This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling  in March 2015.  The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such  topics as multimodal logic, fractional calculus, special functions,  Fourier-like solutions for PDE's,  Rvachev-functions and linear dynamical systems.  Special  chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula.  The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.