[ FreeCourseWeb ] Symmetry and Complexity

[ FreeCourseWeb.com ] Symmetry and Complexity

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English | PDF | 2020 | 190 Pages | ISBN : 303936846X | 6.07 MB

Symmetry and complexity are the two fundamental features of almost all phenomena in nature and science. Any complex physical model is characterized by the existence of some symmetry groups at different scales. On the other hand, breaking the symmetry of a scientific model has always been considered as the most challenging direction for new discoveries. Modeling complexity has recently become an increasingly popular subject, with an impressive growth when it comes to applications. The main goal of modeling complexity is the search for hidden or broken symmetries.
Usually, complexity is modeled by dealing with big data or dynamical systems, depending on a large number of parameters. Nonlinear dynamical systems and chaotic dynamical systems are also used for modeling complexity. Complex models are often represented by un-smooth objects, non-differentiable objects, fractals, pseudo-random phenomena, and stochastic processes.
The discovery of complexity and symmetry in mathematics, physics, engineering, economics, biology and medicine have opened new challenging fields of research. Therefore, new mathematical tools were developed in order to obtain quantitative information from models, newly reformulated in terms of nonlinear differential equations.

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