Abstract
In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol.
Highlights
The dynamics of complex systems [1,2], from functionality and structure points of view, lead to some instabilities
The analysis of complex systems evolution showed that most of them are non-linear and, new mathematical tools were required. These have been provided by the scale relativity theory (SRT) [10,11] and by the extended scale relativity theory (ESRT) [12], i.e., the SRT with an arbitrary constant fractal dimension
In order to overcome the difficulties generated by the fact that the classical theories failed in explaining the dynamics of real complex sytems, i.e., fluid and kinetic models in the study of some explaining the dynamics of real complex sytems, i.e., fluid and kinetic models in the study of some phenomena, such as combustion, drug delivery, solid components separation in mixtures, and plasma phenomena, such as combustion, drug delivery, solid components separation in mixtures, and ablation behavior, the fractal concepts and the corresponding non-differentiable theoretical models plasma ablation behavior, the fractal concepts and the corresponding non-differentiable theoretical can be applied
Summary
The dynamics of complex systems [1,2], from functionality and structure points of view, lead to some instabilities. The complex system’s dynamics are much more complicated and the classical theoretical models failed in the attempt to explain all these aspects, as illustrated by experimental observations [4] These difficulties can be overcome with a complementary approach, using fractal concepts, which were defined for the first time by Mandelbrot [5]. These have been provided by the scale relativity theory (SRT) [10,11] and by the extended scale relativity theory (ESRT) [12], i.e., the SRT with an arbitrary constant fractal dimension These theories consider that the motions of the complex system’s structural units take place on continuous but non-differentiable curves (fractal curves).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
