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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v22.i5-6.50
pages 155-175

Nonlinear Science in the Problem of Safety

G. G. Malinetskii
N. A. Mitin


Nonlinear science is the term employed to describe an interdisciplinary approach currently applied to investigation of relations common to a large number of natural and man-made systems.
Nonlinear science is based on a profound analogy that was found to exist between nonlinear mathematical models arising in natural sciences and in many fields of engineering. The existence of common features in the description of various phenomena makes it possible to construct elementary models which clearly and graphically reflect the substance of such processes. These elementary models, known as base models, can be used, just as cubes in children's games, for constructing models of actual systems and processes, by introducing the necessary refinements into the mathematical description.
One of the major places in nonlinear science is occupied by the study of jumps, phase transitions, high-rate processes and qualitative changes in the state of the objects under study. And it is precisely this which is usually the main component in the analysis of catastrophes in natural and man-made environments. We are faced with a paradoxical situations when new, effective, and most probably useful tools are not used in the field for which they have been predominantly designed. In our opinion the main reason for this is that specialists in different fields speak in different languages, which prevents them from understanding one another.
The main purpose of this article is to serve as a kind of dictionary and phrase book that would ensure contact between safety experts and their colleagues in nonlinear science. This dictates the style of the article. In each section we shall formulate an elementary conceptual model of a catastrophe, then its mathematical description and finally, we shall turn to specific studies, where these tools are used for analyzing safety problems.

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