Impulse response function for Brownian motion

Area of Science:

• Physics
• Materials Science
• Rheology

Background:

• Brownian motion is fundamental to understanding particle dynamics in fluids.
• Mean-square displacement (MSD) and velocity autocorrelation function (VACF) are key descriptors.
• Microrheology uses Brownian motion to probe material properties.

Purpose of the Study:

• To clarify the physical meaning of the first time-derivative of MSD in Brownian motion.
• To establish a rheological analogue for Brownian motion in viscoelastic materials.
• To connect particle dynamics to material properties via impulse response functions.

Main Methods:

• Utilized a rheological analogue representing a parallel connection of viscoelastic material and an inerter.
• Derived the impulse response function (h(t)) for this rheological network.
• Applied the analogue to Brownian particles in a Maxwell element-dashpot parallel system.

Main Results:

• The first time-derivative of MSD is identical to the derived impulse response function h(t).
• The impulse response function h(t) relates to the particle response function derived using the fluctuation-dissipation theorem.
• For fluid-like materials, h(t) stabilizes to a constant value over long timescales.

Conclusions:

• The rheological analogue provides a new physical interpretation for the first time-derivative of MSD.
• This approach bridges particle-level Brownian motion with macroscopic rheological properties.
• The long-term behavior of h(t) offers insights into the viscoelastic response of the medium.