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Modeling CO2 Bubbles in Beer with Differential Equations

Explore the behavior of CO2 bubbles in a glass of beer using a 3D model. Discover how physics equations guide the study of bubble growth and movement. Learn how the Jacobian matrix helps analyze fixed points and eigenvalues in the system.

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Modeling CO2 Bubbles in Beer with Differential Equations

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  1. Quenching a Thirst with differential equations By: Emily Clerc, Abigail Martinez, Daniel Mashal

  2. Topic overview Modelling the behavior of CO2 bubbles as they grow and rise from the bottom of a glass of beer.

  3. Major results • Created a three dimensional model for the growing and rising of bubbles. • But, through experimentation, model does not hold.

  4. Physics equations used to make our model

  5. Our model

  6. The jacobian matrix

  7. Our Jacobian We took a Jacobian in order to find a fixed point, eigenvalues, and eigenvectors for our system. • There is not a fixed point since the Jacobian shows that in our first equation the partial derivative is coupled, so it can never be 0. • Since there can never be a fixed point, we cannot find the eigenvalues and eigenvectors at that point in our system.

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