Application Of Fractal Concepts Research Articles

Multifractal Parametrization of Welded Joints Structure as an Instrument of Diagnostics and Detection of Defects

In each particular material the hierarchical peculiarities of defects indicate the corresponding hierarchical peculiarities of mechanisms of damage and limit states accumulation. In accordance with the points of view of V.S. Ivanova, V.V. Bolotin, A.A. Shanyavsky, L.I. Tushinsky, O.B. Naymark, V.V. Lepov, A.A. Bataev, the occurrence of the limiting state on a particular structural level is possible in case of accumulation on it of the ultimate concentration of defects of a certain kind. In such case the “established system” gets a new, additional degree of freedom, which promotes change of the prevailing mechanism of damage accumulation. The acceptability of this concept has been previously determined for a limited range of materials, which usually don’t have evident structural and mechanical heterogeneity. Thus, the extension of available results to the structurally heterogeneous materials and especially to the welded joints of such materials turned out to be a very difficult task. However, the concept of maximum (critical) level of damage accumulation on a particular scale level was introduced not so long ago. When assessing structural and mechanical heterogeneities of the structural material, an important role is played by concepts of similarity of mechanical phenomena, self-similarity of deformation and destruction processes and by the scale factor of reliability, which are considered in their historical development as a part of application of fractal concepts in the materials science. The application of complex synthesized approach (consisting of a set of diagnostic methods in the form of scanning electron microscopy and multifractal parametrization of materials microstructures) for detection of potentially hazardous zones of welded joints with the highest level of structural and mechanical heterogeneity was the main ideology of our study. In order to establish the cause-and-effect relationships of appearance of “macro-corrugations” on the surface of the material, the analysis of the structure of heterogeneous welded joints represented as a hierarchically organized system was performed.

Fractal Theory on Drying: A Review

Fractal geometry has been widely used in various dried materials and drying processes. This review summarizes the related studies and identifies the opportunities for future investigation. The application of fractal concept on drying can be categorized into describing microscopic and macroscopic structure of material in drying with fractal geometry and theoretical models with fractal theory for drying mechanism. And also, the capillary and network models for drying of capillary porous media are discussed and a fractal tortuous capillary model for drying of capillary porous media is proposed. From the selected examples, it is clear that the fractal theory has many advantages for identifying the complex structure of products and investigating drying mechanism. At last, some comments are made for the current investigations and also some prospects for the future development of this field are pointed out.

(MULTI)FRACTALITY OF PHYSIOLOGICAL TIME-SERIES

This paper contains the application of fractal concept in analyzing heartbeat (RR interval) fluctuations measured under controlled physical activity for subjects with stable angina pectoris (SAP). Results that illustrate the separation ability of the nonlinear methods, such as the Hurst R/S method, the detrended fluctuation analysis, DFA, and the method of G-moments, in distinguishing healthy from SAP subjects in scaling parameter space are presented.

Saturation exponent at various wetting condition: fractal modeling of thin-sections

Saturation exponents, along with resistivity log data, are usually needed for evaluating the initial saturation of a hydrocarbon reservoir. A number of experimental investigations have shown that reservoir wettability affects the exponent value. A remarkable divergence of conclusions, however, still appears in the literature. This paper presents the results of a study based on the application of fractal concepts. The concepts have been used to derive parameters such as clay content and electrical tortuosity of thin-sections at a given wetting condition and for various water saturations. A general equation of electrical resistivity was then developed, incorporating these parameters. The advantage of this approach is that, it is independent of rock–fluid equilibrium problems that commonly influence laboratory measurements. The present work employed 20 thin-sections of limestone and sandstone. It was found that the lowest exponent of 1.8 was obtained for strongly water-wet shaley sandstone and the highest value of 5.3 was for strongly oil-wet conditions. The exponent consistently increases as the wetting condition is shifted from strongly water-wet toward oil-wet. It is close to 2.0 for clean sandstone at strongly water-wet conditions; this supports Archie's empirical formula.

Modelling rough interfaces on seismic reflection profiles—The application of fractal concepts

The distortion of reflection continuity and amplitude by overburden structure in seismic reflection images of the subsurface is easily recognised and modelled when the wavelength of the shallower structure is relatively large. The effects of shorter wavelength structure although giving rise to little reflective response itself, cause significant distortion of the propagating wavefield, particularly when a moderate or strong acoustic impedance contrast is present in the shallow sub‐surface. Here we show how short as well as long spatial wavelengths of horizon roughness affect deeper reflection continuity, and develop a new method using fractal interpolation techniques to predict the total roughness of sub‐surface horizons from information contained in seismic reflection sections. Fractally complete depth‐velocity models are used in forward models, using the finite difference technique, to produce synthetic seismic profiles. The technique is illustrated with data from the Edoras Bank area of the Rockall Plateau, NE Atlantic, where apparently discontinuous reflectors underlying basalt flows are shown to be from continuous sedimentary horizons distorted by overlying rough horizons.

地球科学分野へのフラクタルの応用

地球科学分野へのフラクタルの応用

Linear and nonlinear, scalar and vector transport processes in heterogeneous media: Fractals, percolation, and scaling laws

We discuss recent developments in the application of fractal concepts and percolation theory to transport processes in heterogeneous media. The phenomena that we discuss include several types of nonlinear transport processes in disordered systems, which are relevant to the flow of non-Newtonian fluids in porous media, to electrical current in composites and doped polycrystalline semiconductors, to fracture and breakdown in disordered materials and natural rock, to elastic and viscoelastic properties of solids, polymers and gels, to flow in geological formations, and to several other problems. We emphasize the universal aspects of such phenomena, i.e., those that are independent of the microscopic or small-scale features of the systems in which they occur.

Rheological and microstructural characterization of double cream cheese

AbstractFirmness at 5 °C, dynamic viscoelastic moduli (G' G) and capillary extrusion profiles at 20 °C, were obtained on double cream cheese after the different steps of processing (curd obtention, mixing at 70 °C and 500 r.p.m. with heat‐denatured WPC, heating at 85 °C, homogenizing at 20 MPa (1st stage) and 5 MPa (2nd stage) and cooling to 20 °C and 13 °C) and storage 7–9 days at 5 °C. It was found that double cream cheese became firmer and more elastic after heating and homogenization, although it became softer and more viscous after mixing and cooling. Transmission Electron Microscopy (TEM) and cryo‐Scanning Electron Microscopy (SEM) micrographs showed that rheology results could be related to aggregation (during heating and homogenization) and disruption (during cooling) of milk fat globule/casein complexes. Dispersion of homogenization clusters after cooling, and aggregation of milk fat globules during storage caused double cream cheese structural instability to appear. It was suggested that the heterogeneity of capillary extrusion profiles could be quantified through application of fractal concepts and Fourier analysis and related to structure and texture of double cream cheese.

Application of fractal concepts to the study of caseinate aggregation phenomena

SummaryThe concepts of fractals and fractal dimension are introduced and applied to the description of the disordered structures of colloidal aggregates. It is demonstrated that the structure of the aggregates produced by ethanol de-stabilization of casein micelles can be quantitatively characterized by a fractal dimension. The values measured are compared to literature predictions from various computer studies simulating different models of the aggregation process.