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In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter : solid , liquid , and gas , and in rare cases, plasma .
A discontinuous function is a function that is not continuous. Until the 19th century, mathematicians largely relied on intuitive notions of continuity and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.
The function in example 1, a removable discontinuity. Consider the piecewise function = {< = >. The point = is a removable discontinuity.For this kind of discontinuity: The one-sided limit from the negative direction: = and the one-sided limit from the positive direction: + = + at both exist, are finite, and are equal to = = +.
Smooth change can be described by a quasi-linear relationship between fast and slow processes; abrupt change shows a non-linear relationship among fast and slow variables, while discontinuous change is characterized by the difference in the trajectory on the fast variable when the slow one increases compared to when it decreases. [17]
On the other hand, discontinuous development involves distinct and separate stages, with different kinds of behavior occurring in each stage. [ 3 ] [ page needed ] Stage theories of development rest on the assumption that development is a discontinuous process involving distinct stages which are characterized by qualitative differences in behavior.
Discontinuity (geotechnical engineering), a plane or surface marking a change in physical or chemical properties in a soil or rock mass; Discontinuity (mathematics), a property of a mathematical function; Discontinuity (linguistics), a property of tree structures in theoretical linguistics
A discontinuity may exist as a single feature (e.g. fault, isolated joint or fracture) and in some circumstances, a discontinuity is treated as a single discontinuity although it belongs to a discontinuity set, in particular if the spacing is very wide compared to the size of the engineering application or to the size of the geotechnical unit.
The probabilistic, non-unitary, non-local, discontinuous change brought about by observation and measurement (state reduction or collapse). The deterministic, unitary, continuous time evolution of an isolated system that obeys the Schrödinger equation.