緩和時間、休止時間、時定数

関: tau、time constant

WordNet

the 19th letter of the Greek alphabet
set the speed, duration, or execution of; "we time the process to manufacture our cars very precisely"
a period of time considered as a resource under your control and sufficient to accomplish something; "take time to smell the roses"; "I didnt have time to finish"; "it took more than half my time"
a suitable moment; "it is time to go"
adjust so that a force is applied and an action occurs at the desired time; "The good player times his swing so as to hit the ball squarely"
an indefinite period (usually marked by specific attributes or activities); "he waited a long time"; "the time of year for planting"; "he was a great actor in his time"
regulate or set the time of; "time the clock"
the continuum of experience in which events pass from the future through the present to the past
an instance or single occasion for some event; "this time he succeeded"; "he called four times"; "he could do ten at a clip" (同)clip
a persons experience on a particular occasion; "he had a time holding back the tears"; "they had a good time together"
assign a time for an activity or event; "The candidate carefully timed his appearance at the disaster scene"
(physics) the exponential return of a system to equilibrium after a disturbance (同)relaxation behavior
(physiology) the gradual lengthening of inactive muscle or muscle fibers
a method of solving simultaneous equations by guessing a solution and then reducing the errors that result by successive approximations until all the errors are less than some specified amount (同)relaxation method
an occurrence of control or strength weakening; "the relaxation of requirements"; "the loosening of his grip"; "the slackening of the wind" (同)loosening, slackening
shrub with terminal tufts of elongated leaves used locally for thatching and clothing; thick sweet roots are used as food; tropical southeastern Asia, Australia and Hawaii (同)Cordyline terminalis
the syllable naming the seventh (subtonic) note of any musical scale in solmization (同)te, si
the regulation of occurrence, pace, or coordination to achieve a desired effect (as in music, theater, athletics, mechanics)
the time when something happens
a more or less definite period of time now or previously present; "it was a sign of the times"

PrepTutorEJDIC

タウ(ギリシア語アルファベットの第19字T,т;英語のT,tに相当)
〈U〉《冠詞をつけずに》(空間に対しての)『時間』,時 / 〈U〉(時計で示される)『時刻』 / 〈U〉(ある方式で決められる)『時間』,標準時 / 〈C〉〈U〉(特定の)『時』,おり,ころ / 〈U〉《しばしば A ~》(ある長さの)『時間』,期間 / 〈U〉(要する)『時間』;暇 / 《しばしば複数形で》(歴史上の)『時代』 / 《複数形で》時勢,景気 / 《one's ~》(個人の)一生;若いころ;生涯の特定の時期 / 〈U〉《しばしば A ~》(ある経験をした)『時間』 / 〈C〉『…回』,度 / 〈C〉『…倍』 / …の時間を定める / (…に)…の調子を合わせる《+名+to+名》 / …の時間を計る
(…を)ゆるめること,緩和すること;(…を)ゆるみ;(規則などの)緩和,軽減《+『of』+『名』》 / 休養,くつろぎ,気晴らし,娯楽(diversion)
シ(全音階の第7音)
時間の調節;時間を測定[記録]すること
…掛ける

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/02/08 21:47:25」(JST)

wiki en

[Wiki en表示]

In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be characterized by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp(-t/τ).

1 Relaxation in simple linear systems
- 1.1 Mechanics: Damped unforced oscillator
- 1.2 Electronics: The RC circuit
2 Relaxation in condensed matter physics
- 2.1 Stress relaxation
- 2.2 Dielectric relaxation time
- 2.3 Liquids and amorphous solids
- 2.4 Spin relaxation in NMR
3 Chemical relaxation methods
4 Relaxation in atmospheric sciences
- 4.1 Desaturation of clouds
5 Relaxation in astronomy
6 See also
7 References

Relaxation in simple linear systems

Mechanics: Damped unforced oscillator

Let the homogeneous differential equation:

model damped unforced oscillations 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.

Electronics: The RC circuit

In an RC circuit containing a charged capacitor and a resistor, the voltage decays exponentially:

The constant is called the relaxation time of the circuit. A nonlinear oscillator circuit which generates a repeating waveform by the repetitive discharge of a capacitor through a resistance is called a relaxation oscillator.

Relaxation in condensed matter physics

In condensed matter physics, relaxation is usually studied as a linear response to a small external perturbation. Since the underlying microscopic processes are active even in the absence of external perturbations, one can also study "relaxation in equilibrium" instead of the usual "relaxation into equilibrium" (see fluctuation-dissipation theorem).

Stress relaxation

In continuum mechanics, stress relaxation is the gradual disappearance of stresses from a viscoelastic medium after it has been deformed.

Dielectric relaxation time

In dielectric materials, the dielectric polarization P depends on the electric field E. If E changes, P(t) reacts: the polarization relaxes towards a new equilibrium.

The dielectric relaxation time is closely related to the electrical conductivity. In a semiconductor it is a measure of how long it takes to become neutralized by conduction process. This relaxation time is small in metals and can be large in semiconductors and insulators.

Liquids and 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.

The term "structural relaxation" was introduced in the scientific literature in 1947/48 without any explanation, applied to NMR, and meaning the same as "thermal relaxation".^[1]

Spin relaxation in NMR

In nuclear magnetic resonance, relaxation is of prime importance. See Relaxation (NMR).

Chemical relaxation methods

In chemical kinetics, relaxation methods are used for the measurement of very fast reaction rates. A system initially at equilibrium is perturbed by a rapid change in a parameter such as the temperature (most commonly), the pressure, the electric field or the pH of the solvent. The return to equilibrium is then observed, usually by spectroscopic means, and the relaxation time measured. In combination with the chemical equilibrium constant of the system, this enables the determination of the rate constants for the forward and reverse reactions.^[2]

Relaxation in atmospheric sciences

Desaturation of clouds

Consider a supersaturated portion of a cloud. Then shut off the updrafts, entrainment, or any other vapor sources/sinks and things that would induce the growth of the particles (ice or water). Then wait for this supersaturation to reduce and become just saturation (relative humidity = 100%), which is the equilibrium state. The time it took for this to happen is called relaxation time. It will happen as ice crystals or liquid water content grow within the cloud and will thus consume the contained moisture. The dynamics of relaxation are very important in cloud physics modeling because if models do not take relaxation time into account, then it is highly probable that error will creep into the system.

In water clouds where the concentrations are larger (hundreds per cm³) and the temperatures are warmer (thus allowing for much lower supersaturation rates as compared to ice clouds), the relaxation times will be very low (seconds to minutes).

In ice clouds the concentrations are lower (just a few per liter) and the temperatures are colder (very high supersaturation rates) and so the relaxation times can be hours and hours.

τ=(4πDNRK)⁻¹

where

D = diffusion coefficient [m²/s]
N = concentration (of ice crystals or water droplets) [m⁻³]
R = mean radius of particles [m]
K = capacitance [unitless]

Relaxation in astronomy

In astronomy, relaxation time relates to clusters of gravitationally interacting bodies, for instance, stars in a galaxy. The relaxation time is a measure of the time it takes for one object in the system (the "test star") to be significantly perturbed by other objects in the system (the "field stars"). It is most commonly defined as the time for the test star's velocity to change by of order itself.

Suppose that the test star has velocity v. As the star moves along its orbit, its motion will be randomly perturbed by the gravitational field of nearby stars. The relaxation time can be shown to be ^[3]

T_r = {0.34\sigma^3\over G^2 m\rho\ln\Lambda}

\approx 0.95\times 10^{10} \!\left({\sigma\over 200\,\mathrm{km\,s}^{-1}}\right)^{\!3} \!\!\left({\rho\over 10^6\,M_\odot\,\mathrm{pc}^{-3}}\right)^{\!-1} \!\!\left({m_\star\over M_\odot}\right)^{\!-1} \!\!\left({\ln\Lambda\over 15}\right)^{\!-1}\!\mathrm{yr}

where ρ is the mean density, m is the test-star mass, σ is the 1d velocity dispersion of the field stars, and ln Λ is the Coulomb logarithm.

Various events occur on timescales relating to the relaxation time, including core collapse, energy equipartition, and formation of a Bahcall-Wolf cusp around a supermassive black hole.

References

^ Kittel, Rep. Progr. Phys. 1947; Hall, Phys. Rev. 1948; Wintner Phys. Rev. 1948.
^ Atkins P. and de Paula J. Atkins' Physical Chemistry (8th ed., W.H.Freeman 2006) p.805-7, ISBN 0-7167-8759-8
^ Spitzer, Lyman (1987). Dynamical evolution of globular clusters. Princeton, NJ: Princeton University Press. p. 191. ISBN 0691083096.

UpToDate Contents

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English Journal

Left ventricular function during porcine-resuscitated septic shock with pre-existing atherosclerosis.

Nußbaum BL1,2, McCook O3, Hartmann C4,3, Matallo J3, Wepler M4,3, Antonucci E5, Kalbitz M6, Huber-Lang M6, Georgieff M4, Calzia E3, Radermacher P3, Hafner S4,3.
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PMID 27271248

Fluorescence relaxation kinetics of poly(methylphenylsilane) film and nanocomposites.

Ostapenko N1, Gulbinas V2, Augulis R2, Boiko A1,2, Chursanova M3, Volkov A4, Telbiz G5.
Nanoscale research letters.Nanoscale Res Lett.2016 Dec;11(1):185. doi: 10.1186/s11671-016-1368-y. Epub 2016 Apr 12.
A comparative study of fluorescence relaxation kinetics of σ-conjugated poly(methylphenylsilane) (PMPS) polymer film and nanocomposites has been performed by ultrafast time-gated fluorescence measurements at various temperatures. Investigations have revealed a fine structure of excitonic σ-σ* ban
PMID 27067733

Rapid method for monitoring chitosan coagulation using low-field NMR relaxometry.

Kock FV1, Colnago LA2.
Carbohydrate polymers.Carbohydr Polym.2016 Oct 5;150:1-4. doi: 10.1016/j.carbpol.2016.05.007. Epub 2016 May 6.
Time-domain NMR relaxometry was proposed as a simple, rapid method to monitor chitosan (CS) coagulation as a function of pH. The longitudinal (T1) and transverse (T2) relaxation times of three CS concentrations (0.022, 0.22, and 2.2gL(-1)) were simultaneously measured by CP-CWFPx-x pulse sequences i
PMID 27312606

Japanese Journal

Acoustic Properties of Crystals with Jahn–Teller Impurities: Elastic Moduli and Relaxation Time. Application to SrF<sub>2</sub>:Cr<sup>2+</sup>

Journal of the Physical Society of Japan 86(11), 2017-10-16
NAID 160000038660

Synchrotron radiation-based quasi-elastic scattering using time-domain interferometry with multi-line gamma rays

Scientific Reports 7, 2017-10-02
NAID 120006349312

Temperature evolution of central peaks and effect of electric field in relaxor ferroelectric 0.83Pb(Mg

Jpn. J. Appl. Phys. 56(10S), 10PB03, 2017-09-14
NAID 150000114732

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★リンクテーブル★

リンク元	「tau」「休止時間」「緩和時間」
拡張検索	「isovolumic relaxation time」「isovok」mic relaxation time」
関連記事	「time」「relaxation」「timing」