<P> The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880 . This was followed independently by Louis Bachelier in 1900 in his PhD thesis "The theory of speculation", in which he presented a stochastic analysis of the stock and option markets . The Brownian motion model of the stock market is often cited, but Benoit Mandelbrot rejected its applicability to stock price movements in part because these are discontinuous . </P> <P> Albert Einstein (in one of his 1905 papers) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules . Their equations describing Brownian motion were subsequently verified by the experimental work of Jean Baptiste Perrin in 1908 . </P> <P> There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities . In this way Einstein was able to determine the size of atoms, and how many atoms there are in a mole, or the molecular weight in grams, of a gas . In accordance to Avogadro's law this volume is the same for all ideal gases, which is 22.414 liters at standard temperature and pressure . The number of atoms contained in this volume is referred to as Avogadro's constant, and the determination of this number is tantamount to the knowledge of the mass of an atom since the latter is obtained by dividing the mass of a mole of the gas by Avogadro's constant . </P> <P> The first part of Einstein's argument was to determine how far a Brownian particle travels in a given time interval . Classical mechanics is unable to determine this distance because of the enormous number of bombardments a Brownian particle will undergo, roughly of the order of 10 collisions per second . Thus Einstein was led to consider the collective motion of Brownian particles . </P>

What does brownian movement have to do with diffusion
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