[ FreeCourseWeb.com ] Symmetry and Complexity 2019
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English | PDF | 2020 | 314 Pages | ISBN : 3039368443 | 28 MB
Symmetry and complexity are 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 the most challenging direction for discoveries. Modeling complexity has recently become an increasingly popular subject, with impressive growth in applications.
The main goal of modeling complexity is to 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 have been developed to obtain quantitative information from models, newly reformulated in terms of nonlinear differential equations. This Special Issue focuses on the most recent advances in calculus, applied to dynamical problems, linear and nonlinear (fractional, stochastic) ordinary and partial differential equations, integral differential equations, and stochastic integral problems, arising in all fields of science, engineering applications, and other applied fields dealing with complexity.
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