# Relaxation time

Relaxation time

Relaxation time is a general concept in physics for the characteristic time in which a system changes to an equilibrium condition from a non-equilibrium condition. It can measure the time-dependent response of a system to well-defined external stimuli.

Examples

Dielectric relaxation time

Amorphous solids

An amorphous solid, such as amorphous indomethacin displays a temperature dependence of molecular motion, which can be quantified as the average relaxation time for the solid in a metastable supercooled liquid or glass to approach the molecular motion characteristic of a crystal. Differential scanning calorimetry can be used to quantify enthalpy change due to molecular structural relaxation [cite journal | author=Bruno C. Hancock, Sheri L. Shamblin | title=Molecular mobility of amorphous pharmaceuticals determined using differential scanning calorimetry | journal=THERMOCHIMICA ACTA | volume=380 | issue=2 | year=2001 | pages=95–107 |url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6THV-44HXV9B-3&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=030cf07b4a20ec20be9da496b35c704a | doi=10.1016/S0040-6031(01)00663-3 ] .

Mathematical example: Damped unforced oscillator

Let the homogenous differential equation:$mfrac\left\{d^2 y\right\}\left\{d t^2\right\}+gammafrac\left\{d y\right\}\left\{d t\right\}+ky=0$model damped unforced oscillations of a weight on a spring.

The displacement will then be of the form $y\left(t\right) = A e^\left\{-t/T\right\} cos\left(mu t - delta\right)$. The constant T is called the relaxation time of the system and the constant μ is the quasi-frequency.

Astronomy

In astronomy, relaxation time relates to clusters of gravitationally-interacting bodies (star clusters, galaxy clusters, globular clusters). The relaxation time is a measure of the time it takes for one object in a system to be significantly perturbed by other objects in the system. In the case of stars in a galaxy, the relaxation time measures the time for one star to undergo a strong encounter with another star. Various events occur on timescales relating to the relaxation time, including core collapse and energy exchange between stars (minimization of the total energy in a cluster).

The relaxation time is related to the velocity of a body (typically a star) and the perturbation rate. In the example of a star cluster, a particular star will have an orbit with a velocity "v". As the star passes by other stars, the orbit will be perturbed by the gravitational field of nearby stars. The relaxation time is similar to the ratio of the velocity to the time derivative of the perturbation.

Further reading

*Sparke, L. & Gallagher, J. (2000). "Galaxies in the Universe: An Introduction," 1st ed., Sec. 3.2. Cambridge University Press. ISBN 0-521-59241-0

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### См. также в других словарях:

• relaxation time —  Relaxation Time  Время релаксации   Время, за которое измеряемая характеристика системы уменьшится в е раз по сравнению с исходным значением. Replica: Реплика: Способ получения отпечатка поверхности твердого тела для ее изображения методом… …   Толковый англо-русский словарь по нанотехнологии. - М.

• relaxation time — noun the time constant of an exponential return of a system to equilibrium after a disturbance (Freq. 2) • Hypernyms: ↑time constant * * * noun 1. : the time required for an exponentially decreasing variable (as the amplitude of a damped… …   Useful english dictionary

• relaxation time — relaksacijos trukmė statusas T sritis Standartizacija ir metrologija apibrėžtis Dydis, atvirkščiai proporcingas sistemos slopimo koeficientui, t. y. τ = 1/δ ; čia δ – slopimo koeficientas. atitikmenys: angl. relaxation time vok. Relaxationszeit,… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

• relaxation time — relaksacijos trukmė statusas T sritis Standartizacija ir metrologija apibrėžtis Eksponentinio grįžimo į pusiausvyrą vyksmo trukmės konstanta. atitikmenys: angl. relaxation time vok. Relaxationszeit, f rus. время релаксации, n pranc. constante de… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

• relaxation time — relaksacijos trukmė statusas T sritis Standartizacija ir metrologija apibrėžtis Laiko tarpas, per kurį tam tikro dydžio vertės nuokrypis nuo pradinės arba pusiausvirosios vertės sumažėja e (e = 2,71828…) kartų. atitikmenys: angl. relaxation time… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

• relaxation time — relaksacijos trukmė statusas T sritis fizika atitikmenys: angl. relaxation time vok. Erholungszeit, f; Relaxationszeit, f rus. время релаксации, n; период релаксации, m pranc. temps de relaxation, m …   Fizikos terminų žodynas

• relaxation time — relaksacijos trukmė statusas T sritis chemija apibrėžtis Laikas, per kurį kurio nors dydžio nuokrypis nuo pusiausvirojo sumažėja e kartų. atitikmenys: angl. relaxation time rus. время релаксации; период релаксации …   Chemijos terminų aiškinamasis žodynas

• relaxation time — Time taken for a system to return to the resting or ground state or a new equilibrium state following perturbation. Often used in context of receptor systems that have a refractory period after responding and then relax to a competent state. Can… …   Dictionary of molecular biology

• relaxation time — any of several measures of loss of energy by magnetized materials (particularly hydrogen ions) after a magnetizing current is cut off; in magnetic resonance imaging two particularly useful measures are T1 relaxation t. and T2 relaxation t. (q.v.) …   Medical dictionary

• relaxation time — noun a) The characteristic time for a system to reach an equilibrium condition after a disturbance b) The time taken for a muscle to revert to its resting state after being used …   Wiktionary

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