Definitions

# What is Brownian Movement definition/concept

The physical phenomenon of movement Brownian refers to erratic displacement of small particles which are immersed in a substance. The discovery of this phenomenon was carried out in the beginning of the 19th century by the Scottish and botanical physician: Robert Brown.

### Observations of erratic pollen movement

After analyzing the random movement of pollen grains within a liquid substance, the Scottish scientist observed a series of phenomena: Brownian Movement

1) that the pollen trajectories were continuous,

2) that pollen displacements were erratic and apparently unrelated to each other at various time intervals,

3) that the pollen particles had numerous collisions with the molecules of the liquid substance.

### A scientific discovery that can be demonstrated with a simple experiment

If we fill a glass with hot water and another with cold water and introduce a few drops of coloring in each one of them, the result will be quite different: in a few seconds the contents of the hot glass will have a homogeneous color, while the glass with cold water will present a coloration at the bottom of the same.

The phenomenon happens for a reason: the higher the temperature , the greater the agitation of the molecules in a liquid (inversely, if the temperature is lower, the movement of molecules will be reduced).

### Robert Brown’s observations recorded a stochastic-type mathematical model

A stochastic process is an infinite collection of random variables. Thus, any phenomenon that evolves over time can be measured and evaluated. Stochastic calculus is a discipline of mathematics that makes it possible to explain the movement of particles that are subject to random forces. Brownian Movement

Brownian motion is an example of a simple stochastic process, but Robert Brown is not the one who explained this phenomenon in a mathematical language . Stochastic phenomena began to be understood from the advances in kinematics , a discipline of physics aimed at moving objects that are not subject to original forces. In other words, kinematics describes the movements of particles or objects, but their causes are unknown.

This type of calculation has numerous applications, as it allows a better understanding of the path of a molecule in a liquid or gas, the path of an animal during a migration, stock price variations or the financial situation of an entity. Brownian Movement