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simulation home page Introduction to Monte Carlo method, Page 1 monte carlo introduction

This is a powerful simulation technique which find much of its use in physical sciences. It has its name derived from the use of ‘random numbers’. Basically, a MC technique involves the use of a random approach to find solutions to problems which cannot be solved mathematically. Make no mistake, MC is NOT a gambling technique that you can use in a casino in Monte Carlo!

In this section, we are going to use the MC technique to simulate polymer chains. However, without going into mathematical details, we will first look at a simple example model to understand the basis of the technique. Later in the following sections we will discuss briefly what is a polymer; why and how MC could be used in calculations. Consider nine identical molecules, represented as blue disks, enclosed in a square as shown below:

molecular ensembles
Nine molecules enclosed in a square. The diagram shows five different patterns out of a huge number of ways these molecule can be arranged in the box.

At a temperature of T degree Celcius (exact value of T is not important here) these molecules are constantly moving to give different arrangement at all times. There is an energy associates with each particular arrangement. Provided that no extra energy is added into the box the energy arises is solely due to the interactions among the molecules. In fact these energies account for the state of a matter, that, for example, your desk is in one piece and does not fall apart spontaneously. This is due to the attractive interactions between atoms of the desk. We will come back to this issue later.

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