Search results for: K. Lamrini Uahabi

Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: O. Boussoufi, K. Lamrini Uahabi, M. Atounti

Abstract:

The main purpose of this paper is to calculate the fractal dimension of some Julia Sets and Mandelbrot Set in the Misiurewicz Points. Using Matlab to generate the Julia Sets images that match the Misiurewicz points and using a Fractal software, we were able to find different measures that characterize those fractals in textures and other features. We are actually focusing on fractal dimension and the error calculated by the software. When executing the given equation of regression or the log-log slope of image a Box Counting method is applied to the entire image, and chosen settings are available in a FracLAc Program. Finally, a comparison is done for each image corresponding to the area (boundary) where Misiurewicz Point is located.

Keywords: box counting, FracLac, fractal dimension, Julia Sets, Mandelbrot Set, Misiurewicz Points

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Authors: Oktay Celenk, Ugur Karanfil, Iskender Demir, Samir Lamrini, Jorg Neumann, Arif Demir

Abstract:

Due to its favourable material characteristics, fiber reinforced plastics are amongst the main topics of all actual lightweight construction megatrends. Especially in transportation trends ranging from aeronautics over the automotive industry to naval transportation (yachts, cruise liners) the expected economic and environmental impact is huge. In naval transportation components like yacht bodies, antenna masts, decorative structures like deck lamps, light houses and pool areas represent cheap and robust solutions. Commercially available laser tools like carbon dioxide gas lasers (CO₂), frequency tripled solid state UV lasers, and Neodymium-YAG (Nd:YAG) lasers can be used. These tools have emission wavelengths of 10 µm, 0.355 µm, and 1.064 µm, respectively. The scientific goal is first of all the generation of a parameter matrix for laser processing of each used material for a Tm-fiber laser system (wavelength 2 µm). These parameters are the heat affected zone, process gas pressure, work piece feed velocity, intensity, irradiation time etc. The results are compared with results obtained with well-known material processing lasers, such as a Yb-fiber lasers (wavelength 1 µm). Compared to the CO₂-laser, the Tm-laser offers essential advantages for future laser processes like cutting, welding, ablating for repair and drilling in composite part manufacturing (components of cruise liners, marine pipelines). Some of these are the possibility of beam delivery in a standard fused silica fiber which enables hand guided processing, eye safety which results from the wavelength, excellent beam quality and brilliance due to the fiber nature. There is one more feature that is economically absolutely important for boat, automotive and military projects manufacturing that the wavelength of 2 µm is highly absorbed by the plastic matrix and thus enables selective removal of it for repair procedures.

Keywords: Thulium (Tm) fiber laser, laser processing of fiber-reinforced plastics (FRP), composite, heat affected zone

Procedia PDF Downloads 167