telescopes met in Beijing for a review of LOT’s three- or four-mirror optical design, where the conclusion was overwhelmingly in favour of the three-mirror system. “The four-mirror SYZ optical system cannot compete with the standard RC solution in meeting the government and scientific demands on limiting magnitude, field of view, operational flexibility and total budget,” the review read. “The SYZ optical system is therefore eliminated from further consideration.”

Foreign meddling

However, NIAOT researchers did not back down, questioning China’s support of innovation and the US involvement in the three-mirror system. “Why should foreigners be meddling with our own telescope?” they wrote on social media. CAS then organized a re-evaluation on 10 July with the absence of three-mirror representatives and a panel made up of 21 domestic scientists only. The panel gave their support for the four-mirror system.

The dispute was intended to stay private but went viral on Chinese social-media platforms when it was leaked early last month. NIAOT’s Ming Liang, who is one of the designers of the four-mirror system, says public debate is good because it is a chance to familiarize people with their innovative design. He points out that many of the criticisms of their design are unfair and wrong. “I’ve never heard of such international reviews for any big telescope in the world,” he wrote on one Chinese social-media site. “For a telescope funded by the Chinese government, the design should come from within [China]. We will take good suggestions from foreigners, but they don’t get to decide how our telescope will be built.”

Focus on science

Sandra Faber, an astrophysicist from the University of California, Santa Cruz, US, who was not a member of the international advisory panel, says that the four-mirror system will “seriously” limit the telescope’s field of view. Yet her main concern is that good science needs to be done with the instrument. “The astronomical world will not care whether there are three mirrors, or five mirrors, or 10 mirrors – they will only care about the brilliance of the science results,” she says. “If China wants to become a leader on the world astronomical stage, it needs to focus on good science, not on telescope design.”

Ho, who says that he is “shocked and dejected by the chain of events”, adds that scientists in China need to “rise to the challenge” or they will never catch up with other countries.

Toward noninvasive assessment of intracranial pressure

Intracranial pressure (ICP) is an important parameter in the monitoring of critical-care patients, but it can currently only be obtained accurately via invasive methods. Researchers from Germany have now shown that a new commercial device could offer a non-invasive alternative that they believe could pave the way to safer and more widespread ICP monitoring (J. Neurosurg. doi: 10.3171/2016.11.JNS152268).

The research team, from Klinikum Stuttgart and the University of Erlangen, tested the performance of the HS-1000 system from HeadSense Medical Ltd. Positioned close to the ear, the device emits a short burst of sound at 66 dB, generating an acoustic wave that travels through the cranium. The acoustic signal, along with other physiological sounds, is collected at the opposite ear, with subsequent signal processing yielding a measurement of ICP.

The experiment involved 14 patients who were being treated for traumatic brain injury or subarachnoid haemorrhage (bleeding between the brain and its surrounding tissues). In total, more than 2000 pressure points were acquired using the acoustic method, and then compared with conventional ICP measurements taken at the same time.

The statistical analysis seems to indicate that the method could offer a viable way to measure ICP non-invasively. Comparing the data revealed a strong correlation between the two methods (r=0.82; p<0.0001), with a more refined analysis showing that 63% of the paired-data measurements were ±3 mmHg of each other and 85% within ±5 mmHg. Similar differences have been reported between current gold-standard invasive methods.

An important clinical parameter

ICP is commonly recorded in intensive care units to track changes in pressure and prevent further damages to the brain. The gold standard method requires a hole to be drilled in the patient’s skull to allow a catheter to be inserted into brain tissue or the ventricle, the part of the brain that is filled with cerebrospinal fluid. In the latter instance, the catheter can both monitor ICP and reduce it by extracting excess cerebrospinal fluids. But despite this advantage, ICP recording via catheters is technically difficult and carries risks of infection, bleeding or further damages to the brain tissues.

This is not the first time that researchers have attempted to develop non-invasive methods as an alternative to catheter-based ICP recordings. Previous studies have investigated, for example, surrogate techniques such as Doppler ultrasound scanning of the brain, or tracking the tympanic membrane displacement and optic-nerve sheath diameter. However, they have all so far proved too inaccurate to be used routinely. The normal ICP in humans is usually around 20 mmHg, which means that an error of more than 5 mmHg could have fatal consequences for the patient.

A first step toward easier ICP monitoring

Although the results presented in the study are only preliminary and requires further investigations, this is the first time that a non-invasive technique exhibits such accuracy in ICP measurements. This new technology therefore offers a promising route to making ICP monitoring easier and more widespread in clinical practices.

Team sizes up packaged water waste in West Africa

Packaged drinking water is increasingly important in low- and middle-income countries but to combat plastic pollution, it’s crucial to know what’s being consumed, where, and why. In some regions, even basic information on how much people rely on packaged water is lacking. Now, an international team has examined household surveys from Ghana, Nigeria and Liberia to determine packaged water consumption and what happens to the waste.

Combined, the three west African countries produce around 28,000 tonnes of plastic waste from packaged drinking water per year, the researchers found. “This has significant environmental implications,” said Nicola Wardrop from the University of Southampton, UK.

As waste collection and disposal facilities are limited, much of this plastic ends up back in the environment. In Nigeria alone, nearly 5000 tonnes of plastic water sachets are dumped in unauthorised heaps each year, the study suggests. In Ghana and Liberia, some plastic waste is burned – a concern for both the environment and public health.

Ghana is the biggest consumer of packaged water, with 11.3 million litres bought each day, the team estimated. To cut such consumption, governments could invest in drinking-water supply to households. This would ensure safe water provision and the best outlook for the environment, but Wardrop and colleagues stress that this can’t be implemented fast enough to deal with the waste. Instead, they believe, the focus should be on improving waste collection routes, as they will immediately reduce the impact of plastics on the environment.

“The results really highlight the joint impact of sachet consumption and lack of recycling services,” said Wardrop.

Currently, demand for waste disposal far exceeds supply, with 63% of Nigerian households, 57% of Liberian households and 20% of those in Ghana lacking formal waste-disposal facilities, let alone a means of recycling the waste. Grass-roots initiatives are tackling some of the shortfalls. With the help of these and private companies, governments could better tackle plastic pollution.

At nearly 150 litres, the amount of packaged water consumed per head each year in Ghana is comparable with levels in the US, where there is access to ample safe water on tap. Levels in Liberia (31 litres) are similar to those in the UK.

Wardrop and colleagues reported their findings in Environmental Research Letters (ERL).

US eclipse spoiler alert

Later today, parts of 14 US states will witness a total solar eclipse. The umbra – the shadow cast when the Moon fully eclipses the Sun – will first be seen on the coast of Oregon at 10:18 PDT. The 70 mile-wide path of totality will then sweep across the US, seen last in South Carolina. The event offers solar scientists a unique chance to study the Sun’s outer atmosphere – the corona – which will be visible in much greater detail while the Sun’s brightness is blocked by the Moon. The eclipse also allows scientists to test their predictions of the Sun’s behaviour.

A team at Predictive Science, Inc. in the US has been running large-scale simulations of the Sun’s surface, and hence corona, since 28 July, working alongside NASA, the Air Force Office of Scientific Research and the National Science Foundation. Using multiple massive supercomputers, the researchers have created highly detailed solar simulations timed to the moment of the eclipse, including visualizations of what people in the path of totality will see. They will then compare their predictions to observations made during the eclipse to test the viability of their models.

Better than powerful telescopes

“The solar eclipse allows us to see levels of the solar corona not possible even with the most powerful telescopes and spacecraft,” says Niall Gaffney of the Texas Advanced Computing Center, which is home to one of the supercomputers used, Stampede2. “It also gives high-performance computing researchers who model high-energy plasmas the unique ability to test our understanding of magnetohydrodynamics at a scale and environment not possible anywhere else.”

To create the models, the researchers used magnetic-field maps, solar rotation rates, data from the Helioseismic and Magnetic Imager (HMI) on board NASA’s Solar Dynamics Observatory , and mathematical models of how magnetohydrodynamics – the interplay of electrically conducting fluids like plasmas and powerful magnetic fields – effect the corona.

Coronal prediction

One of the team’s simulations predicted a coronal mass ejection – a large release of plasma and magnetic fields – for during today’s total eclipse. If it occurs, it will be near the east limb of the Sun and provide a spectacular sight for the millions of people watching in the US.

But as well as potentially providing spoilers for spectators, the simulations are important for predicting powerful solar storms, such as one that occurred in 1859. Known as the Carrington Event, the storm caused telegraphs to short and catch fire, and auroras were visible from the Caribbean. In 2008, the National Academy of Science predicted that such an event today would cause more than $2 trillion in damages. “The ability to more accurately model solar plasmas helps reduce the impacts of space weather on key pieces of infrastructure that drive today’s digital world,” Gaffney says.

The work will be presented at the Solar Physics Division meeting of the American Astronomical Society.

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