Hello readers!
I'm starting a short series of basic simulations using MS Excel using this post. We will not enter any advanced topics in simulation, yet try to understand how some common problems can be simulated with a wellknown tool.
Title: Random
Walk (movement) of multiple particles (points) in 2D plain.
Initial
Condition: a) No. of Particles = 100
b) Particles start to move from origin
(0,0)
Basic
Theory:
In this lab, we are
trying to simulate the motion of particles in a 2D space for discrete time
frames. As per our assumption, we have 100 particles, all of which start moving
from (0,0) coordinates and move randomly. Hence, it has been called as “Random
Walk”.
Procedure:
We perform our basic
simulation in Microsoft Excel using the “Scatter Plot” feature. We achieve this
by organizing the random data in a spreadsheet and applying formulae to the
spreadsheet cells. In it, we employ a random function to generate a random
(stochastic) sample of data for 100 particles in 11 discrete time frames (t0, t1…
t11). For the initial state (t0), all the particles stay at (0,0) coordinates,
and the next position of the particle is calculated using the formula:
Xposition
at last time + 12*RAND() and Yposition at last time + 12*RAND(),
in which 12*RAND() gives us a value between 1 and 1.
Thus, the next position
of the particle becomes unknown to us, and we can simulate random movement of
the particles in 2D space. Finally, we can see the results by selecting the data
for one particular time, clicking the “Insert” menu and selecting “Scatter”.
The sample data for 4
particles is tabulated in next section (as showing 100 becomes very long).
Sample
Data:
Table1: Sample Data for 4
particles for 4 discrete time frames.
Time = 0

Time = 1

Time = 2

Time = 3


X

Y

X

Y

X

Y

X

Y


Particle1

0

0

0.230713

0.414474

0.197587

0.397396

0.705377

0.43751

Particle2

0

0

0.97556

0.74393

1.06599

0.3071

0.95934

0.72553

Particle3

0

0

0.530602

0.295072

0.233677

0.53365

0.74835

0.83489

Particle4

0

0

0.57715

0.912138

0.028148

1.523969

0.1651

1.801373

Output:
Below are the scatter
plots for four different time frames. We can clearly see the randomness in the
plotted data.
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