Changes

==Origin==

==Origin==

[[Latin]] ''dissipātiōn''-''em'' , n. of [[action]] from ''dissipāre''

[[Latin]] ''dissipātiōn''-''em'' , n. of [[action]] from ''dissipāre''

*[http://en.wikipedia.org/wiki/15th_century 15th Century]

*[https://en.wikipedia.org/wiki/15th_century 15th Century]

==Definitions==

==Definitions==

*1: the [[action]] or [[process]] of dissipating : the state of being dissipated: a : [[dispersion]], [[diffusion]]  

*1: the [[action]] or [[process]] of dissipating : the state of being dissipated: a : [[dispersion]], [[diffusion]]  

*2: an [[act]] of self-indulgence; especially : one that is not harmful : amusement  

*2: an [[act]] of self-indulgence; especially : one that is not harmful : amusement  

==Description==

==Description==

In [[physics]], '''dissipation''' embodies the [[concept]] of a [http://en.wikipedia.org/wiki/Dynamical_system dynamical system] where important [[mechanical]] [[models]], such as [[waves]] or [http://en.wikipedia.org/wiki/Oscillation oscillations], lose [[energy]] over time, typically from [[friction]] or [[turbulence]]. The lost energy converts into [[heat]], which raises the [[temperature]] of the system. Such systems are called [http://en.wikipedia.org/wiki/Dissipative_system dissipative systems].

In [[physics]], '''dissipation''' embodies the [[concept]] of a [https://en.wikipedia.org/wiki/Dynamical_system dynamical system] where important [[mechanical]] [[models]], such as [[waves]] or [https://en.wikipedia.org/wiki/Oscillation oscillations], lose [[energy]] over time, typically from [[friction]] or [[turbulence]]. The lost energy converts into [[heat]], which raises the [[temperature]] of the system. Such systems are called [https://en.wikipedia.org/wiki/Dissipative_system dissipative systems].

For example, a [[wave]] that loses [http://en.wikipedia.org/wiki/Amplitude amplitude] is said to dissipate. The [[precise]] [[nature]] of the [[effects]] depends on the [[nature]] of the [[wave]]: an [http://en.wikipedia.org/wiki/Atmospheric_wave atmospheric wave], for instance, may dissipate close to the [[surface]] due to [[friction]] with the [[land]] mass, and at higher levels due to [http://en.wikipedia.org/wiki/Radiative_cooling radiative cooling].

For example, a [[wave]] that loses [https://en.wikipedia.org/wiki/Amplitude amplitude] is said to dissipate. The [[precise]] [[nature]] of the [[effects]] depends on the [[nature]] of the [[wave]]: an [https://en.wikipedia.org/wiki/Atmospheric_wave atmospheric wave], for instance, may dissipate close to the [[surface]] due to [[friction]] with the [[land]] mass, and at higher levels due to [https://en.wikipedia.org/wiki/Radiative_cooling radiative cooling].

Dissipating forces are those that can not be described by [http://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian] formalism. Loosely speaking, this includes [[friction]], and all similar [[forces]] that result in decoherency of [[energy]]—that is, conversion of coherent or directed energy [[flow]] into an indirected or more [http://en.wikipedia.org/wiki/Isotropic isotropic] [[distribution]] of [[energy]].

Dissipating forces are those that can not be described by [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian] formalism. Loosely speaking, this includes [[friction]], and all similar [[forces]] that result in decoherency of [[energy]]—that is, conversion of coherent or directed energy [[flow]] into an indirected or more [https://en.wikipedia.org/wiki/Isotropic isotropic] [[distribution]] of [[energy]].

In [http://en.wikipedia.org/wiki/Computational_physics computational physics], numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [http://en.wikipedia.org/wiki/Advection advection] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way [[analogous]] to a diffusional [[process]]. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [http://en.wikipedia.org/wiki/Numerical_stability numerical stability] characteristics of the solution.  

In [https://en.wikipedia.org/wiki/Computational_physics computational physics], numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [https://en.wikipedia.org/wiki/Advection advection] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way [[analogous]] to a diffusional [[process]]. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [https://en.wikipedia.org/wiki/Numerical_stability numerical stability] characteristics of the solution.  

A [[formal]], mathematical [[definition]] of dissipation, as commonly used in the mathematical study of [http://en.wikipedia.org/wiki/Measure-preserving_dynamical_system measure-preserving dynamical systems], is given in the article [http://en.wikipedia.org/wiki/Wandering_set wandering set].

A [[formal]], mathematical [[definition]] of dissipation, as commonly used in the mathematical study of [https://en.wikipedia.org/wiki/Measure-preserving_dynamical_system measure-preserving dynamical systems], is given in the article [https://en.wikipedia.org/wiki/Wandering_set wandering set].

[[Category: Physics]]

[[Category: Physics]]