nonhomogen

Nonhomogen is a term used to describe situations where a region, material, or system does not have uniform properties throughout. It is essentially a less common form of the word nonhomogeneous, and may appear as nonhomogen in older texts or as shorthand in some disciplines. In practice, the concept is equivalent to heterogeneity: spatial or temporal variation in composition, structure, or properties.

In mathematics, the term nonhomogeneous (sometimes colloquially shortened to nonhomogen) describes equations or systems that are not invariant under the same transformations as a homogeneous one. In linear differential equations, a nonhomogeneous equation has a nonzero forcing term. Example: y'' + y = sin t is nonhomogeneous; the corresponding homogeneous equation is y'' + y = 0.

In materials science and physics, a nonhomogeneous or heterogeneous material has properties that vary with position, such as composition, density, stiffness, or thermal conductivity. Examples include sedimentary rocks, composite materials, and functionally graded materials designed to tailor property variation.

In probability, a nonhomogeneous (inhomogeneous) Poisson process has a rate parameter that varies with time or space, λ(t). This contrasts with a homogeneous Poisson process with constant rate.

See also: homogeneous, heterogeneity, inhomogeneous, nonhomogeneous.

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