CMX Special Seminar

Motivated by the formation of fingerprint patterns we consider a class of interaction models with short-range repulsive, long-range attractive forces whose orientations depend on an underlying stress field. This stress field introduces an anisotropy leading to complex patterns which do not occur in the associated isotropic models. The transition between the isotropic and the anisotropic model can be characterized by one of the model parameters and we study the variation of this parameter both analytically and numerically. We analyze the steady states and their stability by considering the particle model and the associated mean-field equations. Besides, we propose a bio-inspired model to simulate fingerprint patterns as stationary solutions by choosing the underlying tensor field appropriately.