Brownian motion is a physical phenomenon

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Reference no: EM13161728

Brownian motion is a physical phenomenon which can be observed, for instance, when a small particle is immersed in a liquid. One method for describing this motion (in one -dimension) involves modelling the particles as "jumping" once per microsecond a random distance. The Brownian model predicts how far the particle moves after waiting a certain amount of time. Because the model is based onrandom numbers , we are interested in the average distance the particle moves. Write a program that will simulate Brownian motion by doing ALL of the following: 1) Ask the user how many trials to run. 2) Run the requested number of trials. For each trial you will si mulate the Brownian motion of one particle over 10 microseconds (10 jumps). The particle should jump up to 1 nanometer to the left or right with each jump . 3) Calculate the average absolute value of the distance that the particle has moved. 4) Print the average absolute value of the distance to the screen. Hints: 1) You will need rand() from to generate random numbers to simulate the jum ping. Note that rand() generates random integers, but for Brownian motion the jumps must be floating point values. 2) The code is easiest if you consider negative numbers as movement to the left and positive numbers as movement to the right. Then you can simulate a jump by generating a random number between- 1 and 1. The position of the particle is simply the sum of all the jumps. 3) You can use abs() from to take the absolute value of the final distance. Do not take the absolute value of each jump or you will lose the left/right information. 4 ) You will probably need two loops. One to loop thr ough each trial, and one to loop through each of the 10 jumps. 5 ) Because we are taking the absolute value of the final distance, the average displacement of the particles after 10 jumps should not be 0. 6 ) Because the code is based on a random number generator, you should get a slightly different answer each time you run the code.

Reference no: EM13161728

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