Chaotic invariants like the fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. In this work, three algorithms are applied to non-linear time series: spectral analysis, rescaled range analysis and Higuchi's algorithm. The analyzed time series are associated with natural phenomena. The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a self-similar behavior, which depends on the time scale of measurements. It is also observed that fractal dimensions, D, calculated with Higuchi's method may not be constant over-all time scales. This work shows that during 2001, D reaches its lowest values in March and November. The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed.

The quality of steel produced by continuous casting depends mainly on the characteristics of the liquid steel flow pattern within the mold. This pattern depends on the flow dynamics of the nozzle that is immersed in liquid steel. This work characterizes the fluid dynamics within two separate submerged entry nozzle models with a square cross section bore. The Froude similarity criterion and water as working fluid have been used. The models consist of a square-shaped tube with one inlet and two lateral squared exits at the bottom. To enhance the flow visualization, the models do not have exit ports. Moreover, one of the models has a pool, a volume at the bottom, and the other prescinds of it. The geometrical parameters and operational conditions of physical experiments were reproduced in the numerical simulations. The turbulence model used in this work is large eddy simulation (LES) with dynamic k-equation filtering. It was found that transient numerical simulations reproduce the dynamic nature of the internal flow pattern seen in physical experiments. The results show that the flow pattern within the pool nozzle is defined by only one large vortex; on the other hand, in the nozzle, without the pool, the flow pattern achieves a complex behavior characterized by two small vortexes. This study will allow to build nozzles that produce a symmetric, regular fluid flow pattern inside the mold, which leads to improvements on the process such as low energy consumption and finally in cost reductions.