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Topic Review
Water Retention on Mathematical Surfaces
Water retention on mathematical surfaces is the catching of water in ponds on a surface of cells of various heights on a regular array such as a square lattice, where water is rained down on every cell in the system. The boundaries of the system are open and allow water to flow out. Water will be trapped in ponds, and eventually all ponds will fill to their maximum height, with any additional water flowing over spillways and out the boundaries of the system. The problem is to find the amount of water trapped or retained for a given surface. This has been studied extensively for two mathematical surfaces: magic squares and random surfaces. The model can also be applied to the triangular grid.
  • 541
  • 01 Nov 2022
Topic Review
Auger Electron Spectroscopy
thumb|A Hanford scientist uses an Auger electron spectrometer to determine the elemental composition of surfaces. Auger electron spectroscopy (AES; pronounced [oʒe] in French) is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials science. Underlying the spectroscopic technique is the Auger effect, as it has come to be called, which is based on the analysis of energetic electrons emitted from an excited atom after a series of internal relaxation events. The Auger effect was discovered independently by both Lise Meitner and Pierre Auger in the 1920s. Though the discovery was made by Meitner and initially reported in the journal Zeitschrift für Physik in 1922, Auger is credited with the discovery in most of the scientific community. Until the early 1950s Auger transitions were considered nuisance effects by spectroscopists, not containing much relevant material information, but studied so as to explain anomalies in X-ray spectroscopy data. Since 1953 however, AES has become a practical and straightforward characterization technique for probing chemical and compositional surface environments and has found applications in metallurgy, gas-phase chemistry, and throughout the microelectronics industry.
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Topic Review
Identification of Soccer Scoring Techniques
The immense charm of soccer to millions of players and spectators can be traced back to the most prime idea of the game: to score goals—an idea that will always be captivating. This basic idea shapes the soccer scoring technique (SST) to be the crucial and final determinant of every offensive-maneuver fate of any team. Therefore, the identification of SSTs is particularly important.
  • 495
  • 01 Nov 2022
Topic Review
Osmium-180
Osmium (76Os) has seven naturally occurring isotopes, five of which are stable: 187Os, 188Os, 189Os, 190Os, and (most abundant) 192Os. The other natural isotopes, 184Os, and 186Os, have extremely long half-life (1.12×1013 years and 2×1015 years, respectively) and for practical purposes can be considered to be stable as well. 187Os is the daughter of 187Re (half-life 4.56×1010 years) and is most often measured in an 187Os/188Os ratio. This ratio, as well as the 187Re/188Os ratio, have been used extensively in dating terrestrial as well as meteoric rocks. It has also been used to measure the intensity of continental weathering over geologic time and to fix minimum ages for stabilization of the mantle roots of continental cratons. However, the most notable application of Os in dating has been in conjunction with iridium, to analyze the layer of shocked quartz along the Cretaceous–Paleogene boundary that marks the extinction of the dinosaurs 66 million years ago. There are also 30 artificial radioisotopes, the longest-lived of which is 194Os with a half-life of six years; all others have half-lives under 94 days. There are also nine known nuclear isomers, the longest-lived of which is 191mOs with a half-life of 13.10 hours. All isotopes and nuclear isomers of osmium are either radioactive or observationally stable, meaning that they are predicted to be radioactive but no actual decay has been observed.
  • 316
  • 01 Nov 2022
Topic Review
Phosphorus (Morning Star)
Phosphorus (Greek Φωσφόρος Phōsphoros) is the Morning Star, the planet Venus in its morning appearance. Φαοσφόρος (Phaosphoros) and Φαεσφόρος (Phaesphoros) are forms of the same name in some Greek dialects. This celestial object was named when stars and planets were not always distinguished with modern precision. Another Greek name for the Morning Star is Heosphoros (Greek Ἑωσφόρος Heōsphoros), meaning "Dawn-Bringer". The form Eosphorus is sometimes met in English, as if from Ἠωσφόρος (Ēōsphoros), which is not actually found in Greek literature, but would be the form that Ἑωσφόρος would have in some dialects. As an adjective, the Greek word φωσφόρος is applied in the sense of "light-bringing" to, for instance, the dawn, the god Dionysos, pine torches, the day; and in the sense of "torch-bearing" as an epithet of several god and goddesses, especially Hecate but also of Artemis/Diana and Hephaestus. The Latin word lucifer, corresponding to Greek φωσφόρος, was used as a name for the morning star and thus appeared in the Vulgate translation of the Hebrew word הֵילֵל (helel), meaning Venus as the brilliant, bright or shining one, in Isaiah 14:12, where the Septuagint Greek version uses, not φωσφόρος, but ἑωσφόρος. As a translation of the same Hebrew word the King James Version gave "Lucifer", a name often misunderstood as a reference to Satan. Modern translations of the same passage render the Hebrew word instead as "morning star", "daystar", "shining one" or "shining star". In Revelation 22:16, Jesus is referred to as the morning star, but not as lucifer in Latin, nor as φωσφόρος in the original Greek text, which instead has ὁ ἀστὴρ ὁ λαμπρὸς ὁ πρωϊνός (ho astēr ho lampros ho prōinos), literally: the star, the shining one, the dawn. In the Vulgate Latin text of 2 Peter 1:19 the word "lucifer" is used of the morning star in the phrase "until the day dawns and the morning star rises in your hearts", the corresponding Greek word being φωσφόρος.
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  • 31 Oct 2022
Topic Review
Transmission Electron Microscopy DNA Sequencing
Transmission electron microscopy DNA sequencing is a single-molecule sequencing technology that uses transmission electron microscopy techniques. The method was conceived and developed in the 1960s and 70s, but lost favor when the extent of damage to the sample was recognized. In order for DNA to be clearly visualized under an electron microscope, it must be labeled with heavy atoms. In addition, specialized imaging techniques and aberration corrected optics are beneficial for obtaining the resolution required to image the labeled DNA molecule. In theory, transmission electron microscopy DNA sequencing could provide extremely long read lengths, but the issue of electron beam damage may still remain and the technology has not yet been commercially developed.
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Topic Review
Zodiac
The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are within the belt of the zodiac. In Western astrology, and formerly astronomy, the zodiac is divided into twelve signs, each occupying 30° of celestial longitude and roughly corresponding to the following star constellations: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. These astrological signs form a celestial coordinate system, or more specifically an ecliptic coordinate system, which takes the ecliptic as the origin of latitude and the Sun's position at vernal equinox as the origin of longitude.
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  • 31 Oct 2022
Topic Review
Stellar Constellations in Fiction
Some stellar constellations have been featured in fictional works.
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Topic Review
Refractive Index and Extinction Coefficient of Thin-Film Materials
The derivation of the Forouhi–Bloomer dispersion equations is based on obtaining an expression for k as a function of photon energy, symbolically written as k(E), starting from first principles quantum mechanics and solid state physics. An expression for n as a function of photon energy, symbolically written as n(E), is then determined from the expression for k(E) in accordance to the Kramers–Kronig relations which states that n(E) is the Hilbert Transform of k(E). The Forouhi–Bloomer dispersion equations for n(E) and k(E) of amorphous materials are given as: [math]\displaystyle{ k(E) = \frac{A(E-E_g)^2}{E^2-BE+C} \ }[/math] [math]\displaystyle{ n(E) = n(\infty)+\frac{(B_0 E + C_0 )}{E^2-BE+C} \ }[/math] The five parameters A, B, C, Eg, and n(∞) each have physical significance. Eg is the optical energy band gap of the material. A, B, and C depend on the band structure of the material. They are positive constants such that 4C-B2 > 0. Finally, n(∞), a constant greater than unity, represents the value of n at E = ∞. The parameters B0 and C0 in the equation for n(E) are not independent parameters, but depend on A, B, C, and Eg. They are given by: [math]\displaystyle{ B_0 = \frac{A}{Q} \ \left (\frac{-B^2}{2} \ + E_gB - {E_g}^2 + C \right) }[/math] [math]\displaystyle{ C_0 = \frac{A}{Q} \ \left [({E_g}^2 + C) \frac{B}{2} \ - 2E_g C \right] }[/math] where [math]\displaystyle{ Q = \frac{1}{2} \ (4C - B^2 )^{\frac{1}{2}} }[/math] Thus, for amorphous materials, a total of five parameters are sufficient to fully describe the dependence of both n and k on photon energy, E. For crystalline materials which have multiple peaks in their n and k spectra, the Forouhi–Bloomer dispersion equations can be extended as follows: [math]\displaystyle{ k(E) = \sum_{i=1}^q \left [\frac{A_i(E - E_{g_i})^2}{E^2-B_iE+C_i} \right] }[/math] [math]\displaystyle{ n(E) = n(\infty)+\sum_{i=1}^q \left [\frac{B_{0_i}E+C_{0_i}}{E^2-B_iE+C_i} \right] }[/math] The number of terms in each sum, q, is equal to the number of peaks in the n and k spectra of the material. Every term in the sum has its own values of the parameters A, B, C, Eg, as well as its own values of B0 and C0. Analogous to the amorphous case, the terms all have physical significance.
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  • 31 Oct 2022
Topic Review
Loopholes in Bell Tests
In Bell tests, there may be problems of experimental design or set-up that affect the validity of the experimental findings. These problems are often referred to as "loopholes". See the article on Bell's theorem for the theoretical background to these experimental efforts (see also John Stewart Bell). The purpose of the experiment is to test whether nature is best described using a local hidden-variable theory or by the quantum entanglement theory of quantum mechanics. The "detection efficiency", or "fair sampling" problem is the most prevalent loophole in optical experiments. Another loophole that has more often been addressed is that of communication, i.e. locality. There is also the "disjoint measurement" loophole which entails multiple samples used to obtain correlations as compared to "joint measurement" where a single sample is used to obtain all correlations used in an inequality. To date, no test has simultaneously closed all loopholes. Ronald Hanson of the Delft University of Technology claims the first Bell experiment that closes both the detection and the communication loopholes. (This was not an optical experiment in the sense discussed below; the entangled degrees of freedom were electron spins rather than photon polarization.) Nevertheless, correlations of classical optical fields also violate Bell's inequality. In some experiments there may be additional defects that make "local realist" explanations of Bell test violations possible; these are briefly described below. Many modern experiments are directed at detecting quantum entanglement rather than ruling out local hidden-variable theories, and these tasks are different since the former accepts quantum mechanics at the outset (no entanglement without quantum mechanics). This is regularly done using Bell's theorem, but in this situation the theorem is used as an entanglement witness, a dividing line between entangled quantum states and separable quantum states, and is as such not as sensitive to the problems described here. In October 2015, scientists from the Kavli Institute of Nanoscience reported that the quantum nonlocality phenomenon is supported at the 96% confidence level based on a "loophole-free Bell test" study. These results were confirmed by two studies with statistical significance over 5 standard deviations which were published in December 2015. However, Alain Aspect writes that No experiment can be said to be totally loophole-free.
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