Modes, fluctuations, structures

V.V.Afanasyev, M.P.Danilaev, Yu.E.Polsky

Russia

The modern development of complex dynamic systems (CDS) and structures (plasma, lasers, crystal lattices, semi-conductor structures, etc.) is aimed at:

-              revealing approaches to formation of CDS and structures with given properties;

-              revealing ways of CDS and structure formation mechanisms;

-              analysis and diagnostics of complex structures as well as mechanisms of their formation.

Solution of these problems stimulates the development of existing and new approaches to formation of such systems and structures. One of the promising methods of CDS modeling is based on their multimode model. This model implies the structure to be split into the subsystems (modes). In our opinion, multimode model can be very effective in revealing the ways of different CDS and structure formation, including nanostructures (for example, nanotubes). The existing modeling methods and formation control models of such structures require the solution of nonlinear differential equation system, which has no general solution. The system can be solved only with simplifications of CDS real physical model. This complicates formation, formation mechanism control, analysis and diagnostics of CDS and structures.

The purpose of this paper is the following: to reveal the ways of

-              structure, CDS structure formation in the framework of multimode model;

-              controlling the formation mechanism of CDS and structures taking into account the fluctuations;

-              analysis and diagnostics of CDS and structures.

The submitted multimode model allows:

-              carrying out the structural analysis on the basis of initial cell assembly of this structure formation;

-              revealing the methods of behavior mode control considering the fluctuations to provide the required behavior mode assembly or regimes of CDS;

-              creating the basis for fluctuation diagnostics; revealing the borders of such diagnostics applicability.