Discontinuity, Nonlinearity, and Complexity

Alejaily, Ejaily Milad
Akhmet, Marat
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which govern a relation between subsets of a metric space to build a porous self-similar structure. Examples are provided to confirm that the definition satisfies a large class of self-similar fractals. The new concepts create new frontiers for fractals and chaos investigations.
Discontinuity, Nonlinearity, and Complexity


Generation of fractals as Duffing equation orbits
Akhmet, Marat; Alejaily, Ejaily Milad (AIP Publishing, 2019-05-01)
Dynamics are constructed for fractals utilizing the motion associated with Duffing equation. Using the paradigm of Fatou-Julia iteration, we develop iterations to map fractals accompanied with a criterion to ensure that the image is again a fractal. Because of the close link between mappings, differential equations and dynamical systems, one can introduce dynamics for fractals through differential equations such that they become points of the solution trajectory. There is no doubt that the differential equa...
Nonlinear Structural Coupling: Experimental Application
Kalaycioglu, Taner; Özgüven, Hasan Nevzat (2014-02-06)
In this work, the nonlinear structural modification/coupling technique proposed recently by the authors is applied to a test system in order to study the applicability of the method to real structures. The technique is based on calculating the frequency response functions of a modified system from those of the original system and the dynamic stiffness matrix of the nonlinear modifying part. The modification can also be in the form of coupling a nonlinear system to the original system. The test system used i...
Bergson’s method of intuition: towards a philosophy of life /
Koçkan, Zöhre; Çırakman, Elif; Department of Philosophy (2014)
The purpose of this study is to show how a possible philosophy of life can arise by following Bergson’s method of intuition and to make emphasis on how Bergson’s two fundamental notions (intuition and duration) are capable of grasping the flux of life. The scientific methods, static concepts and classical philosophy are not able to understand the flow of life. Throughout this study it is pointed out a possible philosophy that is able to grasp the flow and the evolution of life. For this aim, Bergson’s metho...
Oscillation of second order dynamic equations on time scales
Kütahyalıoğlu, Ayşen; Ağacık, Zafer; Department of Mathematics (2004)
During the last decade, the use of time scales as a means of unifying and extending results about various types of dynamic equations has proven to be both prolific and fruitful. Many classical results from the theories of differential and difference equations have time scale analogues. In this thesis we derive new oscillation criteria for second order dynamic equations on time scales.
Vector meson dominance, chiral loops, sigma meson, and omega-rho mixing in omega ->pi(0)pi(0)gamma decay
Gokalp, A; Kucukarslan, A; Yılmaz, Osman (2003-04-01)
In an attempt to explain the latest experimental result about the branching ratio of omega-->pi(0)pi(0)gamma decay, we reexamine the mechanism of this decay in a phenomenological framework in which the contributions of vector meson dominance, chiral loops, sigma-meson intermediate state amplitudes, and the effects of omega-rho mixing are considered. We conclude that in order to obtain the experimental value of the branching ratio B(omega-->pi(0)pi(0)gamma) the sigma-meson amplitude, which makes a substantia...
Citation Formats
E. M. Alejaily and M. Akhmet, “Discontinuity, Nonlinearity, and Complexity,” Discontinuity, Nonlinearity, and Complexity, pp. 135–142, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85101764170&origin=inward.