What for and which exaflops supercomputers are necessary in natural sciences

An approach is considered that makes it possible to identify problems for solving which both modern supercomputers and the supercomputers of the pre-ex-flop class currently being created are needed. The possibilities of the approach are considered on the examples of actual problems of mechanics, physics, chemistry and biology. Both atomistic modeling and continuum mechanics are included. The advantages of toroidal topology are shown. Recommendations are offered on the procedures for choosing the design of planned supercomputers. Key words and phrases: atomistic modeling, electronic structure, molecular dynamics, multiscale modeling, radiation aging, laser ablation, nucleation, polymers, parallel efficiency