Growth Morphology

red ball Isotropy of growth further restricts the parameters:

   

yellow ball Uniform growth with velocity  v  normal to the front leads to the further restrictions:

            

yellow ball Morphology of isotropically competing species now depends on parameters     and  :

 

α  >> 0                                                                          α < 0

  (v > 0)

yellow ball The bulging circular arc is a common morphology for growth of a fitter mutant:

"Selective sweeps in growing microbial colonies," K.S. Korolev, M.J.I. Muller, N, Karahan, A.W. Murray, O. Halatschek, D.R. Nelson, Phys. Biol 9, 026008 (2012)

yellow ball Recent observation of a V-shaped dent morphology in take-over of a slower growing mutant was somewhat surprising:

"Slow expanders invade by forming dented fronts in microbial colonies," Hyunseok Lee, J. Gore1 and K.S. Korolev, PNAS 119, e2108653119.

red ball Anisotropic of growth models are easily implemented in simulations:

 

yellow ball The simple ``brick wall" model leads to  λ< 0

   

α < 0                                                                          α > 0

  λ< 0