Abstract In this paper, a model for defects in nematic liquid crystals that was introduced Zhang et al. (Physica D Nonlinear Phenom 417:132828, 2021) is studied. the literature, setting of many models function space SBV (special functions bounded variation). However, considered herein regularizes director field to be Sobolev by introducing second vector tracking defect. A relaxation result case...

The geometrical effect is one of the most important factors in kinetic modeling crowd evacuation, besides interaction between agents. More precisely, process agents have desire to reach exit, and ability avoid walls or obstacles. In this study, we propose evacuation vector field which incorporates effects evacuation. This useful for from complex venue.