Brownian motion displacement response

Particulate diffusion does not play a significant role in the deposition of pharmaceutical aerosols. However, it is worth noting the mechanism by which diffusion of particles occurs in the lungs. The principle of Brownian motion is responsible for particle deposition under the influence of impaction with gas molecules in the airways. The amplitude of particle displacement is given by the following equation ... 

Hair cells are the sensory cells of the auditory and vestibular systems. Hair cells are the sensory cells of the internal ear, essential for the senses of sound and balance. The hair cell s transduction apparatus, the molecular machinery that converts forces and displacements into electrical responses, can respond to mechanical stimuli of less than 1 nm in amplitude, and of tens or even hundreds of kilohertz in frequency. Indeed, our hearing is ultimately limited by Brownian motion of water molecules impinging on the transduction apparatus. 

Longitudinal molecular diffusion. Solute molecules are engaged in ceaseless Brownian motion, which is responsible for diffusion. The component of this erratic motion along the column axis, superimposed on the downstream displacement caused by flow, is one source of zone broadening. 

For a particle evolving in a thermal bath, we focused our interest on the particle displacement, a dynamic variable which does not equilibrate with the bath, even at large times. As far as this variable is concerned, the equilibrium FDT does not hold. We showed how one can instead write a modified FDT relating the displacement response and correlation functions, provided that one introduces an effective temperature, associated with this dynamical variable. Except in the classical limit, the effective temperature is not simply proportional to the bath temperature, so that the FDT violation cannot be reduced to a simple rescaling of the latter. In the classical limit and at large times, the fluctuation-dissipation ratio T/Teff, which is equal to 1 /2 for standard Brownian motion, is a self-similar function of the ratio of the observation time to the waiting time when the diffusion is anomalous. 

Brownian motion is a random thermal motion of a particle inside a fluid medium. The collision between the fluid molecules and suspended microparticles are responsible for the Brownian motion. The Brownian motion consists of high frequencies and is not possible to be resolved easily. Average particle displacement after many velocity fluctuations is used as a measure of Brownian motion. The mean square diffusion distance, is proportional to DAt, where D is diffusion coefficient of the particle given by Einstein relation as... 

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