Plasma Physics Seminar ( Phys 769)

Prof. Dionisios Margetis, Department of Mathematics & IPST, University of Maryland

Recent surprizes in asymptotics for continuum mechanics

Asymptotic techniques have been used widely in continuum mechanics, offering insights into physical quantities of interest when a variable or parameter is assumed to be large (or small). In this talk I will present recent, non-traditional applications of perturbation theory in two different physical contexts. First, a classical, linear advection-diffusion problem is solved analytically via regular perturbations of integral relations. The results yield the dependence of the concentration field for **all** values of the Peclet number and space variables. Second, a nonlinear PDE for the evolution of crystal surfaces is analyzed via boundary layer theory, where boundary conditions account for the discrete nature of crystals. Scaling laws and an ODE for the surface slope profile are derived and discussed.