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A mass flow meter, also known as an inertial flow meter, is a device that measures mass flow rate of a fluid traveling through a tube. The mass flow rate is the mass of the fluid traveling past a fixed point per unit time. The mass flow meter does not measure the volume per unit time (e.g. cubic meters per second) pass... | {
"page_id": 1575643,
"source": null,
"title": "Mass flow meter"
} |
pushed back to the axis of rotation must exert a force on the fluid to decrease the fluid's angular momentum again, hence that arm will bend forward. In other words, the inlet arm (containing an outwards directed flow), is lagging behind the overall rotation, the part which in rest is parallel to the axis is now skewed... | {
"page_id": 1575643,
"source": null,
"title": "Mass flow meter"
} |
are out of sync: the inlet arm is behind, the outlet arm is ahead. The two vibrations are shifted in phase with respect to each other, and the degree of phase-shift is a measure for the amount of mass that is flowing through the tubes and line. == Density and volume measurements == The mass flow of a U-shaped Coriolis ... | {
"page_id": 1575643,
"source": null,
"title": "Mass flow meter"
} |
through pressure and temperature zero and span compensation factors. Additional effects on tube rigidity will cause shifts in the calibration factor over time due to degradation of the flow tubes. These effects include pitting, cracking, coating, erosion or corrosion. It is not possible to compensate for these changes ... | {
"page_id": 1575643,
"source": null,
"title": "Mass flow meter"
} |
A taxonomic treatment is a section in a scientific publication documenting the features of a related group of organisms or taxa. Treatments have been the building blocks of how data about taxa are provided, ever since the beginning of modern taxonomy by Linnaeus 1753 for plants and 1758 for animals. Each scientifically... | {
"page_id": 67504866,
"source": null,
"title": "Taxonomic treatment"
} |
of European Taxonomic Facilities (CETAF), and the National Museum of Natural History, France. The TreatmentBank service provided by Plazi to convert taxonomic publications into FAIR data provides access to over 500,000 taxonomic treatments, including over 7,700 treatments for new described species in 2020. They will ev... | {
"page_id": 67504866,
"source": null,
"title": "Taxonomic treatment"
} |
Astrobiology (also xenology or exobiology) is a scientific field within the life and environmental sciences that studies the origins, early evolution, distribution, and future of life in the universe by investigating its deterministic conditions and contingent events. As a discipline, astrobiology is founded on the pre... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
the study of the origin and early evolution of life on Earth to try to understand the conditions that are necessary for life to form on other planets. This research seeks to understand how life emerged from non-living matter and how it evolved to become the diverse array of organisms we see today. Research within this ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
of astrobiology can be traced back to the 1950s and 1960s with the advent of space exploration, when scientists began to seriously consider the possibility of life on other planets. In 1957, the Soviet Union launched Sputnik 1, the first artificial satellite, which marked the beginning of the Space Age. This event led ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
and researched the history of water, and NASA's Curiosity rover, currently probing the environment for past and present planetary habitability of microbial life on Mars. == Theoretical foundations == === Planetary habitability === Astrobiological research makes a number of simplifying assumptions when studying the nece... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
is because very large stars have relatively short lifetimes, meaning that life might not have time to emerge on planets orbiting them; very small stars provide so little heat and warmth that only planets in very close orbits around them would not be frozen solid, and in such close orbits these planets would be tidally ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
to: Deep-sea extremophiles: Researchers are studying organisms that live in the extreme environments of deep-sea hydrothermal vents and cold seeps. These organisms survive in the absence of sunlight, and some are able to survive in high temperatures and pressures, and use chemical energy instead of sunlight to produce ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
of past or present extraterrestrial life utilise methodologies within planetary sciences. These include: The study of microbial life in the subsurface of Mars: Scientists are using data from Mars rover missions to study the composition of the subsurface of Mars, searching for biosignatures of past or present microbial ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
by another technological civilization. Communication attempts by humans have included broadcasting mathematical languages, pictorial systems such as the Arecibo message, and computational approaches to detecting and deciphering 'natural' language communication. While some high-profile scientists, such as Carl Sagan, ha... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
these ingredients could have led to the formation of the first living organisms. This includes the role of water in the formation of the first cells and in catalysing chemical reactions. The study of the role of minerals: Scientists are investigating the role of minerals like clay in catalysing the formation of organic... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
hypotheses and predictions as to its existence and origin vary widely, and at the present, the development of hypotheses firmly grounded on science may be considered astrobiology's most concrete practical application. It has been proposed that viruses are likely to be encountered on other life-bearing planets, and may ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
been considered, most notably NASA's Terrestrial Planet Finder (TPF) and ESA's Darwin programs, both of which have been cancelled. NASA launched the Kepler mission in March 2009, and the French Space Agency launched the COROT space mission in 2006. There are also several less ambitious ground-based efforts underway. Th... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
the Sun) ne = The number of Earth-sized worlds per planetary system fl = The fraction of those Earth-sized planets where life actually develops fi = The fraction of life sites where intelligence develops fc = The fraction of communicative planets (those on which electromagnetic communications technology develops) L = T... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
to understand four areas in the limits of life in planetary context: the potential for panspermia, forward contamination due to human exploration ventures, planetary colonization by humans, and the exploration of extinct and extant extraterrestrial life. Until the 1970s, life was thought to be entirely dependent on ene... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
life need not be sunlight-dependent; it only requires water and an energy gradient in order to exist. Biologists have found extremophiles that thrive in ice, boiling water, acid, alkali, the water core of nuclear reactors, salt crystals, toxic waste and in a range of other extreme habitats that were previously thought ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
chemistry, has made some progress, but it is still unclear whether or not life could have formed in such a manner on Earth. The alternative hypothesis of panspermia is that the first elements of life may have formed on another planet with even more favorable conditions (or even in interstellar space, asteroids, etc.) a... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
science in case intelligent life is found, epistemological questions about the nature of proof, ethical considerations of space exploration, along with the broader impact of discovering extraterrestrial life on human thought and society. Dunér has emphasized philosophy of astrobiology as an ongoing existential exercise... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
astrophilosophy as a more general discipline, to which philosophy is just a subset that deals with questions such as the nature of the human mind and other anthropocentric questions. Most of the philosophy of astrobiology deals with two main questions: the question of life and the ethics of space exploration. Kolb spec... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
life. Missions such as the Phoenix lander, Mars Science Laboratory, ExoMars, Mars 2020 rover to Mars, and the Cassini probe to Saturn's moons aim to further explore the possibilities of life on other planets in the Solar System. Viking program The two Viking landers each carried four types of biological experiments to ... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
in low Earth orbit. Mars Science Laboratory The Mars Science Laboratory (MSL) mission landed the Curiosity rover that is currently in operation on Mars. It was launched 26 November 2011, and landed at Gale Crater on 6 August 2012. Mission objectives are to help assess Mars' habitability and in doing so, determine wheth... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
habitability and potential for preservation of biosignatures and biomolecules within accessible geological materials. The Science Definition Team is proposing the rover collect and package at least 31 samples of rock cores and soil for a later mission to bring back for more definitive analysis in laboratories on Earth.... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
has significant concentrations of organics due to protection by the ice from oxidants and radiation. Journey to Enceladus and Titan Journey to Enceladus and Titan (JET) is an astrobiology mission concept to assess the habitability potential of Saturn's moons Enceladus and Titan by means of an orbiter. Enceladus Life Fi... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
universe. Mix, Lucas; Cady, Sherry L. and McKay, Christopher; eds. (2024). The Astrobiology Primer 3.0 is a special issue of the Astrobiology journal compiled by 12 editors and 60 authors that provides an overview of the current state of research in astrobiology. Chapter 1: The Astrobiology Primer 3.0 Chapter 2: What i... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
Approach. San Francisco: Pearson Addison-Wesley. ISBN 978-0-8053-8042-2. Gilmour, Iain; Mark A. Sephton (2004). An introduction to astrobiology. Cambridge: Cambridge Univ. Press. ISBN 978-0-521-83736-1. Ward, Peter; Brownlee, Donald (2000). Rare Earth: Why Complex Life is Uncommon in the Universe. New York: Copernicus.... | {
"page_id": 2787,
"source": null,
"title": "Astrobiology"
} |
Geoffrey J. Gordon is a professor at the Machine Learning Department at Carnegie Mellon University in Pittsburgh and director of research at the Microsoft Montréal lab. He is known for his research in statistical relational learning (a subdiscipline of artificial intelligence and machine learning) and on anytime dynami... | {
"page_id": 58067684,
"source": null,
"title": "Geoffrey J. Gordon"
} |
The molecular formula C20H16O5 (molar mass: 336.33 g/mol, exact mass: 336.0998 u) may refer to: Alpinumisoflavone Psoralidin | {
"page_id": 26348259,
"source": null,
"title": "C20H16O5"
} |
The Piola transformation maps vectors between Eulerian and Lagrangian coordinates in continuum mechanics. It is named after Gabrio Piola. == Definition == Let F : R d → R d {\displaystyle F:\mathbb {R} ^{d}\rightarrow \mathbb {R} ^{d}} with F ( x ^ ) = B x ^ + b , B ∈ R d , d , b ∈ R d {\displaystyle F({\hat {x}})=B{\h... | {
"page_id": 37358308,
"source": null,
"title": "Piola transformation"
} |
An extended periodic table theorizes about chemical elements beyond those currently known and proven. The element with the highest atomic number known is oganesson (Z = 118), which completes the seventh period (row) in the periodic table. All elements in the eighth period and beyond thus remain purely hypothetical. Ele... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
table. Elements in this region are likely to be highly unstable with respect to radioactive decay and undergo alpha decay or spontaneous fission with extremely short half-lives, though element 126 is hypothesized to be within an island of stability that is resistant to fission but not to alpha decay. Other islands of s... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
and uranium formed part of a 32-element period which would end at a chemically inactive element with atomic weight 292 (not far from the 294 for the only known isotope of oganesson). In 1913, Swedish physicist Johannes Rydberg similarly predicted that the next noble gas after radon would have atomic number 118, and pur... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
synthesize them at accelerators. Many searches for superheavy elements were conducted in the 1970s, all with negative results. As of April 2022, synthesis has been attempted for every element up to and including unbiseptium (Z = 127), except unbitrium (Z = 123), with the heaviest successfully synthesized element being ... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
used in the literature, and the elements are instead referred to by their atomic numbers; hence, element 164 is usually not called "unhexquadium" or "Uhq" (the systematic name and symbol), but rather "element 164" with symbol "164", "(164)", or "E164". === Aufbau principle === At element 118, the orbitals 1s, 2s, 2p, 3... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
and 2 elements or more like group 11 and 12 elements, respectively). Thus, elements 157–164 are placed in their table in a group that the authors do not think is chemically most analogous. === Nefedov === Nefedov, Trzhaskovskaya, and Yarzhemskii carried out calculations up to 164 (results published in 2006). They consi... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
not attempt to break up these series. === Kulsha === Computational chemist Andrey Kulsha has suggested two forms of the extended periodic table up to 172 that build on and refine Nefedov et al.'s versions up to 164 with reference to Pyykkö's calculations. Based on their likely chemical properties, elements 157–172 are ... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
element, is ongoing as of 2025. ==== Ununennium (E119) ==== The synthesis of element 119 (ununennium) was first attempted in 1985 by bombarding a target of einsteinium-254 with calcium-48 ions at the superHILAC accelerator at Berkeley, California: 25499Es + 4820Ca → 302119* → no atoms No atoms were identified, leading ... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
of the fusion reaction. Due to the predicted short half-lives, the GSI team used new "fast" electronics capable of registering decay events within microseconds. No atoms of element 119 were identified, implying a limiting cross section of 70 fb. The predicted actual cross section is around 40 fb, which is at the limits... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
The Russian team planned to upgrade their facilities before attempting the reaction again. In April 2007, the team at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany, attempted to create element 120 using uranium-238 and nickel-64: 23892U + 6428Ni → 302120* → no atoms No atoms were detected, provi... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
cross-section of 200 fb. Jens Volker Kratz predicted the actual maximum cross-section for producing element 120 by any of these reactions to be around 0.1 fb; in comparison, the world record for the smallest cross section of a successful reaction was 30 fb for the reaction 209Bi(70Zn,n)278Nh, and Kratz predicted a maxi... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
with copper-65 ions at the Gesellschaft für Schwerionenforschung in Darmstadt, Germany: 23892U + 6529Cu → 303121* → no atoms No atoms were identified. ==== Unbibium (E122) ==== The first attempts to synthesize element 122 (unbibium) were performed in 1972 by Flerov et al. at the Joint Institute for Nuclear Research (JI... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
to synthesize element 121 from 238U and 65Cu, it was concluded that half-lives of superheavy nuclei must be less than one microsecond or the cross sections are very small. More recent research into synthesis of superheavy elements suggests that both conclusions are true. The two attempts in the 1970s to synthesize elem... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
This result suggests a strong stabilizing effect at Z = 124 and points to the next proton shell at Z > 120, not at Z = 114 as previously thought. A compound nucleus is a loose combination of nucleons that have not arranged themselves into nuclear shells yet. It has no internal structure and is held together only by the... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
This experiment was motivated by the possibility of greater stability for nuclei around Z ~ 126 and N ~ 184, though more recent research suggests the island of stability may instead lie at a lower atomic number (such as copernicium, Z = 112), and the synthesis of heavier elements such as element 125 will require more s... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
elements. In particular, the presence of long-lived (on the order of 109 years) nuclei of elements 124 and 126, along with their decay products, at an abundance of 10−11 relative to their possible congeners uranium and plutonium, was conjectured. Others claimed that none had been detected, and questioned the proposed c... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
sensitivity. This result throws considerable doubt on the results of the Marinov collaboration with regard to their claims of long-lived isotopes of thorium, roentgenium and element 122. It is still possible that traces of unbibium might only exist in some thorium samples, although this is unlikely. The possible extent... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
these elements in a periodic table very difficult. === Chemical and physical properties === ==== Elements 119 and 120 ==== The first two elements of period 8 will be ununennium and unbinilium, elements 119 and 120. Their electron configurations should have the 8s orbital being filled. This orbital is relativistically s... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
actinium; nevertheless, this anomalous configuration does not appear to affect its calculated chemistry, which remains similar to that of actinium. Its first ionization energy is predicted to be 429.4 kJ/mol, which would be lower than those of all known elements except for the alkali metals potassium, rubidium, caesium... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
125) to unbiennium (element 129) are predicted to exhibit a +6 oxidation state and form hexafluorides, though 125F6 and 126F6 are predicted to be relatively weakly bound. The bond dissociation energies are expected to greatly increase at element 127 and even more so at element 129. This suggests a shift from strong ion... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
that point, is deep inside the electron cloud and the 8s and 8p1/2 electrons are bound too strongly to be chemically active. The 5g shell should be filled at element 144 and the 6f shell at around element 154, and at this region of the superactinides the 8p1/2 electrons are bound so strongly that they are no longer act... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
5g and 6f shells, instead of just 14 electrons being filled in the 4f and 5f shells in the lanthanides and actinides, respectively. Pekka Pyykkö divides these superactinides into three series: a 5g series (elements 121 to 138), an 8p1/2 series (elements 139 to 140), and a 6f series (elements 141 to 155), also noting th... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
5g18 subshell, they could be considered analogues of each other as well. As an example from the late superactinides, element 156 is expected to exhibit mainly the +2 oxidation state, on account of its electron configuration with easily removed 7d2 electrons over a stable [Og]5g186f148s28p21/2 core. It can thus be consi... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
that it, especially the isotopes 472164 and 482164 (with 164 protons and 308 or 318 neutrons), would be at the center of a hypothetical second island of stability (the first being centered on copernicium, particularly the isotopes 291Cn, 293Cn, and 296Cn which are expected to have half-lives of centuries or millennia).... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
element 164 should be the second most dense element in the first 172 elements in the periodic table, with only its neighbor unhextrium (element 163) being more dense (at 47 g·cm−3). Metallic element 164 should have a very large cohesive energy (enthalpy of crystallization) due to its covalent bonds, most probably resul... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
periodic table are expected to be the last main-group elements in their period, and are likely to be similar to the 5p elements indium through xenon. In elements 167 to 172, the 9p1/2 and 8p3/2 shells will be filled. Their energy eigenvalues are so close together that they behave as one combined p-subshell, similar to ... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
metals. That being said, the analogy is incomplete for elements 165 and 166; although they do start a new s-shell (9s), this is above a d-shell, making them chemically more similar to groups 11 and 12. ==== Beyond element 172 ==== Beyond element 172, there is the potential to fill the 6g, 7f, 8d, 10s, 10p1/2, and perha... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
likely to be unprofitable; the +4 state should be most common in aqueous solution, with +5 and +6 reachable in solid compounds. === End of the periodic table === The number of physically possible elements is unknown. A low estimate is that the periodic table may end soon after the island of stability, which is expected... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
a 1s electron orbital, v, is given by v = Z α c ≈ Z c 137.04 {\displaystyle v=Z\alpha c\approx {\frac {Zc}{137.04}}} where Z is the atomic number, and α is the fine-structure constant, a measure of the strength of electromagnetic interactions. Under this approximation, any element with an atomic number of greater than ... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
such states in a multi-electron system, needed to extend calculations and the periodic table past Zcr ≈ 172, are still open problems. Atoms with atomic numbers above Zcr ≈ 172 have been termed supercritical atoms. Supercritical atoms cannot be totally ionised because their 1s subshell would be filled by spontaneous pai... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
heavy as electrons. ===== Quark matter ===== It has also been posited that in the region beyond A > 300, an entire "continent of stability" consisting of a hypothetical phase of stable quark matter, comprising freely flowing up and down quarks rather than quarks bound into protons and neutrons, may exist. Such a form o... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
Z = 126 as a closed proton shell. In this region of the periodic table, N = 184, N = 196, and N = 228 have been suggested as closed neutron shells. Therefore, the isotopes of most interest are 310126, 322126, and 354126, for these might be considerably longer-lived than other isotopes. Element 126, having a magic numbe... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
might not be doubly magic and stability will instead be primarily determined by strong neutron shell closures. Additionally, due to the enormously greater forces of electromagnetic repulsion that must be overcome by the strong force at the second island (Z = 164), it is possible that nuclei around this region only exis... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
defines an element to exist if its lifetime is longer than 10−14 seconds, which is the time it takes for the nucleus to form an electron cloud. However, a nuclide is generally considered to exist if its lifetime is longer than about 10−22 seconds, which is the time it takes for nuclear structure to form. Consequently, ... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
one microsecond is unknown, though various models suggest that isotopes of elements heavier than unbinilium that may be produced in fusion reactions with available targets and projectiles will have half-lives under one microsecond and therefore may not be detected. It is consistently predicted that there will exist reg... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 6s2 6p6 6d10 7s2 7p6. Similarly, the [172] in the configurations for elements 173, 174, and 184 denotes the likely closed-shell configuration of element 172. Beyond element 123, no complete calculations are available and hence the data in this table must be taken as tentative. I... | {
"page_id": 68326,
"source": null,
"title": "Extended periodic table"
} |
A DNA clamp, also known as a sliding clamp, is a protein complex that serves as a processivity-promoting factor in DNA replication. As a critical component of the DNA polymerase III holoenzyme, the clamp protein binds DNA polymerase and prevents this enzyme from dissociating from the template DNA strand. The clamp-poly... | {
"page_id": 6425322,
"source": null,
"title": "DNA clamp"
} |
bacteriophage also uses a sliding clamp, called gp45 that is a trimer similar in structure to PCNA but lacks sequence homology to either PCNA or the bacterial beta clamp. === Bacterial === The beta clamp is a specific DNA clamp and a subunit of the DNA polymerase III holoenzyme found in bacteria. Two beta subunits are ... | {
"page_id": 6425322,
"source": null,
"title": "DNA clamp"
} |
a strong selective pressure for structure conservation, and suggesting that this type of DNA replication mechanism is conserved throughout eukaryotes. In eukaryotes, a homologous, heterotrimeric "9-1-1 clamp" made up of RAD9-RAD1-HUS1 (911) is responsible for DNA damage checkpoint control. This 9-1-1 clamp mounts onto ... | {
"page_id": 6425322,
"source": null,
"title": "DNA clamp"
} |
completed. The binding sites for these initiator proteins overlap with the binding sites for the DNA polymerase, so the clamp cannot simultaneously associate with a clamp loader and with a polymerase. Thus the clamp will not be actively disassembled while the polymerase remains bound. DNA clamps also associate with oth... | {
"page_id": 6425322,
"source": null,
"title": "DNA clamp"
} |
Chladni's law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of the numbers m of diametric (linear) nodes and n of radial (circular) nodes. It is stated as the equation f = C ( m + 2 n ) p {\displaystyle f=C(m+2n)^{p}} where C and p are... | {
"page_id": 1903345,
"source": null,
"title": "Chladni's law"
} |
In mycology, a sanctioned name is a name that was adopted (but not necessarily coined) in certain works of Christiaan Hendrik Persoon or Elias Magnus Fries, which are considered major points in fungal taxonomy. == Definition and effects == Sanctioned names are those, regardless of their authorship, that were used by Pe... | {
"page_id": 27921142,
"source": null,
"title": "Sanctioned name"
} |
names adopted by Persoon in his 1801 Synopsis, and by Fries in both the Systema and the Elenchus. Soon after, in 1983, Richard P. Korf proposed the now widely accepted "colon-author indication", whereby sanctioned names are indicated by including ": Pers." or ": Fr." when fully citing the species author. Formal approva... | {
"page_id": 27921142,
"source": null,
"title": "Sanctioned name"
} |
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompress... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
Mémoires de l'Académie des Sciences de Berlin in 1757 (although Euler had previously presented his work to the Berlin Academy in 1752). Prior work included contributions from the Bernoulli family as well as from Jean le Rond d'Alembert. The Euler equations were among the first partial differential equations to be writt... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
}}} denotes its material derivative in time with respect to the advective field v {\displaystyle \mathbf {v} } and ∇ w {\displaystyle \nabla w} is the gradient of the specific (with the sense of per unit mass) thermodynamic work, the internal source term, and ∇ ⋅ u {\displaystyle \nabla \cdot \mathbf {u} } is the flow ... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
time, the continuity equation to be added to the above set would correspond to: ∂ ρ ∂ t = 0. {\displaystyle {\frac {\partial \rho }{\partial t}}=0.} So the case of constant and uniform density is the only one not requiring the continuity equation as additional equation regardless of the presence or absence of the incom... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
of Einstein notation (where the sum is implied by repeated indices instead of sigma notation) is also frequent. === Properties === Although Euler first presented these equations in 1755, many fundamental questions or concepts about them remain unanswered. In three space dimensions, in certain simplified scenarios, the ... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
apix): Euler equations in the Froude limit (no external field) are named free equations and are conservative. The limit of high Froude numbers (low external field) is thus notable and can be studied with perturbation theory. === Conservation form === The conservation form emphasizes the mathematical properties of Euler... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
Euler equations in case of density variable in space are: where the additional variables are: ρ {\displaystyle \rho } is the fluid mass density, p {\displaystyle p} is the pressure, p = ρ w {\displaystyle p=\rho w} . The first equation, which is the new one, is the incompressible continuity equation. In fact the genera... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
define: y = ( ρ j 0 ) ; F = ( j j ⊗ 1 ρ j + p I j ρ ) , {\displaystyle {\mathbf {y} }={\begin{pmatrix}\rho \\\mathbf {j} \\0\end{pmatrix}};\qquad {\mathbf {F} }={\begin{pmatrix}\mathbf {j} \\\mathbf {j} \otimes {\frac {1}{\rho }}\,\mathbf {j} +p\mathbf {I} \\{\frac {\mathbf {j} }{\rho }}\end{pmatrix}},} where j = ρ u {... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
t}+\mathbf {u} \cdot \nabla e+{\frac {p}{\rho }}\nabla \cdot \mathbf {u} &=0.\end{aligned}}} === Incompressible constraint (revisited) === Coming back to the incompressible case, it now becomes apparent that the incompressible constraint typical of the former cases actually is a particular form valid for incompressible... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
∇ ⋅ u + D p D t ) . {\displaystyle {De \over Dt}={Dh \over Dt}-{\frac {1}{\rho }}\left(p\nabla \cdot \mathbf {u} +{Dp \over Dt}\right).} And by substituting the latter in the energy equation, one obtains that the enthalpy expression for the Euler energy equation: D h D t = 1 ρ D p D t . {\displaystyle {Dh \over Dt}={\f... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
v , s ) . {\displaystyle e=e(v,s).} The fundamental equation of state contains all the thermodynamic information about the system (Callen, 1985), exactly like the couple of a thermal equation of state together with a caloric equation of state. === Conservation form === The Euler equations in the Froude limit are equiva... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
in the case of a thermodynamic fluid are more simply expressed as: where S = ρ s {\displaystyle S=\rho s} is the entropy density, a thermodynamic conservation variable. Another possible form for the energy equation, being particularly useful for isobarics, is: ∂ H t ∂ t + ∇ ⋅ ( H t u ) = u ⋅ f − ∂ p ∂ t , {\displaystyl... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
case of Euler equations) are all real the system is defined hyperbolic, and physically eigenvalues represent the speeds of propagation of information. If they are all distinguished, the system is defined strictly hyperbolic (it will be proved to be the case of one-dimensional Euler equations). Furthermore, diagonalisat... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
of the original conservative variables is obtained by transforming back: y = P w , {\displaystyle \mathbf {y} =\mathbf {P} \mathbf {w} ,} this computation can be explicited as the linear combination of the eigenvectors: y ( x , t ) = ∑ i = 1 m w i ( x − λ i t , 0 ) p i . {\displaystyle \mathbf {y} (x,t)=\sum _{i=1}^{m}... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
s {\displaystyle s} the specific entropy, the corresponding jacobian matrix is: A = ( u − v 0 − e v v v u − e v s v 0 0 u ) . {\displaystyle {\mathbf {A} }={\begin{pmatrix}u&-v&0\\-e_{vv}v&u&-e_{vs}v\\0&0&u\end{pmatrix}}.} At first one must find the eigenvalues of this matrix by solving the characteristic equation: det... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
energy expressed as function of specific volume and specific entropy: ( e v v e v s e v s e s s ) , {\displaystyle {\begin{pmatrix}e_{vv}&e_{vs}\\e_{vs}&e_{ss}\end{pmatrix}},} is defined positive. This statement corresponds to the two conditions: { e v v > 0 e v v e s s − e v s 2 > 0 {\displaystyle \left\{{\begin{align... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
a 0 ) . {\displaystyle \mathbf {p} _{1}={\begin{pmatrix}v\\a\\0\end{pmatrix}}.} The other two eigenvectors can be found with analogous procedure as: p 2 = ( e v s 0 − ( a v ) 2 ) , p 3 = ( v − a 0 ) . {\displaystyle \mathbf {p} _{2}={\begin{pmatrix}e_{vs}\\0\\-\left({\frac {a}{v}}\right)^{2}\end{pmatrix}},\qquad \mathb... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
depends only on its temperature: a s ( T ) = γ T m . {\displaystyle a_{s}(T)={\sqrt {\gamma {\frac {T}{m}}}}.} Since the specific enthalpy in an ideal gas is proportional to its temperature: h = c p T = γ γ − 1 T m , {\displaystyle h=c_{p}T={\frac {\gamma }{\gamma -1}}{\frac {T}{m}},} the sound speed in an ideal gas ca... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
( u 2 ) − u × ( ∇ × u ) + ∇ p ρ . {\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}+{\frac {1}{2}}\nabla \left(u^{2}\right)+(\nabla \times \mathbf {u} )\times \mathbf {u} +{\frac {\nabla p}{\rho }}=\mathbf {g} ={\frac {\partial \mathbf {u} }{\partial t}}+{\frac {1}{2}}\nabla \left(u^{2}\right)-\mathbf {u} \tim... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
projecting the momentum equation on the flow direction, i.e. along a streamline, the cross product disappears because its result is always perpendicular to the velocity: u ⋅ ∇ ( 1 2 u 2 + ϕ + p ρ ) = − p ρ 2 u ⋅ ∇ ρ . {\displaystyle \mathbf {u} \cdot \nabla \left({\frac {1}{2}}u^{2}+\phi +{\frac {p}{\rho }}\right)=-{\f... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
⋅ u . {\displaystyle \mathbf {u} \cdot \nabla \left({\frac {1}{2}}u^{2}+\phi +{\frac {p}{\rho }}\right)={\frac {p}{\rho }}\nabla \cdot \mathbf {u} .} The right-hand side appears on the energy equation in convective form, which on the steady state reads: u ⋅ ∇ e = − p ρ ∇ ⋅ u . {\displaystyle \mathbf {u} \cdot \nabla e=... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
Euler momentum equation, one arrives to: D u D t = T ∇ s − ∇ h . {\displaystyle {\frac {D\mathbf {u} }{Dt}}=T\nabla \,s-\nabla \,h.} Friedmann deduced this equation for the particular case of a perfect gas and published it in 1922. However, this equation is general for an inviscid nonconductive fluid and no equation of... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
{\displaystyle T\nabla s=\nabla (Ts),} by defining the specific total Gibbs free energy: g t ≡ h t + T s , {\displaystyle g^{t}\equiv h^{t}+Ts,} the Crocco's form can be reduced to: u × ∇ × u − ∇ g t = g , u ⋅ ∇ g t = 0. {\displaystyle {\begin{aligned}\mathbf {u} \times \nabla \times \mathbf {u} -\nabla g^{t}&=\mathbf ... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
many space points and time steps would be necessary for the memory of computers now and in the near future. In these cases it is mandatory to avoid the local forms of the conservation equations, passing some weak forms, like the finite volume one. === Rankine–Hugoniot equations === Starting from the simplest case, one ... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
Or, if one performs an indefinite integral: F − F 0 = 0 . {\displaystyle \mathbf {F} -\mathbf {F} _{0}=\mathbf {0} .} On the other hand, a transient conservation equation: ∂ y ∂ t + ∇ ⋅ F = 0 , {\displaystyle {\partial y \over \partial t}+\nabla \cdot \mathbf {F} =\mathbf {0} ,} brings to a jump relation: d x d t Δ u =... | {
"page_id": 396022,
"source": null,
"title": "Euler equations (fluid dynamics)"
} |
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