Application of Fractal Dimension in Industry Practice

Today, industrial production lines commonly use off-line and automatic on-line quality monitoring and control. Monitoring and control units analyse data from a production process, and analysis should be able to obtain reliable information that correspond with the character of the data obtained. The character of the data set obtained from production processes or from products can be highly structured in all industrial areas. Structured surface, complex time series (topologically one dimensional signals), difficulty to describe dividing curves are much more common than it can be expected. For this kind of data set, a powerful tool for analysis of complexity —fractal geometry (especially a fractal dimension) should be used. The fractal dimension with a combination of statistical tools is an interesting and powerful tool for complex data quantification, for tracing the source of poor quality, production optimization and investigating the source of instability of production process subsystems in industrial applications. The methodology for evaluation of complex and irregular data was developed and applied in industrial practice. This methodology searches appropriated parameters for a complex evaluation of data. Only the chosen parameters are used for a complete analysis of the data in order to reduce processing time

Defining urban and rural regions by multifractal spectrums of urbanization

The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns associated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on the generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanization. The census data of America and China are adopted to show how to make empirical analyses of urban-rural multifractals. This work is not so much a positive analysis as a normative study, but it proposes a new way of investigating urban and rural regional systems using fractal theory.Comment: 21 pages, 4 figures, 6 table

Biomimetic flow fields for proton exchange membrane fuel cells: A review of design trends

Bipolar Plate design is one of the most active research fields in Polymer Electrolyte Membrane Fuel Cells (PEMFCs) development. Bipolar Plates are key components for ensuring an appropriate water management within the cell, preventing flooding and enhancing the cell operation at high current densities. This work presents a literature review covering bipolar plate designs based on nature or biological structures such as fractals, leaves or lungs. Biological inspiration comes from the fact that fluid distribution systems found in plants and animals such as leaves, blood vessels, or lungs perform their functions (mostly the same functions that are required for bipolar plates) with a remarkable efficiency, after millions of years of natural evolution. Such biomimetic designs have been explored to date with success, but it is generally acknowledged that biomimetic designs have not yet achieved their full potential. Many biomimetic designs have been derived using computer simulation tools, in particular Computational Fluid Dynamics (CFD) so that the use of CFD is included in the review. A detailed review including performance benchmarking, time line evolution, challenges and proposals, as well as manufacturing issues is discussed.Ministerio de Ciencia, Innovación y Universidades ENE2017-91159-EXPMinisterio de Economía y Competitividad UNSE15-CE296

Water Absorption Properties of Cement Pastes: Experimental and Modelling Inspections

An intermingled fractal units’ model is shown in order to simulate pore microstructures as pore fraction and pore size distribution. This model is aimed at predicting capillary water absorption coefficient and sorptivity values in cement pastes. The results obtained are in good agreement with the experimental ones. For validating this model, a comparison with other procedures has been shown. It is possible to establish that the newly proposed method matches better with the experimental results. That is probably due to the fact that pore size distribution has been considered as a whole. Moreover, even though the proposed model is based on fractal base units, it is able to simulate and predict different properties as well as nonfractal porous microstructure

Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures

A correct statistical model of soil pore structure can be critical for understanding flow and transport processes in soils, and creating synthetic soil pore spaces for hypothetical and model testing, and evaluating similarity of pore spaces of different soils. Advanced visualization techniques such as X-ray computed tomography (CT) offer new opportunities of exploring heterogeneity of soil properties at horizon or aggregate scales. Simple fractal models such as fractional Brownian motion that have been proposed to capture the complex behavior of soil spatial variation at field scale rarely simulate irregularity patterns displayed by spatial series of soil properties. The objective of this work was to use CT data to test the hypothesis that soil pore structure at the horizon scale may be represented by multifractal models. X-ray CT scans of twelve, water-saturated, 20-cm long soil columns with diameters of 7.5 cm were analyzed. A reconstruction algorithm was applied to convert the X-ray CT data into a stack of 1480 grayscale digital images with a voxel resolution of 110 microns and a cross-sectional size of 690 × 690 pixels. The images were binarized and the spatial series of the percentage of void space vs. depth was analyzed to evaluate the applicability of the multifractal model. The series of depth-dependent macroporosity values exhibited a well-defined multifractal structure that was revealed by singularity and Rényi spectra. The long-range dependencies in these series were parameterized by the Hurst exponent. Values of the Hurst exponent close to one were observed indicating the strong persistence in variations of porosity with depth. The multifractal modeling of soil macropore structure can be an efficient method for parameterizing and simulating the vertical spatial heterogeneity of soil pore space