Скачать или смотреть The Keller-Segel model on the sphere in higher resolution

This is a variant of the simulation of the Keller-Segel model on the sphere, shown in the video    • The Keller-Segel model on the sphere with ...   , with slightly larger nutrient diffusion and a higher resolution. The number of grid points is about 50% higher (452'000 instead of 311'000).
Chemotaxis is the motion of life forms induced by a chemical, such as a nutrient. The Keller-Segel model involves two fields: the concentration of the life form, for instance slime molds, and the concentration of the nutrient. The organisms follow the gradient of concentration of the nutrient to reach higher concentrations, thereby depleting the nutrient, which regenerates at a given rate. If u and v denote the concentrations of slime molds and nutrient, the equations are reaction-diffusion equations of the form
d_t u = Delta(u) - div(k(u)*grad(v)) + u(1-u)
d_t v = D*Delta(v) + u-a*v,
where Delta denotes the Laplace operator, div is the divergence and grad is the gradient. D measures the diffusion of the nutrient, while a measures how fast the organisms deplete the nutrient. k(u) measure the influence of the organisms' concentration on how quickly they follow the nutrient gradient, and is given here by k(u) = c*u*(1+u²). The usual choice is k(u) = c*u/(1+u²), but I did not find parameter values leading to interesting dynamics with that k.
This video has two parts, showing the same simulation with two different representations.
3D view: 0:00
2D view: 1:02
The color hue and the z-coordinate depend on the concentration of the organisms. The peaks have been truncated at a given height for more visibility, actually they form much higher cusps. The observer rotates around the sphere on a circular orbit in a plane containing the center of the sphere.

This simulation is inspired by the online simulator
https://visualpde.com/sim/?preset=Kel...
that allows you to explore the effect of the different parameters on the system.

Render time: 3D part - 1 hour 23 minutes
2D part - 1 hour 24 minutes
Color scheme: Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
https://github.com/BIDS/colormap

Music: "The Marble Cinematic Univeersity" by Ezra Lipp‪@Ezralipp‬

See also https://images.math.cnrs.fr/Des-ondes... for more explanations (in French) on a few previous simulations of wave equations.

#chemotaxis #reaction_diffusion #Keller_Segel

The simulation solves a partial differential equation by discretization.
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...