Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
AsthenosphereThe asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~ below the surface, and extends as deep as . However, the lower boundary of the asthenosphere is not well defined. The asthenosphere is almost solid, but a slight amount of melting (less than 0.1% of the rock) contributes to its mechanical weakness. More extensive decompression melting of the asthenosphere takes place where it wells upwards, and this is the most important source of magma on Earth.
Weierstrass elliptic functionIn mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the theory of elliptic functions. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.
Elliptic curveIn mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K^2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: for some coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections.
MagmaMagma () is the molten or semi-molten natural material from which all igneous rocks are formed. Magma (sometimes colloquially but incorrectly referred to as lava by laypeople) is found beneath the surface of the Earth, and evidence of magmatism has also been discovered on other terrestrial planets and some natural satellites. Besides molten rock, magma may also contain suspended crystals and gas bubbles. Magma is produced by melting of the mantle or the crust in various tectonic settings, which on Earth include subduction zones, continental rift zones, mid-ocean ridges and hotspots.
SubductionSubduction is a geological process in which the oceanic lithosphere and some continental lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, the heavier plate dives beneath the second plate and sinks into the mantle. A region where this process occurs is known as a subduction zone, and its surface expression is known as an arc-trench complex.
Magma chamberA magma chamber is a large pool of liquid rock beneath the surface of the Earth. The molten rock, or magma, in such a chamber is less dense than the surrounding country rock, which produces buoyant forces on the magma that tend to drive it upwards. If the magma finds a path to the surface, then the result will be a volcanic eruption; consequently, many volcanoes are situated over magma chambers. These chambers are hard to detect deep within the Earth, and therefore most of those known are close to the surface, commonly between 1 km and 10 km down.
BasaltBasalt (UKˈbæsɔːlt,_-əlt; USbəˈsɔːlt,_ˈbeɪsɔːlt) is an aphanitic (fine-grained) extrusive igneous rock formed from the rapid cooling of low-viscosity lava rich in magnesium and iron (mafic lava) exposed at or very near the surface of a rocky planet or moon. More than 90% of all volcanic rock on Earth is basalt. Rapid-cooling, fine-grained basalt is chemically equivalent to slow-cooling, coarse-grained gabbro. The eruption of basalt lava is observed by geologists at about 20 volcanoes per year.
Cumulate rockCumulate rocks are igneous rocks formed by the accumulation of crystals from a magma either by settling or floating. Cumulate rocks are named according to their texture; cumulate texture is diagnostic of the conditions of formation of this group of igneous rocks. Cumulates can be deposited on top of other older cumulates of different composition and colour, typically giving the cumulate rock a layered or banded appearance. Cumulate rocks are the typical product of precipitation of solid crystals from a fractionating magma chamber.
Divergent boundaryIn plate tectonics, a divergent boundary or divergent plate boundary (also known as a constructive boundary or an extensional boundary) is a linear feature that exists between two tectonic plates that are moving away from each other. Divergent boundaries within continents initially produce rifts, which eventually become rift valleys. Most active divergent plate boundaries occur between oceanic plates and exist as mid-oceanic ridges.
