The American Institute of Physics 2 страница

Using a tabletop terawatt laser one-thousandth the power of the Petawatt, University of Michigan researchers produce 10 billion protons with about a tenth the energy of those reported at Livermore. In addition, the Michigan team has announced that they can produce a confined beam of ions pointing roughly in the direction of the laser beam.

Employing the VULCAN laser at the Rutherford Appleton Laboratory, researchers there, generated lead ions with energies up to 420 MeV (and protons up to 17 MeV). The mechanism behind each demonstration is similar. A single laser pulse strikes a thin target, ejecting electrons, which form a cloud of negative charge around the back of the target. The cloud pulls positively charged ions from the back of this target and rapidly accelerates the ions to high energies. All of this occurs over a very short distance-almost 1 MeV/micron for protons in the Livermore case, which is an order of magnitude higher than conventional ion accelerators.

20,000 LEAGUES UNDER THE FERMIS SEA. Recently Stanford and UC Santa Barbara physicists used two alternating-current voltage sources to skew the quantum states in a tiny semi-conducting quantum dot in such a way as to produce (without any net applied bias) a nonzero current through the dot. This was an experimental realization of a “Thouless pump” (named for David Thouless), which pumps electrons much as an Archimedean screw pump lifts water (Switkes et al., Science, 19 March 1999; see also the commentary in the same issue by Altshuler and Glazman). Now, Mathias Wagner (Hitachi Cambridge Laboratory, 011-44-1223-44-2911, [email protected]) and Fernando Sols (Universidad Aut-noma de Madrid) predict that a similar principle will also apply to electrons far beneath the Fermi-sea surface. The Fermi surface or Fermi level represents (in an abstract space in which all electrons are described by their momentum vectors) the highest energy an electron may possess-at zero temperature-in the conduction band of a metal or semi-conductor material. Conduction electrons, those that stray from their home atoms, are usually drawn from electrons very near the Fermi surface. Electrons with lesser energies, and occupying rungs further down on an energy-level diagram, are said to reside in the “Fermi sea” and normally do not effectively contribute to the current.

Wagner and Sols suggest that with high enough ac power, the resulting pump current might actually consist mostly of electrons from far beneath the Fermi-sea surface. These subsea currents would be largely immune from temperature effects (just as submarines are less vulnerable to surface storms), a very useful property in the electronics world. (Wagner and Sols, Physical Review Letters, 22 November 1999)

THE SHADOW OF A PLANET slipping across the face of a distant star has been detected, for the first time, by veteran extrasolar-planet stalkers Geoffrey Marcy of UC Berkeley and Paul Butler of the Carnegie Institution, working with Greg Henry of Tennessee State University. Prior indirect “sightings” of extrasolar planets consisted of small feints in the apparent position of the stars caused by the suspected gravity pull of an orbiting planet. Astronomers have felt that from among the growing sample of such planets (up to 25 as of now) a few (whose orbits would be viewed at Earth edge-on) might be detected directly as they pass in front of the star. One such candidate was HD 209458. Prediction of a planetary transit for the night of November 7 proved accurate and a 1.7% dimming in the star’s light was seen. (Announcement made in an International Astronomical Union circular.)

MICROFLUIDICS CAN BE DRIVEN BY HEAT rather than by electric fields. Microfluidics is to the mixing of fluids (including studies of blood, DNA, etc.) what integrated circuits are to the processing of electrical signals: transactions occur quickly, controllably, in a very small space. But instead of excavating small channels in a substrate and propelling tiny fluid volumes around the nano-sized system of aqueducts customary in microfluidics, Princeton professor Sandra M. Troian and Dawn Kataoka, now at Sandia Laboratories (CA), have moved tiny liquid rivulets around a silicon wafer using temperature gradients. The capillary movement of the micro-fluids can be programmed because (1) the liquid surface tension varies with temperature and even a gradient of 3 or 4 K will cause a fluid to seek out a cold region, and (2) a lithographically applied pattern of chemical modifications on the substrate (the equivalent of an invisible scent marker or a chemical levee) further constrains the droplet rivercourses. Thus streams of hydrophilic and hydrophobic molecules, zooming across the substrate along neighboring lanes, can be shunted together at some desired meeting point. The advantages of thermo-capillary action over electronic-driven fluidics are that the use of high electric fields and the precision carving of channels are not necessary; everything happens on a plane, making easier the task of building micro-electromechanical (MEMS) “labs-on-a-chip.” Troian will report on her research at the APS division of fluid dynamics meeting in New Orleans, November 21-23: http://www.nd.edu/-apsnd/)

HYDROGEN STORAGE IN NANOTUBES. Hydrogen is a potent fuel: combined with oxygen it can power spacecraft to the Moon.

Storing such a dangerous substance, however, is difficult. Physicists at MIT have now succeeded in canning hydrogen in side carbon nanotubes. Actually, hydrogen sausage has been encased in a carbon skin before, but the MIT efforts are the first to achieve reliably such a high hydrogen uptake (one hydrogen for every two carbons) at room temperature. And like a jack-in-the-box, the hydrogen came shooting out of the tubes (80% of them anyway) when the packing pressure was relaxed. (Liu et al., Science, 5 November 1999.)

THE ONLINE JOURNAL PUBLISHING SERVICE (OJPS) constitutes a shopping mall for the physics journals published by the American Institute of Physics (AIP), many of its member societies, and other scientific and engineering societies. From this site (http://ojps.aip.org/) one can handily visit the homepage for such journals as Physical Review, Applied Physics Letters, Optics Letters, and Chaos. Nonsubscribers can view tables of contents and look at all the abstracts, including those from some issues not yet published. (You can even search the full SPIN database of abstracts if you have a subscription to at least one of the OJPS journals.) In general the full texts are available only to subscribers, although a few prominent articles are supplied to science writers via a separate website called Physics News Select Articles.

UNDERSEA VOLCANO. Like astronomers who team up to view supernova eruptions at a variety of wavelengths, geophysicists have been able to mount an in-depth study of the eruption in January 1998 of the Axial Volcano, lying 1500 m underwater about 200 miles off the Oregon-Washington coast. Axial, which is a large volcanic edifice lying along a rift zone in the North-east Pacific where new ocean floor is being created, is one of the few places on the worldwide 60,000-km mid-ocean ridge system (Iceland and the Azores are other examples) where volcanic activity can be monitored in real time. In this case, the coverage consisted of Navy hydrophone arrays (listening for quarks rather than subs), surface ships, moored sensors, and instruments placed on the very summit of the caldera in anticipation of an eruption. The 1998 event is chronicled in a variety of ways in a series of articles in the December 1 and 15 issues of Geophysical Research Letters. For example, C.G. Fox reports (via on-the-spot seafloor measurements) a 3-meter drop in the caldera floor; Baker et al. provide the first incite observation of the water temperature change above an erupting rift zone (constituting the “largest vent field heat flux yet measured”); Embley et al estimate that up to 76 million cubic meters of lava were produced, modest by land volcano standards, but the largest outpouring in 20 years of monitoring along the Juan de Fuca Ridge. (Robert Embley, Pacific Marine Environmental Laboratory)

SWIRLED SPHERE MAGIC NUMBERS. Physicists love to detect patterns in nature, whether in the crystalline structures of atoms in solids, or the groupings into “shells” of electrons inside atoms or protons and neutrons within nuclei. Even in a system as simple as a bunch of spheres swirled around in a dish patterns can emerge. Scientists at the Max Planck Institute in Dortmund, Germany, and the University of Chile have determined that for certain “magic” numbers of spheres, such as 19, 21, or 30, the spheres congregate into solid-like shell structures with stable rings.

The swirled balls are a form of granular material. Studies of agitated grains had uncovered stable structures before (such as “oscillons”) but not any that had depended on the number of particles present. The researchers noticed that when they increased the size of the dish a puzzling transition between stable and disordered states would occur intermittently. (Kotter et al., Physical Review E, December 1999; Select Article.)

THE TOP PHYSICISTS IN HISTORY are, according to a poll of scientists conducted by Physics World magazine, 1. Albert Einstein, 2. Isaac Newton, 3. James Clerk Maxwell, 4. Niels Bohr, 5. Werner Heisenberg, 6. Galileo Galilei, 7. Richard Feynman, 8. Paul Dirac, 9. Erwin Schrodinger, and 10. Ernest Rutherford. Other highlights of Physics World’s millennium canvas: the most important physics discoveries are Einstein’s relativity theories, Newton’s mechanics, and quantum mechanics. Most physicists polled (70%) said that if they had to do it all over again, they would choose to study physics once more. Most do not believe that progress in constructing unified field theories spells the end of physics. Ten great unsolved problems in physics: quantum gravity, understanding the nucleus, fusion energy, climate change, turbulence, glassy materials, high-temperature superconductivity, solar magnetism, complexity, and consciousness. (December issue of Physics World, published by the Institute of Physics, the British professional organization of physicists celebrating its 125th anniversary this year.)

MEASUREMENTS OF THE COSMIC MICROWAVE BACKGROUND (CMB) provide new evidence that the expansion of the universe is accelerating. One of the greatest issues in cosmology is whether the current expansion will continue, reverse, or proceed at a diminishing rate. Supernova observations two years ago suggested that not only would the expansion not reverse but that it was in fact getting faster. The new CMB mappings, carried out with telescopes on mountains and on balloons, reveal that the temperature of the microwave background varies in clumps with an angular size of about one degree on the sky, a result indicative of an overall “flat” geometry for the universe (New York Times, 26 November 1999). Another way of saying this is that the observed energy density of the universe is apparently equal to the critical density value of about 10-29 gm/cm3. But the amount of known matter (luminous and dark) is insufficient for producing a flat geometry, so additional energy, probably hiding in the universal vacuum, is needed. This energy, according to many theorists, would exert an effect equivalent to a repulsive form of gravity, thus working against the mutual gravitational attraction of galaxies. Much of the new work is available only in preprint form. For example, papers for one of the experiments, the “Boomerang” collaboration, which measures the CMB with a balloon-mounted detector, can be found on the Los Alamos server.

COOPERATIVE EVAPORATION, a process whereby droplets on a substrate do not evaporate independently but in a coordinated fashion, has been observed for the first time by physicists at the University of Konstanz. The researchers begin by laying down a periodic array of diethylene glycol drops 0.75 microns in radius and spaced by 2.5 microns.

(Condensing the droplets out of a supersaturated vapor onto a patterned grid of adsorption sites imposed on the surface with microcontact-printing was itself something of a feat). The Konstanz scientists found that some rows of droplets evaporated faster than other rows, leading to a sort of “superstructure.” In other words, some drops would survive at the expense of the preferential evaporation of other drops in a methodical way.

Previously scientists have considered how gas sensors comprised of liquid droplet arrays could be designed. The droplet size in such sensors can be made sensitive to environmental conditions by selective uptake of certain molecules. When monitoring the average droplet size by light scattering techniques, the concentration of the molecules can be determined. But for this to work the cooperative evaporation effect will have to be taken into effect. (Schafle et al., Physical Review Letters, 20 December 1999; Select Aricle.)

ATOM TRAP TRACE ANALYSIS, the search for tiny isotope fractions among atoms using a magneto-optic trap, may soon be preferable to accelerator mass spectrometry (in which atoms are heated, accelerated, and sent through a strong magnet, which sorts the atoms by mass) for certain radio-dating purposes. To demonstrate this idea, physicists at Argonne have detected traces of krypton-85 (with an abundance of only 10-11) and krypton-81 (abundance of 10-13) in an atom trap with an efficiency of 1 part in 10ˆ7; accelerator mass spectrometry, which requires an accelerator, currently has a counting efficiency of a part in 105. Keeping track of Kr-85 atoms is important since they are produced chiefly in nuclear-fuel reprocessing plants, and (arising mostly since the 1950s) are used as a tracer of air and ocean currents. Kr-81, in contrast, is made in cosmic-ray showers in the upper atmosphere and (with a half life 40 times longer than C-14’s) is preferable to carbon-dating for calibrating the antiquity of million-year-old samples of ice and ground water. (Chen et al., Science, 5 November 1999.)

NATURALLY OCCURING RADIATION LEVELS ARE MUCH LOWER TODAY on Earth than when life first appeared, a new analysis has shown, suggesting that all living organisms – which have mutation-repair mechanisms very similar to those first developed by primordial life forms were once equipped to handle larger doses of background nuclear radiation than modern life forms. Presently, humans receive a dose of about 360 millirems per year of radiation from natural sources, plus typically about 63 mrem/yr from anthropogenic sources. Perhaps surprisingly, a major source (about 40 mrem/yr) of naturally occurring radiation is inside our bodies – in the form of potassium, a nutrient essential for many things such as generating signals between cells. All natural sources of potassium contain some radioactive potassium-40 (K-40). But life first began about 4 billion years ago – about 3 K-40 half-lives ago – meaning that the radiation dose from potassium today is about one-eighth of what it was 4 billion years ago. Geologic sources of radiation (about 28mrem/yr) include uranium, thorium, and potassium present in rocks and minerals in the earth’s crust. Studying published data of 1100 rocks, and assuming that the continental crust had formed early (a scenario favored by the rock record), the researchers estimated that radiation from these sources is now about one-half of what it was 4 billion years ago, because many of these radioisotopes decayed in the intervening time. Not considered in the present study were cosmic sources (about 27 mrem/yr) and radon (typically about 200 mrem/yr); the authors are making these the subject of ongoing research. (Karam and Leslie, Health Physics, December 1999.)

MAXWELL’S DEMON MADE OF SAND. The second law of thermodynamics states that within a closed system heat cannot flow unassisted from a cold to a warm place. To ponder this issue, James Clerk Maxwell, one of the pioneers of statistical mechanics, posed this thought experiment: could not a clever microscopic creature, poised at a pinhole in a baffle dividing an insulated box into two equal chambers, sort molecules in such a way that the hotter (faster) molecules would be directed into one chamber while cooler (slower) molecules would be directed into the other. “Maxwell’s demon,” as the sorter came to be known, itself requires energy to operate, and so the segregation of hot from cold cannot really happen as advertised.

And yet in an experiment conducted at the University of Essen in Germany in which agitated sand in a two-chamber vessel (the halves being connected by a hole) “hot”, quickly moving sand migrated to one side while cool sand spontaneously condensed and congregated on the other side (see sketch at www.aip.org/physnews/graphics). Jens Eggers explains that, no, the second law is not violated in this case since although moving sand can be considered as a gas, individual grains can absorb heat and dissipate heat (that is, individual grains can gain temperature), unlike the ideal gas molecules described by Maxwell, whose “temperature” is a measurement of gas motion.

Thus when sand grains start to congregate in one chamber (the segregation begins as an act of spontaneous symmetry breaking) more and more grains will partake of a growing ordered state consisting of grains falling to the bottom of the container (where the grains are denser there are more collisions and hence faster cooling, leading to more congregation, etc.), while the unaffiliated grains will tend to be on the other side, still in “gaseous” form. (Eggers, Physical Review Letters, 20 December; Select Articles.)

COMPETING ARROWS OF TIME. Lawrence S. Schulman of Clarkson University has found that time might actually flow backwards in certain regions of space. This time reversal has nothing to do with quantum fluctuations or the spacetime-warping effects of a black hole.

It’s just ordinary matter obeying the ordinary and mostly time-symmetric laws of physics. The difference lies in its statistics. If the laws of physics have no preferred direction then why do we never see a shattered wineglass jump back up on the table and reassemble itself?

The “arrow of time” concept enshrines this domestic disaster in the form of a law, the second law of thermodynamics. The arrow describes the tendency for macroscopic systems consisting of many particles (the falling wineglass) to evolve in time in such a way that disorder grows and information decreases. This tendency is statistical and does not prevail at the microscopic level, where a movie of two atoms colliding would seem credible if run in the forward or reverse direction. The wineglass, however, consist of zillions of atoms. The reason we never see the glass re-assemble and lift itself (courtesy of the warmth of the original breakage returning from the floor and air) back onto the table is that this highly specialized (and, as we would say, unlikely) scenario is but one of a myriad of possible configurations, in most of which the glass shards stay on the floor. This statistical explanation leads to two puzzles.

First, why does this arrow point the way it does? Why not the other way? And second, why should it point at all? On the first question, Schulman subscribes to the view that the “thermodynamic” arrow of time is a consequence of the “cosmological” arrow reflected in the one-way expansion of the universe, a theory advanced some years ago by Thomas Gold of Cornell. As to the second question, that’s exactly where Schulman’s new results have their impact. The prevailing view holds that if opposite-arrow systems came into even the mildest of contact, the order in at least one of them would be destroyed. This is because from the perspective of one observer the coordination needed to reassemble the other’s wineglass would be so fantastic that even a single photon could disrupt it. Not so, says Schulman who, in his computer modeling of the universe, specifies not one boundary condition in time (the big bang) but two, the other being a supposed “big crunch” when the universe would contact (or so it would seem to us; from the perspective of that arrow, the universe would be expanding). In his model, the two arrows of time (one growing out of either end of the “timeline”; see the figure at www.aip.org/physnews/graphics) can be mildly in contact and nevertheless each have its wineglass break and its rain fall appropriately. Observers associated with either arrow might even watch the other grow young – from a distance.

Some relatively-isolated relics of matter subject to the opposite arrow might be found in our vicinity. By its own clock such a region would be very old and no longer luminous, although gravitationally it would not be anomalous, exactly the hallmark of dark matter. Or we might see an opposite-arrow black hole giving matter back to an accretion disk, which in turn would feed it back to a companion star, which would seem (to us) to be coming into existence. Schulman concedes that recent observations may rule out a final crunch in our actual universe but argues that there is still a lot we don’t understand about our thermodynamic arrow, and that a competing time arrow might arise from another, as yet unknown, cause. (Physical Review Letters, 27 Dec.)

STARLIGHT REFLECTED FROM AN EXTRASOLAR PLANET has been reported by University of St. Andrews astronomers. Roughly, 30 planets have been detected around nearby stars through an indirect method, which monitors fluctuations in the stars’ positions. More recently, the shadow of an extrasolar planet was observed to transit across the face of its star. Now light has been detected which apparently comes to us directly from a planet circling the star tau Bootis, some 50 light years away. The main difficulty was of course discerning the reflected light while blocking out the glare of the star itself. The planet seems to be blue-green in color, is twice the size of Jupiter, and 8 times as massive. (Cameron et al., Nature, 16 December 1999.)

THE SOLAR WIND DISAPPEARED for a day back on May 10/11, allowing Earth’s magnetosphere to balloon out to the orbit of the Moon. Ironically, the greatly lowered solar wind flux of particles and solar magnetic field allowed high-energy electrons from the sun’s corona to penetrate directly to our upper atmosphere unadulterated, where the electrons’ characteristic x-ray emissions were observed by satellites over the North Pole for the first time. Such a “polar rain” had been predicted years before.

Normally the coronal electrons (with energies of tens of keV, corresponding to temperatures of millions of degrees) lose much of their energy through scatterings with other particles on their ride from sun to Earth and in the topsy-turvy trajectories experienced at our magnetosphere. At last week’s meeting of the American Geophysical Union in San Francisco, these results were reported by a number of speakers, including David Chenetter of Lockhead, Jack Scudder of the University of lowa, and Keith Ogivie of NASA Goddard.

SPONGELIKE STRUCTURES NEAR THE SUN’S SURFACE, newly observed by the TRACE satellite (at extreme ultraviolet wavelengths) and the SOHO satellite (in x rays), lie between the 10,000-K chromospheres and the corona at a temperature of several million K. These filamentary structures (dubbed “solar mass” by Lockhead scientists reporting at the AGU meeting) are typically 6000-12,000 miles in size and about 1000-1500 miles above the photosphere; occur at various places around the sun’s surface, usually near the footprint of huge coronal loops. The moss blobs seem to be stable for hours but can also change brightness over periods as short as 30 seconds do. Thomas Berger of Lockhead said that the new structures might provide information on how the corona gets so hot, an issue that remains one of the great unsolved mysteries of solar physics.

THE RAREST NATURALLY OCCURING ISOTOPE, tantalum-180, is rare because it is bypassed in the two processes that produced most of the heavy elements we dig out of the ground here on Earth: the so called s process (slow neutron capture in stars) and the r process (rapid neutron capture in supernova explosions). What little Ta-180 that is produced (in stars or in ractors) is quite robust; its half life is more than 10ˆ17! This rules out the nuleosynthesis of Ta-180 within the “canonical” s process; however, in a more realistic version of the theory, the tantalum can survive if it rapidly mixes with cooler layers of the star. (Belic et al., Physical Review Letters, 20 December 1999. Select Article.)

SUPERCONDUCTING BALLS, a new phenomenon, have been observed by physicist at Southern Illinois University. Rongjia ao (618-536-2117, [email protected]) and his colleagues began by wanting to observe the motion of micron-sized copper oxide (e.g., Br-Sr-Ca-Cu-O) superconducting particles (suspended in liquid nitrogen) in an electric field running between electrodes. Metal particles in this situation would bounce between the two electrodes or tend to line up; after all, an electric field helps to define a preferred direction in space. The superconducting particles ignored this hind and, to the researchers’ great surprise, formed themselves into a ball. The ball, about 25 mm across and containing over a million particles, formed quickly and was quite sturdy, surviving constant collisions with the electrodes (see figure at www.aip.org/physnews/graphics). What binds the ball together against the dictates of the rectilinear field? Tao and his collaborator, Princeton theorist Philip Anderson, have concluded that the effect is an artifact of superconductivity (the same particles, above their superconducting transition temperature, do not ball up but instead queue into lines), perhaps something to do with the way in which the surface energy of the particle ensemble is reduced by self-assembly into a ball. This unprecedented new surface energy is related to the acquired surface charges on the particles and the reactions among the layers of the balls. Granular properties fo the particles might also play a role in the process and in the balls’s internal structure, but this is difficult to gauge since the inter-particle interactions (frictional dissipation being the hallmark of granular materials) are mitigated by the liquid nitrogen needed in the experiment to neutralize gravity. A way around this is to do the experiment in the microgravity of space. The basic scientific novelty of this new phenomenon is paramount, but Tao is also turning his attention to possible applications in the area of superconducting thin films and unusual forms of wetting. (Select Tao at al., Physical Review Letters, 27 Dec.)

TWO-DIMENSIONAL COLLOIDAL CRYSTALS SEEMINGLY DEFY COULOMB’S LAW as they form, experiments have shown.

A colloidal crystal is a regular arrangement of tiny particles suspended in a liquid. Three-dimensional examples have long been known. Now free-floating 2D “crystallites” of colloidal particles, lashed together by bilayer membranes similar to those surrounding living cells, have been created, offering intriguing possibilities for using them as templates for artificial biomaterials and industrial catalysts. University of Pennsylvania researchers (Laurence Ramos, now at Universite de Montellier, France, [email protected]) created the system by adding negatively charged latex beads to a suspension of positively charged soaplike (surfactant) membranes in water. As expected, initially the beads avidly stuck to the memberanes. To the researchers’ surprise, though, in many cases the beads formed rafts floating on the membrane. Outside the raft the membrane actually repelled additional beads, even though they were highly oppositely charged. The researchers agreed that the source of this paradoxical behavior lay in the migration of negative ions trapped on the side of the membrane opposite to the beads. With time the fluid rafts solidify into rigid, flat crystallites, near-perfect 2D crystalline structures some tens of microns on a side. (Ramos et all., Science, 17 December 1999; and Aranda-Espinoza et al., 16 June.)

AMPLIFYING AN ATOM WAVE while maintaining its original phase has been demonstrated for the first time, bringing about an atom laser that is the closest equivalent yet to an optical laser. The first atom lasers were passive devices: researchers simply prepared a Bose-Einstein condensate of atoms, and then extracted some of the BEC atoms to form a beam. In the latest round of demonstrations, two research groups (one at MIT and one at the University of Tokyo) have independently demonstrated an atom laser that amplifies its initial beam, in a way that’s remarkably similar to how optical lasers augment an initial light wave. Unlike light, however, atoms cannot be created from the vacuum, so researchers must rely on a pre-existing supply of atoms to serve as the initial beam to be amplified. In the MIT demonstration, researchers shine a pair of laser pulses on sodium BEC. First, some of the BEC atoms absorb a photon from a high-frequency beam and emit a photon towards a lower-frequency beam. These atoms recoil in the same direction, forming a weak atom weave. Then the lower-frequency beam is shut off, and some of the other BEC atoms absorb light from an intensified pulse coming from the high-frequency laser. The presence of the initial atom wave stimulates these atoms to emit a photon in the direction of the lower-frequency beam. This resulted in a phase-coherent amplified beam about 4 times as strong as the initial atom wave. The Tokyo group demonstrated similar results with a rubidium-87 BEC. In both demonstrations, the amplification is limited by the size of the BEC, which is depleted in the process. However, an atom-wave amplifier promises improvements in such applications as atom-wave gyroscopes and lithography. (Inouye at al., Nature, 9 December 1999; Kozuma et al., Science, 17 December.)

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