Structural Properties of Vicsek-like Deterministic Multifractals

Review about the Application of Fractal Theory in the Research of Packaging Materials

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

Small-Angle Scattering and Multifractal Analysis of DNA Sequences

The arrangement of A, C, G and T nucleotides in large DNA sequences of many prokaryotic and eukaryotic cells exhibit long-range correlations with fractal properties. Chaos game representation (CGR) of such DNA sequences, followed by a multifractal analysis, is a useful way to analyze the corresponding scaling properties. This approach provides a powerful visualization method to characterize their spatial inhomogeneity, and allows discrimination between mono- and multifractal distributions. However, in some cases, two different arbitrary point distributions, may generate indistinguishable multifractal spectra. By using a new model based on multiplicative deterministic cascades, here it is shown that small-angle scattering (SAS) formalism can be used to address such issue, and to extract additional structural information. It is shown that the box-counting dimension given by multifractal spectra can be recovered from the scattering exponent of SAS intensity in the fractal region. This approach is illustrated for point distributions of CGR data corresponding to Escherichia coli, Phospholamban and Mouse mitochondrial DNA, and it is shown that for the latter two cases, SAS allows extraction of the fractal iteration number and the scaling factor corresponding to "ACGT" square, or to recover the number of bases. The results are compared with a model based on multiplicative deterministic cascades, and respectively with one which takes into account the existence of forbidden sequences in DNA. This allows a classification of the DNA sequences in terms of random and deterministic fractals structures emerging in CGR.

Valentinite and Colloform Sphalerite in Epithermal Deposits from Baia Mare Area, Eastern Carpathians

Valentinite forms through the alteration of stibnite in sulphide deposits. Colloform sphalerite is a widespread mineral in low-temperature deposits, particularly those of the Mississippi-Valley type. We identified valentinite and colloform sphalerite in hydrothermal deposits occurring in the Baia Mare area. The Baia Mare metallogenic district of Neogene age occurs in the northwestern part of the Neogene volcanic chain within the Eastern Carpathians. The Neogene volcanism from Baia Mare area is related to the subduction processes of the East European plate under two microplates, Alcapa and Tisza-Dacia/Tisia, in the post-collisional compressive phase. We have identified valentinite in the Dealul Crucii and Baia Sprie deposits, associated with other epithermal minerals, in the absence of the stibnite. Valentinite is deposited in the final phase of the epithermal process after calcite and manganese-bearing calcite. Micro-Raman and microprobe determinations indicate the presence of valentinite. The formula of valentinite is close to stoichiometric Me2O3 and contains small amounts of tin as an antimony substituent. Colloform sphalerite was identified in the Baia Sprie ore deposit associated with minerals formed in the final epithermal phase. It was deposited on idiomorphic crystals of stibnite, which it corrodes. Its structure and an alternate banding, exhibited on the nano-/microscale, were identified by optical microscopy, SEM (scanning electron microscopy), and BSE (backscattered electron microscopy) imaging. These structures are typical for colloform sphalerite and suggest a genesis due to episodic precipitation. The spherical nano/micro-particles (nodules) are characteristic of the colloform sphalerite from Baia Sprie. Raman analysis indicates the presence of a colloform sphalerite with low iron content. The typical diffraction lines for sphalerite were identified in X-ray diffraction: 3.118 Å (111), 1.907 Å (220), 1.627 Å (311). Microprobe analysis certifies the presence of sphalerite with the stoichiometric formula close to ZnS. Iron content is low (0%–0.0613%), but Sb (0.7726%–2.6813%), Pb (0.56%–1.1718%), Bi (0%–0.1227%) are also present. The negative correlation between Zn and Sb suggests the simultaneous deposition from the same epithermal fluids. Valentinite and colloform sphalerite were formed at low temperatures (100–150 °C) at the end of the epithermal process.

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

Small-angle scattering (SAS; X-rays, neutrons, light) is being increasingly used to better understand the structure of fractal-based materials and to describe their interaction at nano- and micro-scales. To this aim, several minimalist yet specific theoretical models which exploit the fractal symmetry have been developed to extract additional information from SAS data. Although this problem can be solved exactly for many particular fractal structures, due to the intrinsic limitations of the SAS method, the inverse scattering problem, i.e., determination of the fractal structure from the intensity curve, is ill-posed. However, fractals can be divided into various classes, not necessarily disjointed, with the most common being random, deterministic, mass, surface, pore, fat and multifractals. Each class has its own imprint on the scattering intensity, and although one cannot uniquely identify the structure of a fractal based solely on SAS data, one can differentiate between various classes to which they belong. This has important practical applications in correlating their structural properties with physical ones. The article reviews SAS from several fractal models with an emphasis on describing which information can be extracted from each class, and how this can be performed experimentally. To illustrate this procedure and to validate the theoretical models, numerical simulations based on Monte Carlo methods are performed.

Fractal Analysis of the Fracture Evolution of Freeze-Thaw Damage to Asphalt Concrete

AC (asphalt concrete)-13, as the main material used in pavement construction, has been applied widely in seasonal frozen areas. In order to understand the fracture mechanism in the freeze-thaw (F-T) damage process, the mesoscale structure of AC-13 is obtained by computed tomography (CT). The fractal dimension of cracks is used as a damage evaluation index. Most previous studies have only focused on the fractal dimensions of whole cracks, while ignoring the fractal tectonic process and the self-similarity degree of a single fracture. Therefore, in this study, the intrinsic mechanism of fractures and damage were investigated. In addition, the critical crack stress and fracture toughness models of a single fracture in a freeze-thaw damage process are established for AC-13. The results indicate that in terms of the critical crack stress and fracture toughness, with the increase of F-T times, there is an obvious decreasing trend. The fracture model can effectively describe the fracture toughness calculated by ABAQUS in the process of freeze-thaw cycles.