Systems simulated by a simple percolation model using python

[dilloncyh]

I'm a first year physics student, and one of my assignment for my programming class is about percolation. I need to create some disks randomly distributed in an area (this is a 2-D), and then by varying the density of the disk, I need to figure out the percolation threshold such that the two sides of the square area is connected by the clusters of disks.
The worksheet also suggests some extension to the essential tasks, like making it 3-D and including disks with different radius, both of which I manage to do. But I'm wondering if there are some physical systems or phenomena that I can actually simulate using this simple model. Since I need to submit a report by the end, I expect I can use my model to simulate something to get some data (density, radius of disks, etc), then I can compare the results I get with some accepted value in literature to see how well my model does (which is similar to what I usually do for my first-year lab).
Are there any particular theories or models that I can test or simulate? Any recommended books for me to learn more about the basic of percolation?

The attached file is what I get using my program (300 disks with r=0.03 and 400 disks with r=0.02) for your reference.

thanks

 

[jedishrfu]

I can't comment much on your work except for the picture looking really cool ( future game?) but there's a Wikipedia article that delves into percolation theory in greater detail with some applications mentioned:

http://en.m.wikipedia.org/wiki/Percolation_theory

And this one on percolation itself with applications in various fields of study:

http://en.m.wikipedia.org/wiki/Percolation

 

[JorisL]

I know of some simple models describing Metal-Insulator transitions that use percolation.

I myself have, however, not found any decent references for this. The notes I have are quite useless without a reference.
If I do find something, I will link to it here.

[Edit]
Remember the model name (wasn't even in the nodes :-( )
It's about the "Mott Phase Transition in Doped Semiconductors"
Pretty simple model to justify for the specific substances its applied to.

 

[conana]

Any recommended books for me to learn more about the basic of percolation?

This classic: https://www.amazon.com/dp/0748402535/?tag=pfamazon01-20

 

[LudusRex]

Dear first year physics student,

It's great to hear that you are working on a percolation model using python for your programming class. Percolation is a widely studied phenomenon in physics and has applications in various fields such as material science, biology, and network theory.

Your project sounds like an interesting and valuable learning experience, and I'm sure you will learn a lot through it. As for potential physical systems or phenomena that you can simulate using your percolation model, there are many possibilities. Here are a few ideas that you can consider:

1. Conductivity of materials: Percolation theory is often used to study the electrical conductivity of materials. In this case, the disks in your simulation can represent conducting particles in a non-conducting medium. You can vary the parameters such as disk density and radius to see how they affect the overall conductivity of the system.

2. Porous materials: Similarly, percolation models can be used to study the permeability of porous materials. In this case, the disks can represent pores in a solid matrix, and you can investigate how varying the density and size of the pores affects the overall permeability.

3. Epidemic spread: Percolation models have also been used to study the spread of epidemics in a population. Here, the disks can represent individuals, and you can vary the parameters to see how it affects the rate of spread and containment of the epidemic.

4. Network connectivity: Percolation models can be applied to network theory to study the connectivity of networks. In this case, the disks can represent nodes in a network, and you can vary the parameters to see how it affects the overall connectivity and robustness of the network.

As for recommended books to learn more about percolation, I would suggest "Percolation" by Geoffrey Grimmett and "Introduction to Percolation Theory" by Dietrich Stauffer. These books cover the basics of percolation theory and its applications in various fields.

I hope this helps and wish you the best of luck with your project. Keep exploring and learning!

Best,