Rogue heat and diffusion waves

In this paper, we numerically show and discuss the existence and characteristics of rogue heat and dif- fusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the generation of unexpected and large fluctuations in the frame of these models. These fluctuations can be named as rogue heat (diffusion) waves. We discuss the properties and statistics of such rogue waves. Our results can find many important applications in many branches such as the nonlinear heat transfer, turbulence, financial mathematics, chemical or biological diffusion, nu- clear reactions, subsurface water infiltration, and pore water pressure diffusion modeled in the frame of nonlinear Terzaghi consolidation models, just to name a few.