Brownian in a sentence

Brownian motion In 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as " Brownian motion ".

Modeling using differential equations The equations governing Brownian motion relate slightly differently to each of the two definitions of Brownian motion given at the start of this article.

These papers were the foundation for the 1905 paper on Brownian motion, which showed that Brownian movement can be construed as firm evidence that molecules exist.

Meanwhile Ngoma, Coulibaly and company are chasing selfish interests as they run helter-skelter in Brownian motion.

A New Moment Method for Solving the Coagulation Equation for Particles in Brownian Motion.

A year later, botanist Robert Brown discovered Brownian motion : pollen grains in water undergoing movement resulting from their bombardment by the fast-moving atoms or molecules in the liquid.

For a realistic particle undergoing Brownian motion in a fluid many of the assumptions cannot be made.

From this expression Einstein argued that the displacement of a Brownian particle is not proportional to the elapsed time, but rather to its square root.

Hence, Lévy's condition can actually be used as an alternative definition of Brownian motion.

However the mathematical Brownian motion is exempt of such inertial effects.

So, for example, the thought experiment of a Brownian ratchet as a perpetual motion machine was first discussed by Gabriel Lippmann in 1900 but it was not until 1912 that Marian Smoluchowski gave an adequate explanation for why it cannot work.

Some of these collisions will tend to accelerate the Brownian particle; others will tend to decelerate it.

Taylor-Expansion Moment Method for Agglomer- ate Coagulation Due to Brownian Motion in the Entire Size Regime.

The Brownian motion can be modeled by a random walk.

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.

The density function of this distribution can be written as : The delta function is also used in a completely different way to represent the local time of a diffusion process (like Brownian motion ).

The displacement of a particle undergoing Brownian motion is obtained by solving the diffusion equation under appropriate boundary conditions and finding the rms of the solution.

The first moment is seen to vanish, meaning that the Brownian particle is equally likely to move to the left as it is to move to the right.

The first part of Einstein's argument was to determine how far a Brownian particle travels in a given time interval.

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.