•Interparticle and intraparticle are the main pore types in the shale studied.•Clay minerals contribute greatly to the micro and meso pores.•Pores are mainly in 0.4–0.6, 1.7–4, and 10–20 nm ...ranges.•Fractal dimensions and its influencing factors are revealed.
Shales deposited in marine – continental transitional environments are well developed in the Upper Paleozoic in China with abundant gas resources. The pore structure and its controlling factors of the transitional shales may differ compared to marine and continental shales. Therefore, understanding them is of importance to the gas production behavior from transitional shales. In this work, a detailed experimental program combining rock composition analyses of X-ray diffraction (XRD), total organic carbon (TOC) analysis and Rock-Eval pyrolysis, and pore structure characterization by field emission scanning electron microscopy (FE-SEM), and low temperature nitrogen and carbon dioxide adsorption/desorption analysis were conducted on 16 continuously sampled shale cores from the east margin of the Ordos Basin, China. The results show that these transitional shales are rich in clay minerals with an average value of 58.2% (ranging from 47.7% to 85.0%), which is much higher than that in marine and lacustrine shales. The TOC contents are averaged at 1.3 wt%, and the shales are generally in mature to high mature stage (vitrinite reflectance (Ro) between 1.26% and 1.43%). Unlike the marine and lacustrine shales, the pores in the transitional shale are mainly occurred in clay minerals, and the organic matter pores are relatively poor and isolated. The pore shapes are dominantly intra-particle and inter-particle pores of slit-shaped as identified from the FE-SEM observations and the nitrogen adsorption/desorption curves. The meso (2–50 nm) and macro pore (generally of 50–300 nm) size distributions are unimodal to bimodal, and micropores (<2 nm) vary between 0.4 and 0.85 nm. The micropores and mesopores are abundant for all the shale samples, accounting for more than 90% of the total pore volume and specific surface area. The surface fractal dimension D1 and space structure fractal dimension D2 were obtained from the nitrogen adsorption data. The D1 values show no obvious relationship with clay minerals, TOC and quartz contents, which means that the pore surface irregularity is similar for all the samples. The D2 values show a positive relationship with clay mineral content, showing the clay minerals directly influencing the pore structure and pore diameters heterogeneity. For successful development of transitional shales gas, a further investigation on the clay mineral composition are necessary, with an emphasis on its influence on well drilling and hydraulic fracturing.
Superconductivity is ubiquitous as evidenced by the observation in many crystals including carrier-doped oxides and diamond. Amorphous solids are no exception. However, it remains to be discovered in ...quasicrystals, in which atoms are ordered over long distances but not in a periodically repeating arrangement. Here we report electrical resistivity, magnetization, and specific-heat measurements of Al-Zn-Mg quasicrystal, presenting convincing evidence for the emergence of bulk superconductivity at a very low transition temperature of Formula: see text K. We also find superconductivity in its approximant crystals, structures that are periodic, but that are very similar to quasicrystals. These observations demonstrate that the effective interaction between electrons remains attractive under variation of the atomic arrangement from periodic to quasiperiodic one. The discovery of the superconducting quasicrystal, in which the fractal geometry interplays with superconductivity, opens the door to a new type of superconductivity, fractal superconductivity.
Fractal dimension in tribology – an overview Lăpuşteanu, A; Agop, M; Paleu, V
IOP conference series. Materials Science and Engineering,
10/2022, Volume:
1262, Issue:
1
Journal Article
Peer reviewed
Open access
Friction and wear in tribological systems are phenomena that can be interpreted on a macroscopic scale. The emergence of micro and nano-sized systems requires the treatment of tribological phenomena ...through the concept of fractals. Thus, to perceive the tribological phenomena occurring in a macro-system, it is fundamental to think about them at the micro-scale and nano-scale, that center, for case, on the level of hardness and atomic composition. This article realizes a survey of the main concepts about treating the tribological issues in terms of fractals. It is clear that the continuous change of the micro and nano topography of the friction surfaces during the dynamic functioning of various mechanisms and the tribological processes taking place can be treated using the fractals and chaos theory. To this end, it is concluded that all the existing theories in tribology should be adapted to include fractal dimension and fractal roughness.
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•Water treated reduced the pore volume and specific surface area.•Compared with water treated, mesopore volume increased in ionic liquid treated coal.•After ionic liquid treated, the ...pore becomes rougher and more complex.•Ionic liquid treated can change pore structures and improve coalbed methane mining.
In order to study the variation of pore characteristics and fractal dimensions, coal samples are treated by ionic liquid with different concentrations. Then the N2 isotherm adsorption/desorption experiment is carried out. The results show that water treatment caused a decrease in total pore volume. While the total pore volume in ionic liquid treated coal samples are larger than that in water treated coal sample. In comparison with water treated coal sample, the volumes of micropores in ionic liquid treated coal samples are reduced and the specific surface areas are increased. However, the volume and specific surface area of the mesopores are opposite to those in the water treated coal sample. The fractal dimensions D1 and D2 are calculated. The results show D1 decreases in water treated coal sample while increases in ionic liquid treated coal samples. D2 decreases obviously in water treated coal sample. Besides, it is lower than that in ionic liquid treated coal samples. Those indicate single water treatment will decrease the surface roughness and structural complexity of pores, while ionic liquid treatment will increase it. This study is of great significance to enhance the CBM exploitation and reduce the water block effect.
We study dynamical systems generated by skew products:T:0,1)×R→0,1)×RT(x,y)=(bxmod1,γy+ϕ(x)) where integer b≥2, 0<γ<1 and ϕ is a real analytic Z-periodic function. We prove the following dichotomy ...for the SRB measure ω for T: Either the support of ω is a graph of real analytic function, or the dimension of ω is equal to min{2,1+logblog1/γ}. Furthermore, given b and ϕ, the former alternative only happens for finitely many γ unless ϕ is constant.
The absorption Ångström exponent (AAE) is an important aerosol
optical parameter used for aerosol characterization and apportionment
studies. The AAE of black carbon (BC) particles is widely accepted ...to be 1.0,
although observational estimates give quite a wide range of
0.6–1.3. With considerable uncertainties
related to observations, a numerical study is a powerful method, if not the
only one, to provide a better and more accurate understanding on BC AAE. This
study calculates BC AAE using realistic particle geometries based on fractal
aggregate and an accurate numerical optical model (namely the multiple-sphere
T-matrix method), and considers
bulk properties of an ensemble of BC particles following lognormal size
distributions. At odds with the expectations, BC AAE is not 1.0, even when BC
is assumed to have small sizes and a wavelength-independent refractive index.
With a wavelength-independent refractive index, the AAE of fresh BC is
approximately 1.05 and relatively insensitive to particle size. For BC with
geometric mean diameters larger than 0.12 µm, BC AAE becomes
smaller when BC particles are aged (compact structures or coated by other
non-absorptive materials). For coated BC, we prescribe the coating fraction
variation based on a laboratory study, where smaller BC cores are shown to
develop larger coating fractions than those of bigger BC cores. For both compact and coated BC, the AAE is highly
sensitive to particle size distribution, ranging from approximately 0.8 to
even over 1.4 with wavelength-independent refractive index. When the
refractive index is allowed to vary with wavelength, a feature with
observational backing, the BC AAE may show an even wider range. For different
BC morphologies, we derive simple empirical equations on BC AAE based on our
numerical results, which can serve as a guide for the response of BC AAE to
BC size and refractive index. Due to its complex influences, the effects of
BC geometry is better to be discussed at certain BC properties, i.e., known
size and refractive index.
•Bionic topology optimal fins considering natural convection and different objective functions.•Melting/solidification process simulation of different optimization results.•Bionic analysis from the ...morphology and fractal dimension.•Non-linear dynamic analysis in melting process.
The latent heat storage (LHS) technique has been widely applied in various thermal energy conversion and management fields. However, LHS device suffers from very slow heat storage/release process. Here, a bionic topology optimization method is proposed to enhance thermal storage/release performances considering different objective functions and heat transfer mechanisms. Taking minimized capacity dissipation as the optimization function and considering natural convection, the optimized fin structure can reduce the melting and solidification time by 93% and 80%, respectively. The underlying mechanism can be attributed to better synergy between flow and heat transfer. Moreover, the fractal dimension of optimized fins is similar to the leaf structure. This research provides a new route for the design of high performance LHS devices, and promotes the application of bionics in thermal energy storage fields.
In this work, we analyze how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which ...actually behave as fractals, allows for recurrent nonperturbative calculation of any vertex. Some general properties are indeed independent of the perturbative order, what simplifies the nonperturbative calculations. We show that for sufficiently high perturbative orders a statistical approach can be used, the nonextensive statistics is obtained, and the Tsallis index, q, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, where q can be calculated, resulting in a good agreement with the value obtained experimentally. We discuss how this approach allows us to understand some intriguing experimental findings in high energy collisions, as the behavior of multiplicity against collision energy, long-tail distributions, and the fractal dimension observed in intermittency analysis.
Single Point Incremental Sheet Forming (SPISF) is a well-known flexible alternative to conventional generative manufacturing processes. In SPISF, the geometry to be formed is fragmented into series ...of 2D slices and the plastic deformation is achieved through layer by layer movement of a Numerically Controlled (NC), hemispherical or ball end forming tool. The whole plastic deformation is the sum of all localized strains developed during each increment. Spiral, constant z incremental toolpaths, and their variants are common conventional toolpaths for SPISF. Several researchers have investigated these toolpaths extensively. Fractal Geometry Based Incremental Toolpath (FGBIT) is a recently developed toolpath for SPISF that improves the process formability and stress distribution. Unlike conventional toolpaths, FGBIT deforms the base region of the formed geometry which induces work hardening and residual stresses into the work piece. This may lead to the forming of high strength components. The residual stress distribution over the base region of the formed component (square cup) has been investigated in this study.
Further, a comparison based on residual stress distribution between FGBIT and conventional incremental toolpaths is presented. Residual stresses have been measured by using nanoindentation technique. Pile up generation near the periphery of the indent is investigated for conventional and FGBIT based toolpaths. It has been observed from the experimental results that, the strength of the formed component increases due to induced compressive surface residual stresses while using FGBIT hence, metal components with high fatigue life and better strength-to-weight ratio can be formed.
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