Brownian Motion with collision graph

The Brownian motion is the chaotic movement of microscopic particles suspended in a fluid (liquid or gas) due to collisions with the molecules of the surrounding medium. This phenomenon was first observed in 1827 by botanist Robert Brown, who noticed that pollen grains in water exhibited irregular, jittery movements. Although Brown initially thought the motion was due to the particles being alive, later studies showed that the movement was purely physical in nature.
Brownian motion results from the continuous, random collisions between the suspended particles and the fast-moving molecules of the fluid. Since these molecular collisions occur in different directions and with varying intensities, they cause the particle to move unpredictably. The effect is more pronounced with bigger particles and at higher temperatures, as increased thermal energy leads to more frequent and forceful molecular collisions.
In 1905, Albert Einstein provided a theoretical explanation of the Brownian motion modeled using stochastic processes, which describes how a particle’s position changes over time as a function of number and size of particles and their motion energy. Brownian motion is significant in

• Physics & Chemistry: for the theory of gases and diffusion processes
• Biology: to understand cellular transport mechanisms
• Finance: to model stock market fluctuations
• Nanotechnology: to understand behavior and manipulation of nanoparticles