Brownian motion model of nanoparticle considering nonrigidity of matter-a systems modeling approach

The variance models for Brownian motion are developed either using the diffusion equation method or by using spectral analysis with a Langevin equation. The diffusion method approach does not consider properties of matter like inertia, elasticity, and dissipative capabilities whereas in the Langevin equation approach, although based on the property concept, the matter is considered rigid and there are no attempts of inclusion of elastic and other properties to study the Brownian motion. The concept of absoluteness (in rigidity) is debatable in nanodomains, and instead an analytical model for Brownian motion of nanosize particles has been obtained and explored in this work using the Langevin equation considering nonrigidity and dissipative capabilities of matter.