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The species–area relationship or species–area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and empirically, the relative numbers seem to follow systematic mathematical relationships. [ 1 ]
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Kleiber's law, like many other biological allometric laws, is a consequence of the physics and/or geometry of circulatory systems in biology. [5] Max Kleiber first discovered the law when analyzing a large number of independent studies on respiration within individual species. [2]
Mathematically, a strict power law cannot be a probability distribution, but a distribution that is a truncated power function is possible: () = for > where the exponent (Greek letter alpha, not to be confused with scaling factor used above) is greater than 1 (otherwise the tail has infinite area), the minimum value is needed otherwise the ...
In chemistry, mass attenuation coefficients are often used for a chemical species dissolved in a solution.In that case, the mass attenuation coefficient is defined by the same equation, except that the "density" is the density of only that one chemical species, and the "attenuation" is the attenuation due to only that one chemical species.
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [1] and the analytical solution was provided by Harry Bateman in 1910. [2]
In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes , such as random walks , and applied in many other fields, such as materials science , information ...
If we designate the solvent by the subscript "1" and the solute by "2", and the bound state by the superscript "s" (surface/bound) and the free state by the "b" (bulk solution / free), then the equilibrium constant can be written as a ratio between the activities of products over reactants: