Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Sizikov V.P.  

Continuous media in the language of natural differentials

Sizikov V.P.

No matter how original and rigorous some mathematical models of the language of differential equations were, N. N. Yanenko did have saved the dream of models in which the processes would have perhaps more "natural" description. A certain movement towards such a dream can be provided by knowledge about natural differentials in the DIS-technology apparatus developed on the basis of the dynamic information systems theory (DIS, TDIS).
For the continuous media model and for the behavior of some bodies with various forms placed into such media the analysis is made within the scope of the DIS-technology, involving the concept of natural differential. The following questions have been solved.
What is the difference in the DIS-models for solids, liquids and gases? Какова природа эффектов давления, смачивания, трения? What is the nature of the effects of pressure, wetting and friction? What determines the response of the continuum to the bodies placed into the media? What is the difference for the DIS-models with solid and porous medium? What conditions a porous body can float in the continuum under?
There is a software base to carry out numerical experiments within the scope of the Excel and to produce plots of media functioning with their models examples at the rank of the DIS-PCs on the levels 1, 2 and 3. Analysis of the plots behavior allows giving some interpretations of what is going on in the media, in particular, to monitor the special events in the latter.

Abstracts file: СизиковВП.doc
Full text file: СизиковВП.pdf

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