Brownian motion
* WHAT IS BROWNIAN MOTION?
Brownian motion (or Brownian movement) can be defined as “the random movement of microscopic particles suspended in a fluid.” It is the erratic and constant movement of tiny particles when they are suspended in a fluid or gas. The name of the movement was kept after the scientist Robert Brown who first observed the phenomenon. We shall explore how.
* WHERE DO WE OBSERVE BROWNIAN MOTION?
i. Brownian motion in fluids :
The best evidence for the existence and movement of particles in liquid was given by Robert Brown in 1827. He suspended extremely small extremely small pollen grains in water. On looking through the microscope, it was found that the pollen grains were moving rapidly throughout the water in a very irregular or zig-zag way. It was also observed that warmer the water, faster the pollen grains move on the surface of water.
The movement of pollen grains on the surface of water can be explained as follows: Water is made up of tiny particles which are moving very fast. The pollen grains move on the surface of water because they are constantly being hit by fast moving molecules of water. So though the particles of water are too small to be seen, but their effect on the pollen grain could be seen clearly. The random motion of visible particles (pollen grains) caused by much smaller invisible particles of water is an example of Brownian motion.
The Essay on Erosion Water Particles Occurs
Erosion Streams, along with stream erosion, play important parts in the development of the land all over the world. Many important events happen from the result of erosion, including the construction of waterways, erosion of mountains and other natural things, and also deposition of particles. What is Erosion Erosion is the transportation of loose sediments or rock produced by weathering. Moving ...
Pollen grain
Invisible moving particles of water
ii. Brownian motion in gas :
Brownian motion is also observed in gas. For example: Smoke particles or dust particles in a light beam observed using a microscope appear as quivering specks of light, moving about unpredictably and erratically. Thus is caused by repeated and continual impacts on each smoke particles by fast moving air molecules, too small to see but nevertheless able to make the smoke particles move about noticeably. The erratic motion of each smoke particle occurs because the molecules bombard the smoke particles unevenly and at random. Consequently, the overall force of the impacts on each smoke particle continually changes direction at random.
The existence of Brownian motion gives us two conclusions about the nature of matter:
I. Matter is made up of small particles
II. The particles of matter are constantly moving
* ALBERT EINSTEIN’S EXPLANATION OF THE KINETIC THEORY:
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The explanation for this was already thought to be the random motion of molecules “hitting” the spores. But the first satisfactory theoretical treatment of the Brownian motion was made by Albert Einstein in 1905. Einstein’s theory enabled significant statistical predictions about the motion of particles that are randomly distributed in a fluid. These predictions were later confirmed by experiment. Jean Perrin made a quantitative experimental study of the dependence of Brownian motion on temperature and particle size that provided verification for Einstein’s mathematical formulation. Perrin’s work is regarded as one of the most direct verification of the kinetic theory of gases.
* USES OF BROWNIAN MOTION:
* Brownian motion in the Stock Market
The mathematical model of Brownian Motion is used to calculate the fluctuations in the stock market and has proved to be very useful in stock trading. |
The Term Paper on Competitive Analysis: Porter’s Five-Forces Model
The collective impact of competitive forces is so brutal in some industries that the market is clearly “unattractive” from a profit-making standpoint. Rivalry among existing firms is severe, new rivals can enter the industry with relative ease, and both suppliers and customers can exercise considerable bargaining leverage. According to Porter, the nature of competitiveness in a given industry can ...
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A Brownian Motion is stochastic process which has a stationary independent increase along with continuous sample paths. The increments seem to have normal distribution for given period of time, and this is what makes these increments useful in finance; as many financial experts believe that the stocks returns are normally distributed. Financial experts use Brownian Motion to build stock price models that include lognormal process, which is considered to be the exponential of Brownian Motion. Models based on Brownian Motion are very popular because they allow continuous hedging opinions to be used when determining pricing. |
* Investment, Uncertainty, and Price Stabilization Schemes
Another application of Einstein’s theory is seen in the paper done by William Smith, who uses the method of regulated Brownian motion to analyze the effects of price stabilization schemes on investment when demand is uncertain. He investigates the behaviour of investment when price is random, but subject to an exogenous ceiling, and with the aid of the mathematics of regulated Brownian motion, demonstrated that price controls mitigate the response of investment to changes in price, even when controls are not binding. The conclusions developed would be applicable to any economic situation involving smooth costs of adjustments of stocks when prices are uncertain but subject to government control (i.e. rent controls, hiring/firing decisions in the presence of a minimum wage).
* A Brownian motion Model for Decision Making
The Brownian model was also made use of by L.Romanow to develop a model for a decision making process in which action is taken when a threshold criterion level is reached. The model was developed with reference to career mobility, and it provides an explanation of an important feature of promotion processes in internal labour markets. The model assumes continuous observation of behaviour (of employees) and that the only route for leaving a job is by promotion. This suggests that the important mechanisms in the process are the basic evaluation procedure — rating which includes a random component (Brownian motion theory), and the decision rule — promote when an estimated average reaches a criterion level. The model was able to provide substantive qualitative results and hence is of good use to the ‘real’ world in decision making policies.
The Term Paper on Analyzing the Decision Process to Use the Atomic Bombs by Using Various Models
Analyzing the decision process to use the atomic bombs by using various models On the 6th and 9th of August in 1945, the US detonated two nuclear bombs over the Japanese cities of Nagasaki and Hiroshima. Knowing that vast number of casualties that would result from such actions; how were these decisions made and what factors were taken into account? These are the kind of questions that historians ...
