# Discontinuity

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Related to discontinuities: Jump discontinuity

## discontinuity

[dis‚känt·ən′ü·əd·ē]
(electromagnetism)
An abrupt change in the shape of a waveguide. Also known as waveguide discontinuity.
(geology)
An interruption in sedimentation.
A surface that separates unrelated groups of rocks.
(geophysics)
A boundary at which the velocity of seismic waves changes abruptly.
(mathematics)
A point at which a function is not continuous.
(metallurgy)
The place where the structural nature of a weldment is interfered with because of the materials involved or where the mechanical, physical, or metallurgical aspects are not homogeneous.
(physics)
A break in the continuity of a medium or material at which a reflection of wave energy can occur.

## Discontinuity

(or point of discontinuity), a value of the argument at which the continuity of a function is violated. In the simplest case, continuity is violated at some point a in the sense that the right and left limits exist, but at least one of them differs from f(a). When this occurs, a is called a jump discontinuity of f, or the discontinuity of the first kind.

If f(a + 0) = f(a – 0), the discontinuity is said to be removable, since f(x) becomes continuous at a if we set f(a) = f(a + 0) = f(a – 0). For example, the point a = 0 is a removable discontinuity of the function since f is continuous at 0, if we set f(0) = 1. If, however, the jump δ = f(a + 0) – f(a – 0) of the function f(x) at the point is nonzero, then a is a discontinuity for any definition of the value of f(a). An example of such a discontinuity is the point a = 0 for the function f(x)= arc tan 1/x. In this case, the function may not be defined at the point a. The jump discontinuity is called regular if the condition f(a) = ½[f(a – 0) + f(a + 0)] is satisfied. If either of the one-side limits does not exist, then the point a is called the discontinuity point of the second kind. Examples are the point a = 2 for the function f(x) = 1/(x – 2) and the point a = 0 for f(x) = sin 1/x.

References in periodicals archive ?
4) The tensile strength [sigma] of the rock mass and shear strength parameters c and [phi] of rock discontinuities are assumed to be anisotropic, and the spatial variation model of strength parameters is provided in Section 2.
Possible slope face orientations: The pole concentrations of the discontinuities data showed that the quarry sites had three major discontinuity planes (J1 J2 and J3); two of them were steeper while the other one was relatively flat (Table 2).
where Rl and Rs are the large-scale and small-scale roughness of the discontinuity planes, respectively, Im is the infilling material in the discontinuities and Kc is the presence of karst along the discontinuities.
lt;x|x> denotes the inner product, M the number of uniaxial discontinuities, and [?
Hydraulic continuity problems--If persistent and open discontinuities intersect the proposed bore path, then the possibility of a "frac-out" along a discrete joint plane cannot be ruled-out.
c) It can be applied for analyzing any cascaded set of abrupt discontinuities in arbitrary dielectric waveguides.
Discontinuities phase--existing technology can be rendered obsolete by the next innovation.
Discontinuities and defects have to be detected in order to determine the quality of the weld and related to the possible etiology.
If the discontinuities are too close together, multiple reflections may occur as within an interferometer.
The question of discontinuities in meteorological data has not gone away.
Discontinuity detection is limited to surface and near-surface discontinuities.
Discontinuities, a volume that speaks with a distinctly Canadian inflection, offers in composite a most compelling and subtle analysis of current modes of Renaissance studies.

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