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A critical point of a function of a single real variable, f (x), is a value x 0 in the domain of f where f is not differentiable or its derivative is 0 (i.e. ′ =). [2] A critical value is the image under f of a critical point.
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist.
Critical point may refer to: Critical phenomena in physics; Critical point (mathematics), in calculus, a point where a function's derivative is either zero or nonexistent; Critical point (set theory), an elementary embedding of a transitive class into another transitive class which is the smallest ordinal which is not mapped to itself
A saddle point (in red) on the graph of z = x 2 − y 2 (hyperbolic paraboloid). In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. [2]
A typical phase diagram for a single-component material, exhibiting solid, liquid and gaseous phases. The solid green line shows the usual shape of the liquid–solid phase line. The dotted green line shows the anomalous behavior of water when the pressure increases. The triple point and the critical point are shown as red dots.
Critical thinking, in education; Criticality index, in risk analysis; Criticality matrix, a representation (often graphical) of failure modes along with their probabilities and severities; Self-organized criticality, a property of (classes of) dynamical systems which have a critical point as an attractor
Close enough to the critical point, everything can be reexpressed in terms of certain ratios of the powers of the reduced quantities. These are the scaling functions. The origin of scaling functions can be seen from the renormalization group. The critical point is an infrared fixed point. In a sufficiently small neighborhood of the critical ...
In thermodynamics, a critical line is the higher-dimensional equivalent of a critical point. [1] It is the locus of contiguous critical points in a phase diagram.These lines cannot occur for a single substance due to the phase rule, but they can be observed in systems with more variables, such as mixtures.