Levent Yilmaz

By Levent Yilmaz

Fractal dimension, which is a measure for the degree of complexity or that of fractals, is given for the erosion and sedimentation of fluvial beds. An alternative to fractal dimension is ht-index, which quantifies complexity in a unique way while sediment particles begin to move if a situation is eventually reached when the hydrodynamic force exceeds a certain critical value. Back to question, the physical meaning of fractal dimension is that many natural and social phenomena are nonlinear rather than linear, and are fractal rather than Euclidean. We need a new paradigm for studying our surrounding phenomena, not Newtonian physics for simple systems, but complexity theory for complex systems, not linear mathematics such as calculus, Gaussian statistics, and Euclidean geometry, but online mathematics including fractal geometry, chaos theory, and complexity science in general.

Part of the book: Current Practice in Fluvial Geomorphology

By Levent Yilmaz

Monte Carlo in Monaco is given to the theory for mathematics, whose simulation process involves generating chance variables and exhibiting random behaviours in nature. This simulation is a powerful statistical analysis tool and widely used in both non-engineering fields and engineering fields for new perspectives. This simulation has been applied to diverse problems ranging from the simulation of complex physical phenomena such as atom collisions, to the simulation of river boundary layers as meanders and Dow Jones forecasting. It can deal with many random variables, various distribution types and highly nonlinear engineering models, while Monte Carlo is also suitable for solving complex engineering problems in two areas which are varying randomly. Monte Carlo simulation is given as an application for hydrogen energy potential determination.

Part of the book: Public Sector Crisis Management