Chemotaxis (Spring 2023)

a periodic 3d graph

Supervisor: Padi Fuster Aguilera

Description :

From the Greek, taxis meaning movement, chemotaxis is the movement of an organism in response to a chemical stimulus. The movement of sperm towards an egg during fertilization or of bacteria attracted towards a source of food are examples of chemotaxis. This phenomenon is usually modeled by a type of PDE systems called reaction-diffusion equations, which also have applications in epidemiology, ecology, and the social sciences. 

In this lab, we will study a particular PDE model for chemotaxis with logarithmic sensitivity and a generalized logistic growth and understand the qualitative behavior of its solution. We will perform numerical simulations using open sources such as Python and collaborating with CoCalc tools and learn more about how the non-dimensional parameters of our equations affect the behavior of solutions. We will make our code shareable and write a paper with our findings. 

 Students: Graham Mauer, Chelsea Eakins

 

OUTCOMES:

  • Created code in Python for Neumann boundary conditions.
  • Started to analyze the different rates in which the solution achieves the different regimes in terms of the parameters showing up in the model: Î±, r, and ε.
  • Wrote visualization tools for comparing the outcomes for the different parameters on the model and we looked at them and changed ratios of parameters to get a better idea of their effects in the model.
  • Worked on understanding the biological and mathematical meaning of each term on the model and did a presentation to the group about it.
  • Code in Python for Dirichlet boundary conditions.
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