Last updated
Single-bubble sonoluminescence - a single, cavitating bubble. Single bubble cropped.jpg
Single-bubble sonoluminescence – a single, cavitating bubble.

Sonoluminescence is the emission of light from imploding bubbles in a liquid when excited by sound.



The sonoluminescence effect was first discovered at the University of Cologne in 1934 as a result of work on sonar. [1] Hermann Frenzel and H. Schultes put an ultrasound transducer in a tank of photographic developer fluid. They hoped to speed up the development process. Instead, they noticed tiny dots on the film after developing and realized that the bubbles in the fluid were emitting light with the ultrasound turned on. [2] It was too difficult to analyze the effect in early experiments because of the complex environment of a large number of short-lived bubbles. This phenomenon is now referred to as multi-bubble sonoluminescence (MBSL).

In 1960, Peter Jarman from Imperial College of London proposed the most reliable theory of sonoluminescence phenomenon. He concluded that sonoluminescence is basically thermal in origin and that it might possibly arise from microshocks with the collapsing cavities. [3]

In 1989, an experimental advance was introduced which produced stable single-bubble sonoluminescence (SBSL).[ citation needed ] In single-bubble sonoluminescence, a single bubble trapped in an acoustic standing wave emits a pulse of light with each compression of the bubble within the standing wave. This technique allowed a more systematic study of the phenomenon, because it isolated the complex effects into one stable, predictable bubble. It was realized that the temperature inside the bubble was hot enough to melt steel, as seen in an experiment done in 2012; the temperature inside the bubble as it collapsed reached about 12,000 kelvins. [4] Interest in sonoluminescence was renewed when an inner temperature of such a bubble well above one million kelvins was postulated. [5] This temperature is thus far not conclusively proven; rather, recent experiments indicate temperatures around 20,000 K (19,700 °C; 35,500 °F). [6]


Long exposure image of multi-bubble sonoluminescence created by a high-intensity ultrasonic horn immersed in a beaker of liquid Sonoluminescence.jpg
Long exposure image of multi-bubble sonoluminescence created by a high-intensity ultrasonic horn immersed in a beaker of liquid

Sonoluminescence can occur when a sound wave of sufficient intensity induces a gaseous cavity within a liquid to collapse quickly. This cavity may take the form of a pre-existing bubble, or may be generated through a process known as cavitation. Sonoluminescence in the laboratory can be made to be stable, so that a single bubble will expand and collapse over and over again in a periodic fashion, emitting a burst of light each time it collapses. For this to occur, a standing acoustic wave is set up within a liquid, and the bubble will sit at a pressure anti-node of the standing wave. The frequencies of resonance depend on the shape and size of the container in which the bubble is contained.

Some facts about sonoluminescence: [ citation needed ]

Spectral measurements have given bubble temperatures in the range from 2300 K to 5100 K, the exact temperatures depending on experimental conditions including the composition of the liquid and gas. [7] Detection of very high bubble temperatures by spectral methods is limited due to the opacity of liquids to short wavelength light characteristic of very high temperatures.

A study describes a method of determining temperatures based on the formation of plasmas. Using argon bubbles in sulfuric acid, the data shows the presence of ionized molecular oxygen O2+, sulfur monoxide, and atomic argon populating high-energy excited states, which confirms a hypothesis that the bubbles have a hot plasma core. [8] The ionization and excitation energy of dioxygenyl cations, which they observed, is 18 electronvolts. From this they conclude the core temperatures reach at least 20,000 kelvins [6] —hotter than the surface of the sun.

Rayleigh–Plesset equation

The dynamics of the motion of the bubble is characterized to a first approximation by the Rayleigh–Plesset equation (named after Lord Rayleigh and Milton Plesset):

This is an approximate equation that is derived from the Navier–Stokes equations (written in spherical coordinate system) and describes the motion of the radius of the bubble R as a function of time t. Here, μ is the viscosity, is the external pressure infinitely far from the bubble, is the internal pressure of the bubble, is the liquid density, and γ is the surface tension. The over-dots represent time derivatives. This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically driven field except during the final stages of collapse. Both simulation and experimental measurement show that during the critical final stages of collapse, the bubble wall velocity exceeds the speed of sound of the gas inside the bubble. [9] Thus a more detailed analysis of the bubble's motion is needed beyond Rayleigh–Plesset to explore the additional energy focusing that an internally formed shock wave might produce. In the static case, the Rayleigh-Plesset equation simplifies, yielding the Young-Laplace equation.

Mechanism of phenomenon

The mechanism of the phenomenon of sonoluminescence is unknown. Hypotheses include: hotspot, bremsstrahlung radiation, collision-induced radiation and corona discharges, nonclassical light, proton tunneling, electrodynamic jets and fractoluminescent jets (now largely discredited due to contrary experimental evidence).[ citation needed ]

From left to right: apparition of bubble, slow expansion, quick and sudden contraction, emission of light Sonoluminescence.png
From left to right: apparition of bubble, slow expansion, quick and sudden contraction, emission of light

In 2002, M. Brenner, S. Hilgenfeldt, and D. Lohse published a 60-page review that contains a detailed explanation of the mechanism. [10] An important factor is that the bubble contains mainly inert noble gas such as argon or xenon (air contains about 1% argon, and the amount dissolved in water is too great; for sonoluminescence to occur, the concentration must be reduced to 20–40% of its equilibrium value) and varying amounts of water vapor. Chemical reactions cause nitrogen and oxygen to be removed from the bubble after about one hundred expansion-collapse cycles. The bubble will then begin to emit light. [11] The light emission of highly compressed noble gas is exploited technologically in the argon flash devices.

During bubble collapse, the inertia of the surrounding water causes high pressure and high temperature, reaching around 10,000 kelvins in the interior of the bubble, causing the ionization of a small fraction of the noble gas present. The amount ionized is small enough for the bubble to remain transparent, allowing volume emission; surface emission would produce more intense light of longer duration, dependent on wavelength, contradicting experimental results. Electrons from ionized atoms interact mainly with neutral atoms, causing thermal bremsstrahlung radiation. As the wave hits a low energy trough, the pressure drops, allowing electrons to recombine with atoms and light emission to cease due to this lack of free electrons. This makes for a 160-picosecond light pulse for argon (even a small drop in temperature causes a large drop in ionization, due to the large ionization energy relative to photon energy). This description is simplified from the literature above, which details various steps of differing duration from 15 microseconds (expansion) to 100 picoseconds (emission).

Computations based on the theory presented in the review produce radiation parameters (intensity and duration time versus wavelength) that match experimental results[ citation needed ] with errors no larger than expected due to some simplifications (e.g., assuming a uniform temperature in the entire bubble), so it seems the phenomenon of sonoluminescence is at least roughly explained, although some details of the process remain obscure.

Any discussion of sonoluminescence must include a detailed analysis of metastability. Sonoluminescence in this respect is what is physically termed a bounded phenomenon meaning that the sonoluminescence exists in a bounded region of parameter space for the bubble; a coupled magnetic field being one such parameter. The magnetic aspects of sonoluminescence are very well documented. [12]

Other proposals

Quantum explanations

An unusually exotic hypothesis of sonoluminescence, which has received much popular attention, is the Casimir energy hypothesis suggested by noted physicist Julian Schwinger [13] and more thoroughly considered in a paper by Claudia Eberlein [14] of the University of Sussex. Eberlein's paper suggests that the light in sonoluminescence is generated by the vacuum within the bubble in a process similar to Hawking radiation, the radiation generated at the event horizon of black holes. According to this vacuum energy explanation, since quantum theory holds that vacuum contains virtual particles, the rapidly moving interface between water and gas converts virtual photons into real photons. This is related to the Unruh effect or the Casimir effect. The argument has been made that sonoluminescence releases too large an amount of energy and releases the energy on too short a time scale to be consistent with the vacuum energy explanation, [15] although other credible sources argue the vacuum energy explanation might yet prove to be correct. [16]

Nuclear reactions

Some have argued that the Rayleigh–Plesset equation described above is unreliable for predicting bubble temperatures and that actual temperatures in sonoluminescing systems can be far higher than 20,000 kelvins. Some research claims to have measured temperatures as high as 100,000 kelvins, and speculates temperatures could reach into the millions of kelvins. [17] Temperatures this high could cause thermonuclear fusion. This possibility is sometimes referred to as bubble fusion and is likened to the implosion design used in the fusion component of thermonuclear weapons.

On January 27, 2006, researchers at Rensselaer Polytechnic Institute claimed to have produced fusion in sonoluminescence experiments. [18] [19]

Experiments in 2002 and 2005 by R. P. Taleyarkhan using deuterated acetone showed measurements of tritium and neutron output consistent with fusion. However, the papers were considered low quality and there were doubts cast by a report about the author's scientific misconduct. This made the report lose credibility among the scientific community. [20] [21] [22]

Biological sonoluminescence

Pistol shrimp (also called snapping shrimp) produce a type of cavitation luminescence from a collapsing bubble caused by quickly snapping its claw. The animal snaps a specialized claw shut to create a cavitation bubble that generates acoustic pressures of up to 80 kPa at a distance of 4 cm from the claw. As it extends out from the claw, the bubble reaches speeds of 60 miles per hour (97 km/h) and releases a sound reaching 218 decibels. The pressure is strong enough to kill small fish. The light produced is of lower intensity than the light produced by typical sonoluminescence and is not visible to the naked eye. The light and heat produced by the bubble may have no direct significance, as it is the shockwave produced by the rapidly collapsing bubble which these shrimp use to stun or kill prey. However, it is the first known instance of an animal producing light by this effect and was whimsically dubbed "shrimpoluminescence" upon its discovery in 2001. [23] It has subsequently been discovered that another group of crustaceans, the mantis shrimp, contains species whose club-like forelimbs can strike so quickly and with such force as to induce sonoluminescent cavitation bubbles upon impact. [24] A mechanical device with 3D printed snapper claw at five times the actual size was also reported to emit light in a similar fashion, [25] this bioinspired design was based on the snapping shrimp snapper claw molt shed from an Alpheus formosus, the striped snapping shrimp. [26]

See also

Related Research Articles

Bose–Einstein condensate State of matter

In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum mechanical phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density to ultra-low temperatures.

Inflation (cosmology) Theory of rapid universe expansion

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10−36 seconds after the conjectured Big Bang singularity to some time between 10−33 and 10−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old.

Cavitation Low-pressure voids formed in liquids

Cavitation is a phenomenon in which the static pressure of a liquid reduces to below the liquid's vapour pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, called "bubbles" or "voids", collapse and can generate shock waves that may damage machinery. These shock waves are strong when they are very close to the imploded bubble, but rapidly weaken as they propagate away from the implosion.

Photoelectric effect Emission of electrons when light hits a material

The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid state and quantum chemistry to draw inferences about the properties of atoms, molecules and solids. The effect has found use in electronic devices specialized for light detection and precisely timed electron emission.

Supernova remnant Remnants of an exploded star

A supernova remnant (SNR) is the structure resulting from the explosion of a star in a supernova. The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar material it sweeps up and shocks along the way.

Bubble fusion is the non-technical name for a nuclear fusion reaction hypothesized to occur inside extraordinarily large collapsing gas bubbles created in a liquid during acoustic cavitation. The more technical name is sonofusion.

Radiation pressure Pressure exerted upon any surface exposed to electromagnetic radiation

Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is absorbed, reflected, or otherwise emitted by matter on any scale. The associated force is called the radiation pressure force, or sometimes just the force of light.

Ionization Process by which atoms or molecules acquire charge by gaining or losing electrons

Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

Laser cooling Cooling techniques involving lasers

Laser cooling and laser trapping include a number of techniques in which atomic and molecular samples are cooled down to near absolute zero. Laser cooling techniques rely on the fact that when an object absorbs and re-emits a photon its momentum changes. For an ensemble of particles, their thermodynamic temperature is proportional to the variance in their velocity. That is, more homogeneous velocities among particles corresponds to a lower temperature. Laser cooling techniques combine atomic spectroscopy with the aforementioned mechanical effect of light to compress the velocity distribution of an ensemble of particles, thereby cooling the particles. The 1997 Nobel Prize in Physics was awarded to Claude Cohen-Tannoudji, Steven Chu, and William Daniel Phillips "for development of methods to cool and trap atoms with laser light".

False vacuum decay Hypothetical vacuum, less stable than true vacuum

In quantum field theory, a false vacuum is a hypothetical vacuum that is stable, but not in the most stable state possible. It may last for a very long time in that state, but could eventually decay to the more stable state, an event known as false vacuum decay. The most common suggestion of how such a decay might happen in our universe is called bubble nucleation – if a small region of the universe by chance reached a more stable vacuum, this "bubble" would spread.

Pyroelectric fusion refers to the technique of using pyroelectric crystals to generate high strength electrostatic fields to accelerate deuterium ions (tritium might also be used someday) into a metal hydride target also containing deuterium (or tritium) with sufficient kinetic energy to cause these ions to undergo nuclear fusion. It was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from −34 to 7 °C (−29 to 45 °F), combined with a tungsten needle to produce an electric field of about 25 gigavolts per meter to ionize and accelerate deuterium nuclei into an erbium deuteride target. Though the energy of the deuterium ions generated by the crystal has not been directly measured, the authors used 100 keV (a temperature of about 109 K) as an estimate in their modeling. At these energy levels, two deuterium nuclei can fuse to produce a helium-3 nucleus, a 2.45 MeV neutron and bremsstrahlung. Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces.

Plasma acceleration is a technique for accelerating charged particles, such as electrons, positrons, and ions, using the electric field associated with electron plasma wave or other high-gradient plasma structures. The plasma acceleration structures are created either using ultra-short laser pulses or energetic particle beams that are matched to the plasma parameters. These techniques offer a way to build high performance particle accelerators of much smaller size than conventional devices. The basic concepts of plasma acceleration and its possibilities were originally conceived by Toshiki Tajima and John M. Dawson of UCLA in 1979. The initial experimental designs for a "wakefield" accelerator were conceived at UCLA by Chandrashekhar J. Joshi et al. Current experimental devices show accelerating gradients several orders of magnitude better than current particle accelerators over very short distances, and about one order of magnitude better at the one meter scale.

Alpheidae Family of crustacean

Alpheidae is a family of caridean snapping shrimp, characterized by having asymmetrical claws, the larger of which is typically capable of producing a loud snapping sound. Other common names for animals in the group are pistol shrimp or alpheid shrimp.

An electron bubble is the empty space created around a free electron in a cryogenic gas or liquid, such as neon or helium. They are typically very small, about 2 nm in diameter at atmospheric pressure.

In chemistry, the study of sonochemistry is concerned with understanding the effect of ultrasound in forming acoustic cavitation in liquids, resulting in the initiation or enhancement of the chemical activity in the solution. Therefore, the chemical effects of ultrasound do not come from a direct interaction of the ultrasonic sound wave with the molecules in the solution.

High harmonic generation

High harmonic generation (HHG) is a non-linear process during which a target is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high harmonics of the generation beam. Due to the coherent nature of the process, high harmonics generation is a prerequisite of attosecond physics.

Milton S. Plesset American physicist (1908–1991)

Milton Spinoza Plesset was an American applied physicist who worked in the field of fluid mechanics and nuclear energy. He was elected to the National Academy of Engineering in 1979 for his fundamental contributions to multiphase flows, bubble dynamics, and safety of nuclear reactors. Plesset served as Professor of Engineering Science at California Institute of Technology during 1951 to 1978. Notable scientists Andrea Prosperetti and Norman Zabusky finished their doctoral work under Plesset's guidance.

Mechanism of sonoluminescence

Sonoluminescence is a phenomenon that occurs when a small gas bubble is acoustically suspended and periodically driven in a liquid solution at ultrasonic frequencies, resulting in bubble collapse, cavitation, and light emission. The thermal energy that is released from the bubble collapse is so great that it can cause weak light emission. The mechanism of the light emission remains uncertain, but some of the current theories, which are categorized under either thermal or electrical processes, are Bremsstrahlung radiation, argon rectification hypothesis, and hot spot. Some researchers are beginning to favor thermal process explanations as temperature differences have consistently been observed with different methods of spectral analysis. In order to understand the light emission mechanism, it is important to know what is happening in the bubble's interior and at the bubble's surface.

Rayleigh–Plesset equation

In fluid mechanics, the Rayleigh–Plesset equation or Besant–Rayleigh–Plesset equation is an ordinary differential equation which governs the dynamics of a spherical bubble in an infinite body of incompressible fluid. Its general form is usually written as

Diargon Chemical compound

Diargon or the argon dimer is a molecule containing two argon atoms. Normally, this is only very weakly bound together by van der Waals forces. However, in an excited state, or ionised state, the two atoms can be more tightly bound together, with significant spectral features. At cryogenic temperatures, argon gas can have a few percent of diargon molecules.


  1. Farley J, Hough S (2003). "Single Bubble Sonoluminsescence". APS Northwest Section Meeting Abstracts: D1.007. Bibcode:2003APS..NWS.D1007F.
  2. H. Frenzel and H. Schultes, Luminescenz im ultraschallbeschickten Wasser Zeitschrift für Physikalische Chemie International journal of research in physical chemistry and chemical physics, Published Online: 2017-01-12 | DOI:
  3. Jarman, Peter (1960-11-01). "Sonoluminescence: A Discussion". The Journal of the Acoustical Society of America. 32 (11): 1459–1462. Bibcode:1960ASAJ...32.1459J. doi:10.1121/1.1907940. ISSN   0001-4966.
  4. Ndiaye AA, Pflieger R, Siboulet B, Molina J, Dufrêche JF, Nikitenko SI (May 2012). "Nonequilibrium vibrational excitation of OH radicals generated during multibubble cavitation in water". The Journal of Physical Chemistry A. 116 (20): 4860–7. Bibcode:2012JPCA..116.4860N. doi:10.1021/jp301989b. PMID   22559729.
  5. Moss, William C.; Clarke, Douglas B.; White, John W.; Young, David A. (September 1994). "Hydrodynamic simulations of bubble collapse and picosecond sonoluminescence". Physics of Fluids. 6 (9): 2979–2985. Bibcode:1994PhFl....6.2979M. doi:10.1063/1.868124. ISSN   1070-6631.
  6. 1 2 "Temperature inside collapsing bubble four times that of sun | Archives | News Bureau | University of Illinois". 2005-02-03. Retrieved 2012-11-14.
  7. Didenko YT, McNamara WB, Suslick KS (January 2000). "Effect of noble gases on sonoluminescence temperatures during multibubble cavitation". Physical Review Letters. 84 (4): 777–80. Bibcode:2000PhRvL..84..777D. doi:10.1103/PhysRevLett.84.777. PMID   11017370.
  8. Flannigan DJ, Suslick KS (March 2005). "Plasma formation and temperature measurement during single-bubble cavitation". Nature. 434 (7029): 52–5. Bibcode:2005Natur.434...52F. doi:10.1038/nature03361. PMID   15744295. S2CID   4318225.
  9. Barber BP, Putterman SJ (December 1992). "Light scattering measurements of the repetitive supersonic implosion of a sonoluminescent bubble". Physical Review Letters. 69 (26): 3839–3842. Bibcode:1992PhRvL..69.3839B. doi:10.1103/PhysRevLett.69.3839. PMID   10046927.
  10. Brenner MP, Hilgenfeldt S, Lohse D (May 2002). "Single-bubble sonoluminescence". Reviews of Modern Physics. 74 (2): 425–484. Bibcode:2002RvMP...74..425B. doi:10.1103/RevModPhys.74.425.
  11. Matula TJ, Crum LA (January 1998). "Evidence for gas exchange in single-bubble sonoluminescence". Physical Review Letters. 80 (4): 865–868. Bibcode:1998PhRvL..80..865M. doi:10.1103/PhysRevLett.80.865.
  12. Young JB, Schmiedel T, Kang W (December 1996). "Sonoluminescence in high magnetic fields". Physical Review Letters. 77 (23): 4816–4819. Bibcode:1996PhRvL..77.4816Y. doi:10.1103/PhysRevLett.77.4816. PMID   10062638.
  13. Schwinger J (1989-03-23). "Cold Fusion: A History of Mine". Retrieved 2012-11-14.
  14. Eberlein C (April 1996). "Theory of quantum radiation observed as sonoluminescence" (PDF). Physical Review A. 53 (4): 2772–2787. arXiv: quant-ph/9506024 . Bibcode:1996PhRvA..53.2772E. doi:10.1103/PhysRevA.53.2772. PMID   9913192. S2CID   10902274. Archived from the original (PDF) on 2019-03-23.
  15. Milton KA (September 2000). "Dimensional and Dynamical Aspects of the Casimir Effect: Understanding the Reality and Significance of Vacuum Energy". arXiv: hep-th/0009173 .
  16. Liberati S, Belgiorno F, Visser M (2000). "Comment on "Dimensional and dynamical aspects of the Casimir effect: understanding the reality and significance of vacuum energy"". arXiv: hep-th/0010140v1 .
  17. Chen W, Huang W, Liang Y, Gao X, Cui W (September 2008). "Time-resolved spectra of single-bubble sonoluminescence in sulfuric acid with a streak camera". Physical Review E. 78 (3 Pt 2): 035301. Bibcode:2008PhRvE..78c5301C. doi:10.1103/PhysRevE.78.035301. PMID   18851095.
  18. "RPI: News & Events – New Sonofusion Experiment Produces Results Without External Neutron Source". 2006-01-27. Retrieved 2012-11-14.
  19. "Using Sound Waves To Induce Nuclear Fusion With No External Neutron Source". 2006-01-31. Retrieved 2012-11-14.
  20. Purdue physicist found guilty of misconduct, Los Angeles Times, July 19, 2008, Thomas H. Maugh II
  21. Jayaraman KS (2008). "Bubble fusion discoverer says his science is vindicated". Nature India . doi:10.1038/nindia.2008.271.
  22. "Purdue reprimands fusion scientist for misconduct". USA Today. Associated Press. August 27, 2008. Retrieved 2010-12-28.
  23. Lohse D, Schmitz B, Versluis M (October 2001). "Snapping shrimp make flashing bubbles". Nature. 413 (6855): 477–8. Bibcode:2001Natur.413..477L. doi:10.1038/35097152. PMID   11586346. S2CID   4429684.
  24. Patek SN, Caldwell RL (October 2005). "Extreme impact and cavitation forces of a biological hammer: strike forces of the peacock mantis shrimp Odontodactylus scyllarus". The Journal of Experimental Biology. 208 (Pt 19): 3655–64. doi: 10.1242/jeb.01831 . PMID   16169943.
  25. Conover E (15 March 2019). "Some shrimp make plasma with their claws. Now a 3-D printed claw can too". ScienceNews.
  26. Tang X, Staack D (March 2019). "Bioinspired mechanical device generates plasma in water via cavitation". Science Advances. 5 (3): eaau7765. Bibcode:2019SciA....5.7765T. doi:10.1126/sciadv.aau7765. PMC   6420313 . PMID   30899783.

Further reading