PIMS/CSC Seminar: Vladimir Babeshko

Introduction to the block element method, a new mathematical method based on high-level mathematics. The method is applicable to boundary value problems for partial differential equations and their systems. The method includes a number of other mathematical approaches and has numerous applications in many different fields. Thanks to this method, it was possible to investigate and solve a number of problems that could not be solved by any other method. The method, despite numerous applications, is still being developed but applicable towards an increasing number of scientific problems. The advantage of the method is the representation of solutions of boundary problems in the analytical form, in the form of integrals, which makes it possible to identify those properties of solutions that are not apparent when applying traditional numerical methods.

The lecture includes the following sections:

1. The block-element method. Fundamentals of the method. Factorization approaches. Integral (by N.Wiener) and differential methods of factorization. Comparison with known methods. Application to arbitrary block structures, the theory of which is at the initial stage of development. Demonstration of the simplest block structure — a multilayered medium. The basis of the theory of block structures: exterior algebra, external analysis, quotient topology.

2. Application of the method in seismology. Development of the first built model for the preparation of the starting earthquake. Comparison of theoretical results with the consequences of real earthquakes.

3. Application in the theory of strength and rupture of structures and materials. Hidden defects. A new type of dangerous fractures supplementing the Griffith — Irwin fractures.

4. Application in climatology. Identification of dangerous natural phenomena arising from weak energy in the media.

5. Application in tribology. Variables in the contact zone, coefficients of friction.

6. Application in the theory of waves in multicomponent media.

7. Application in the design of complex structures and materials.