Recent Advancements in Fractal Geometric-Based Nonlinear Time Series Solutions to the Micro-Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

Figure 1

Common fractals: (a) the middle-third Cantor set, (b) the von Koch curve, (c) the Weierstrass-Mandelbrot function 𝐶 in the range 0≤𝑥≤3 (𝑝=1.5 and 𝛾=0.5), where 𝑝 and 𝛾 are two numerical parameters (cf. (1.17)), where the trend of the function is ~𝑥², (𝑑) trajectories of a fractional Brownian process for different 𝐻 and 𝐷, and (e) the Sierpinski gasket (triangle), where the four small diagrams show the point of departure of the construction, then its first three stages, while the large diagram shows an advanced stage.

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(b)

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