Frost Spreading with Cellular Automata

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  Various final states for varying humidity and temperature, as controlled by lambda_2 and lambda_3.

• GIF

  Ice from many sites. Varying humidity and temperature. Black represents evaporated sites, light blue the ice and grey still liquid sites.

• GIF

  Ice from many sites. Varying humidity and temperature. Black represents evaporated sites, light blue the ice and grey still liquid sites.

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  This is a phase diagram that shows a phase transition from all evaporated to all frozen. Yellow is frozen, purple is evaporated

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  This is a dragram showing the number of frozen sites going through our rate parameters

• GIF

  Ice from many sites. Varying humidity and temperature. Black represents evaporated sites, light blue the ice and grey still liquid sites.

• GIF

  Ice from many sites. Varying humidity and temperature. Black represents evaporated sites, light blue the ice and grey still liquid sites.

• GIF

  Ice from many sites. Varying humidity and temperature. Black represents evaporated sites, light blue the ice and grey still liquid sites.

• GIF

  Ice spreading from a single sites. Black represents evaporated sites, light blue the ice and grey still liquid sites.

• GIF

  Ice from many sites. Varying humidity and temperature. Black represents evaporated sites, light blue the ice and grey still liquid sites.

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  Frost coverage and fractal dimension evolve with time, depending on humidity and temperature.

Inspiration

This project was inspired by a recent paper published on Physical Review E; Frost spreading and pattern formation on microstructured surfaces Hauer et al 2021. They grew ice crystals by varying humidity and temperature and found that interesting structures form. One of the highlights of their paper was the fractal dimension changes when humidity and temperature change. Here we try to capture this phenomenon by employing a simple frost growing model.

What it does

First we divide up our bed into grids, then our simple model takes into account 3 parameters, lambda_1 - This is the rate at which each grid point spontaneously evaporates. In our later model, this parameter is set by the amount if humidity in the air (1/lambda3)

lambda_2 - This is the rate at which each grid point spontaneously freezes

lambda_3 - This is the likelihood that each frozen grid point will freeze its nearest neighbours. In our later model, this number is an exponential decay as humidity is sapped out of the environment, this parameter is also proportional to humidity.

How we built it

We used the Gillespie algorithm to simulate the growth at each timestep given the definitions for lambda_i.

We used DBSCAN, an unsupervised ML algorithm to find clusters in order to find phase transitions statistics.

We used a Box Counting algorithm to find the fractal dimensions

Challenges we ran into

We found it hard to map our lambda parameters to humidity and temperature

Accomplishments that we're proud of

Our simple model can capture some of the key phenomenons they showed in their experiment

What we learned

We learned that working together in an office is really fun after COVID!

What's next for Frost Spreading with Cellular Automata

Publish?

Built With

• matplotlib
• numpy
• python
• scipy