FractalIn mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.
Core–mantle boundaryThe core–mantle boundary (CMB) of Earth lies between the planet's silicate mantle and its liquid iron–nickel outer core, at a depth of below Earth's surface. The boundary is observed via the discontinuity in seismic wave velocities at that depth due to the differences between the acoustic impedances of the solid mantle and the molten outer core. P-wave velocities are much slower in the outer core than in the deep mantle while S-waves do not exist at all in the liquid portion of the core.
Exploration geophysicsExploration geophysics is an applied branch of geophysics and economic geology, which uses physical methods at the surface of the Earth, such as seismic, gravitational, magnetic, electrical and electromagnetic, to measure the physical properties of the subsurface, along with the anomalies in those properties. It is most often used to detect or infer the presence and position of economically useful geological deposits, such as ore minerals; fossil fuels and other hydrocarbons; geothermal reservoirs; and groundwater reservoirs.
Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
Retention basinA retention basin, sometimes called a retention pond, wet detention basin, or storm water management pond (SWMP), is an artificial pond with vegetation around the perimeter and a permanent pool of water in its design. It is used to manage stormwater runoff, for protection against flooding, for erosion control, and to serve as an artificial wetland and improve the water quality in adjacent bodies of water. It is distinguished from a detention basin, sometimes called a "dry pond", which temporarily stores water after a storm, but eventually empties out at a controlled rate to a downstream water body.
Groundwater modelGroundwater models are computer models of groundwater flow systems, and are used by hydrologists and hydrogeologists. Groundwater models are used to simulate and predict aquifer conditions. An unambiguous definition of "groundwater model" is difficult to give, but there are many common characteristics. A groundwater model may be a scale model or an electric model of a groundwater situation or aquifer. Groundwater models are used to represent the natural groundwater flow in the environment.
Birth rateBirth rate, also known as natality, is the total number of live human births per 1,000 population for a given period divided by the length of the period in years. The number of live births is normally taken from a universal registration system for births; population counts from a census, and estimation through specialized demographic techniques. The birth rate (along with mortality and migration rates) is used to calculate population growth. The estimated average population may be taken as the mid-year population.
Derived functorIn mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. It was noted in various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and clarifies many of these observations. Suppose we are given a covariant left exact functor F : A → B between two A and B.
Derived categoryIn mathematics, the derived category D(A) of an A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology.
Total fertility rateThe total fertility rate (TFR) of a population is the average number of children that would be born to a female over their lifetime if: they were to experience the exact current age-specific fertility rates (ASFRs) through their lifetime they were to live from birth until the end of their reproductive life. It is obtained by summing the single-year age-specific rates at a given time. , the total fertility rate varied widely across the world, from 0.78 in South Korea to 6.73 in Niger.
