- Relaxation time
Relaxation time is a general concept in
physics for thecharacteristic time in which a system changes to anequilibrium 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 amorphousindomethacin displays a temperature dependence of molecular motion, which can be quantified as the average relaxation time for the solid in ametastable supercooled liquid orglass to approach the molecular motion characteristic of acrystal .Differential scanning calorimetry can be used to quantifyenthalpy 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 :model damped unforcedoscillation s of a weight on a spring.The displacement will then be of the form . 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 ofgravitation ally-interacting bodies (star cluster s,galaxy cluster s,globular cluster s). 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, includingcore 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 astar ) 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 thegravitational field of nearby stars. The relaxation time is similar to the ratio of the velocity to thetime 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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