Differential Equations at the Nanoscale

Nanotechnology is a rapidly developing and relatively young subdiscipline of science and engineering. It mainly deals with the preparation, characterization and utilization of nanoparticles—particles of size ranging from 1 to 100 nm. The manipulation of such small objects is demanding and the phenomena involved on the nanoscale are relatively complex, and different, compared with their counterparts at both quantum- and macroscales. Further development of nanoscience requires applications and evolution of mathematical models of nanoscale phenomena, preferably with the aid of advanced mathematical methods such as the ordinary and partial differential equations. This review presents the methodology of usage, along with the applications, of differential equations of various types (ordinary, partial, stochastic) to the nanoscale phenomena, including nanoparticles growth, aggregation, properties, and applications.