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Abstract: A Keller-Segel model describes macroscopic dynamics of bacterial colonies andbiological cells. Bacteria secret chemical which attracts other bacteria sothat they move towards chemical gradient creating nonlocal attraction betweenbacteria. If bacterial density exceeds a critical value then the densitycollapses blows up in a finite time which corresponds to bacterialaggregation. Collapse in the Keller-Segel model has striking qualitativesimilarities with a nonlinear Schrodinger equation including critical collapsein two dimensions and supercritical in three dimensions. A self-similarsolution near blow up point is studied in the critical case and it has a formof a rescaled steady state solution which contains a critical number ofbacteria. Time dependence of scaling of that solution has square root scalinglaw with logarithmic corrections.



Author: Pavel M. Lushnikov

Source: https://arxiv.org/







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