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( Brownian motion)
Brownian motion (named after the botanist Robert Brown) is the random movement of particles suspended in a liquid or gas or the mathematical model used to describe such random movements, often called a particle theory. The mathematical model of Brownian motion has several real-world applications. An often quoted example is stock market fluctuations. Brownian motion is among the simplest continuous-time stochastic processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem). This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience rather than the accuracy of the models that motivates their use. The Roman Lucretius's scientific poem On the Nature of Things (c. 60 BC) has a remarkable description of Brownian motion of dust particles. He uses this as a proof of the existence of atoms "Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e. spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible." Although the mingling motion of dust particles is caused largely by air currents, the glittering, tumbling motion of small dust particles is indeed caused chiefly by true Brownian dynamics.
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