Editing Logistic function (section)

=== In optics: mirage ===
The logistic function also finds applications in optics, particularly in modelling phenomena such as [[Mirage|mirages]]. Under certain conditions, such as the presence of a temperature or concentration gradient due to diffusion and balancing with gravity, logistic curve behaviours can emerge.<ref name="Measuring refractive index gradient of sugar solution">{{cite journal |last1=Tanalikhit |first1=Pattarapon |last2=Worakitthamrong |first2=Thanabodi |last3=Chaidet |first3=Nattanon |last4=Kanchanapusakit |first4=Wittaya |title=Measuring refractive index gradient of sugar solution |journal=Journal of Physics: Conference Series |date=24-25 May 2021 |volume=2145 |issue=1 |page=012072 |doi=10.1088/1742-6596/2145/1/012072 |s2cid=245811843 |doi-access=free |bibcode=2021JPhCS2145a2072T }}</ref><ref>{{cite journal |last1=López-Arias |first1=T |last2=Calzà |first2=G |last3=Gratton |first3=L M |last4=Oss |first4=S |title=Mirages in a bottle |journal=Physics Education |date=2009 |volume=44 |issue=6 |pages=582 |doi=10.1088/0031-9120/44/6/002 |bibcode=2009PhyEd..44..582L |s2cid=59380632 |url=https://iopscience.iop.org/article/10.1088/0031-9120/44/6/002 }}</ref>

A mirage, resulting from a temperature gradient that modifies the refractive index related to the density/concentration of the material over distance, can be modelled using a fluid with a refractive index gradient due to the concentration gradient. This mechanism can be equated to a limiting population growth model, where the concentrated region attempts to diffuse into the lower concentration region, while seeking equilibrium with gravity, thus yielding a logistic function curve.<ref name="Measuring refractive index gradient of sugar solution"/>