Impulse response function for Brownian motion
Motivated from the central role of the mean-square displacement and its second time-derivative - that is the velocity autocorrelation function in the description of Brownian motion and its implications to microrheology, we revisit the physical meaning of the first time-derivative of the mean-square...
Gespeichert in:
Veröffentlicht in: | Soft matter 2021-06, Vol.17 (21), p.541-5426 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | Motivated from the central role of the mean-square displacement and its second time-derivative - that is the velocity autocorrelation function
in the description of Brownian motion and its implications to microrheology, we revisit the physical meaning of the first time-derivative of the mean-square displacement of Brownian particles. By employing a rheological analogue for Brownian motion, we show that the time-derivative of the mean-square displacement
of Brownian microspheres with mass
m
and radius
R
immersed in any linear, isotropic viscoelastic material is identical to
, where
h
(
t
) is the impulse response function (strain history
γ
(
t
), due to an impulse stress
τ
(
t
) =
δ
(
t
− 0)) of a rheological network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance
. The impulse response function
of the viscoelastic material-inerter parallel connection derived in this paper at the stress-strain level of the rheological analogue is essentially the response function
of the Brownian particles expressed at the force-displacement level by Nishi
et al.
after making use of the fluctuation-dissipation theorem. By employing the viscoelastic material-inerter rheological analogue we derive the mean-square displacement and its time-derivatives of Brownian particles immersed in a viscoelastic material described with a Maxwell element connected in parallel with a dashpot and we show that for Brownian motion of microparticles immersed in such fluid-like materials, the impulse response func
t
ion
h
(
t
) maintains a finite constant value in the long term.
Motivated from the central role of the mean-square displacement and its second time-derivative - that is the velocity autocorrelation function in the description of Brownian motion, we revisit the physical meaning of its first time-derivative. |
---|---|
ISSN: | 1744-683X 1744-6848 |
DOI: | 10.1039/d1sm00380a |