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Sea ice growth processes. Sea ice is a complex composite composed primarily of pure ice in various states of crystallization, but including air bubbles and pockets of brine. Understanding its growth processes is important for climate modellers and remote sensing specialists, since the composition and microstructural properties of the ice affect ...
Double exponential function. A double exponential function is a constant raised to the power of an exponential function. The general formula is (where a >1 and b >1), which grows much more quickly than an exponential function. For example, if a = b = 10: f (x) = 10 10x. f (0) = 10.
The stretched exponential function. is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments t between 0 and +∞. With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is ...
RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period. In terms of differential equations, if is the current size, and its growth rate, then relative growth rate is. . If the RGR is constant, i.e., , a solution to this equation is.
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...
Hyperbolic growth. The reciprocal function, exhibiting hyperbolic growth. When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. [1] More precisely, the reciprocal function has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as is ...
Plant growth analysis. Plant growth analysis refers to a set of concepts and equations by which changes in size of plants over time can be summarised and dissected in component variables. It is often applied in the analysis of growth of individual plants, but can also be used in a situation where crop growth is followed over time.
Quadratic growth. In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit ", as the argument or sequence position goes to infinity – in big Theta notation ...
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