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Hydrothermal vent

A hydrothermal vent is a fissure on the seafloor from which geothermally heated water issues. Hydrothermal vents are found near volcanically active places, areas where tectonic plates are moving apart at spreading centers, ocean basins, hotspots. Hydrothermal deposits are rocks and mineral ore deposits formed by the action of hydrothermal vents. Hydrothermal vents exist because the earth is both geologically active and has large amounts of water on its surface and within its crust. Under the sea, hydrothermal vents may form features called white smokers. Relative to the majority of the deep sea, the areas around submarine hydrothermal vents are biologically more productive hosting complex communities fueled by the chemicals dissolved in the vent fluids. Chemosynthetic bacteria and archaea form the base of the food chain, supporting diverse organisms, including giant tube worms, clams and shrimp. Active hydrothermal vents are thought to exist on Jupiter's moon Europa, Saturn's moon Enceladus, it is speculated that ancient hydrothermal vents once existed on Mars.

Hydrothermal vents in the deep ocean form along the mid-ocean ridges, such as the East Pacific Rise and the Mid-Atlantic Ridge. These are locations where two tectonic plates are diverging and new crust is being formed; the water that issues from seafloor hydrothermal vents consists of sea water drawn into the hydrothermal system close to the volcanic edifice through faults and porous sediments or volcanic strata, plus some magmatic water released by the upwelling magma. In terrestrial hydrothermal systems, the majority of water circulated within the fumarole and geyser systems is meteoric water plus ground water that has percolated down into the thermal system from the surface, but it commonly contains some portion of metamorphic water, magmatic water, sedimentary formational brine, released by the magma; the proportion of each varies from location to location. In contrast to the 2 °C ambient water temperature at these depths, water emerges from these vents at temperatures ranging from 60 °C up to as high as 464 °C.

Due to the high hydrostatic pressure at these depths, water may exist in either its liquid form or as a supercritical fluid at such temperatures. The critical point of water is 375 °C at a pressure of 218 atmospheres. However, introducing salinity into the fluid raises the critical point to higher temperatures and pressures; the critical point of seawater is 407 °C and 298.5 bars, corresponding to a depth of ~2,960 m below sea level. Accordingly, if a hydrothermal fluid with a salinity of 3.2 wt. % NaCl vents above 407 °C and 298.5 bars, it is supercritical. Furthermore, the salinity of vent fluids have been shown to vary due to phase separation in the crust; the critical point for lower salinity fluids is at lower temperature and pressure conditions than that for seawater, but higher than that for pure water. For example, a vent fluid with a 2.24 wt. % NaCl salinity has the critical point at 280.5 bars. Thus, water emerging from the hottest parts of some hydrothermal vents can be a supercritical fluid, possessing physical properties between those of a gas and those of a liquid.

Examples of supercritical venting are found at several sites. Sister Peak vents low salinity phase-separated, vapor-type fluids. Sustained venting was not found to be supercritical but a brief injection of 464 °C was well above supercritical conditions. A nearby site, Turtle Pits, was found to vent low salinity fluid at 407 °C, above the critical point of the fluid at that salinity. A vent site in the Cayman Trough named Beebe, the world's deepest known hydrothermal site at ~5,000 m below sea level, has shown sustained supercritical venting at 401 °C and 2.3 wt% NaCl. Although supercritical conditions have been observed at several sites, it is not yet known what significance, if any, supercritical venting has in terms of hydrothermal circulation, mineral deposit formation, geochemical fluxes or biological activity; the initial stages of a vent chimney begin with the deposition of the mineral anhydrite. Sulfides of copper and zinc precipitate in the chimney gaps, making it less porous over the course of time.

Vent growths on the order of 30 cm per day have been recorded. An April 2007 exploration of the deep-sea vents off the coast of Fiji found those vents to be a significant source of dissolved iron; some hydrothermal vents form cylindrical chimney structures. These form from minerals; when the superheated water contacts the near-freezing sea water, the minerals precipitate out to form particles which add to the height of the stacks. Some of these chimney structures can reach heights of 60 m. An example of such a towering vent was "Godzilla", a structure on the Pacific Ocean deep seafloor near Oregon that rose to 40 m before it fell over in 1996. A black smoker or deep sea vent is a type of hydrothermal vent found on the seabed in the bathyal zone, but in lesser depths as well as deeper in abyssal zone, they appear as chimney-like structures that emit a cloud of black material. Black smokers emit particles with high levels of sulfur-bearing minerals, or sulfides. Black smokers are formed in fields hundreds of meters wide when superheated water from below Earth's crust comes through the ocean floor.

This water is most notably sulfides. When it

Delphin

The Delphin was a midget submarine created during World War II. Designed in 1944, only three prototypes were created by Nazi Germany's Kriegsmarine by the end of the war, all of which were destroyed; the Delphin was built for underwater speed attacks, as German engineers under the leadership of Ulrich Gabler discovered that past midget submarines were too slow to match the speeds of large ships in the English Channel. The Delphin weighed 2.5 tonnes and was recognizable due to its tear-drop shape, which allowed the vessel to travel through the water at higher speeds. During trials, the submarine reached a speed of seventeen knots. On 19 January 1945, the first prototype was destroyed after a collision with a boat and resulted in further testing being abandoned. Two other prototypes under construction in Berlin were moved to Pötenitz near Trave, where they were blown up as Allied forces approached. Rossler, Eberhard; the U-Boat: The Evolution and Technical History of German Submarines. London: Cassell.

ISBN 0-304-36120-8. Sieche, Erwin F. "German Human Torpedoes and Midget Submarines". Information on the Delphin class. Archived from the original on July 18, 2006. Retrieved July 30, 2006. Information on the Delphin class and its operations on Uboat.net

Cantor function

In mathematics, the Cantor function is an example of a function, continuous, but not continuous. It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity and measure. Though it is continuous everywhere and has zero derivative everywhere, its value still goes from 0 to 1 as its argument reaches from 0 to 1. Thus, in one sense the function seems much like a constant one which cannot grow, in another, it does indeed monotonously grow, by construction, it is referred to as the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor–Vitali function, the Devil's staircase, the Cantor staircase function, the Cantor–Lebesgue function. Georg Cantor introduced the Cantor function and mentioned that Scheeffer pointed out that it was a counterexample to an extension of the fundamental theorem of calculus claimed by Harnack; the Cantor function was discussed and popularized by Scheeffer and Vitali. See figure. To formally define the Cantor function c: →, let x be in and obtain c by the following steps: Express x in base 3.

If x contains a 1, replace every digit after the first 1 by 0. Replace any remaining 2s with 1s. Interpret the result as a binary number; the result is c. For example: 1/4 is 0.02020202... in base 3. There are no 1s so the next stage is still 0.02020202... This is rewritten as 0.01010101... When read in base 2, this corresponds to 1/3, so c = 1/3. 1/5 is 0.01210121... in base 3. The digits after the first 1 are replaced by 0s to produce 0.01000000... This is not rewritten; when read in base 2, this corresponds to 1/4, so c = 1/4. 200/243 is 0.21102 in base 3. The digits after the first 1 are replaced by 0s to produce 0.21. This is rewritten as 0.11. When read in base 2, this corresponds to 3/4, so c = 3/4. Equivalently, if C is the Cantor set on the Cantor function c: → can be defined as c = { ∑ n = 1 ∞ a n 2 n, x = ∑ n = 1 ∞ 2 a n 3 n ∈ C f o r a n ∈; this formula is well-defined, since every member of the Cantor set has a unique base 3 representation that only contains the digits 0 or 2.. Since c = 0 and c = 1, c is monotonic on C, it is clear that 0 ≤ c ≤ 1 holds for all x ∈ ∖ C.

The Cantor function challenges naive intuitions about measure. The Cantor function is the most cited example of a real function, uniformly continuous but not continuous, it is constant on intervals of the form, every point not in the Cantor set is in one of these intervals, so its derivative is 0 outside of the Cantor set. On the other hand, it has no derivative at any point in an uncountable subset of the Cantor set containing the interval endpoints described above; the Cantor function can be seen as the cumulative probability distribution function of the 1/2-1/2 Bernoulli measure μ supported on the Cantor set: c = μ. This probability distribution, called the Cantor distribution, has no discrete part; that is, the corresponding measure is atomless. This is.