ICTS

Particles in fluid flows are ubiquitous, from micron sized Suspended Particulate Matter (SPM) in atmosphere to centimetre sized droplets as rain. These particles which are much smaller in size compared to any relevant length scale in flow have the property to remember their entire trajectory (their history). This makes the evolution of particle dynamics non-local in time and has been a barrier in understanding dynamics of large number of them. We try to address this issue using boundary-bulk extension ideas from partial differential equation. I will introduce how this non-locality appears in a simple example of 1-D heat equation and try to draw implications for particles.