Modified Catalysts and Their Fractal Properties

Obtaining high-area catalysts is in demand in heterogeneous catalysis as it influences the ratio between the number of active surface sites and the number of total surface sites of the catalysts. From this point of view, fractal theory seems to be a suitable instrument to characterize catalysts’ surfaces. Moreover, catalysts with higher fractal dimensions will perform better in catalytic reactions. Modifying catalysts to increase their fractal dimension is a constant concern in heterogeneous catalysis. In this paper, scientific results related to oxide catalysts, such as lanthanum cobaltites and ferrites with perovskite structure, and nanoparticle catalysts (such as Pt, Rh, Pt-Cu, etc.) will be reviewed, emphasizing their fractal properties and the influence of their modification on both fractal and catalytic properties. Some of the methods used to compute the fractal dimension of the catalysts (micrograph fractal analysis and the adsorption isotherm method) and the computed fractal dimensions will be presented and discussed.

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The application of aromatic probe molecules in the surface acid properties study of modified alumina catalysts by EPR spectroscopy

Российский химический журнал ◽

10.6060/rcj.2018621-2.10 ◽

2019 ◽

Vol 62 (1-2) ◽

pp. 124-130

Author(s):

V.L . Yurpalov ◽

V.A. Drozdov ◽

A.A. Nepomnyashchy ◽

E.A. Buluchevskiy

Keyword(s):

Epr Spectroscopy ◽

Spin Probe ◽

Active Surface ◽

Point Of View ◽

Probe Molecules ◽

Modified Alumina ◽

Acid Properties ◽

Surface Sites ◽

Active Surface Sites ◽

Alumina Catalysts

Current paper systematizes the work devoted to the application of the aromatic spin probe EPR spectroscopy for the study of heterogeneous alumina catalysts, as well as supplemented by new researches carried out in IHP SB RAS. The advances of the method and the mechanism of probe molecules interaction with active surface sites and their nature are considered. There are noted some contradictions in views on mechanisms, nevertheless the modern point of view tends to participate BAS in the ionization of aromatic probe molecules.

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Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

Scientific Reports ◽

10.1038/s41598-021-92277-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Bing Sun ◽

Shun Liu ◽

Sheng Zeng ◽

Shanyong Wang ◽

Shaoping Wang

Keyword(s):

Fractal Dimension ◽

Crack Propagation ◽

Crack Growth ◽

Impact Test ◽

Fractal Theory ◽

Dynamic Change ◽

Fractal Dimensions ◽

Peak Stress ◽

Dynamic Mechanical Properties ◽

Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

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Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

MATEC Web of Conferences ◽

10.1051/matecconf/201815901006 ◽

2018 ◽

Vol 159 ◽

pp. 01006

Author(s):

Bagus Hario Setiadji ◽

Supriyono ◽

Djoko Purwanto

Keyword(s):

Fractal Dimension ◽

Fractal Theory ◽

Asphalt Mixture ◽

Fractal Dimensions ◽

Calculation Model ◽

Careful Consideration ◽

Upper And Lower Bounds ◽

Aggregate Gradation ◽

Fractal Characteristic ◽

Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

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FRACTALS, NATURAL DISASTERS AND ECOLOGICAL PROBLEMS OF MALDIVES

10.32006/eeep.2018.2.1825 ◽

2018 ◽

pp. 18-25

Author(s):

Boyko Ranguelov ◽

Fathimath Shadiya

Keyword(s):

Local Population ◽

Fractal Dimensions ◽

Point Of View ◽

Negative Consequences ◽

Fractal Nature ◽

Fractal Properties ◽

Level Increase ◽

Ocean Level ◽

Ecological Problems ◽

Negative Phenomena

A new idea about the fractal nature of Maldives archipelago is under investigation. The origin of this famous Maldivian islands’ country is still questionable from geodynamic point of view. The present study is focused to the assessment of the fractal properties and the coefficients of the nonlinearity (fractal dimensions) of the areal spatial distribution of the major atolls of the Maldives. This is the most vulnerable area in the world from point of view of the global warming and the possible negative consequences to the country and population from the ocean level increase. From another side the natural hazards (tsunamis, storms, etc.) are common negative phenomena attacking the country. The strongly developed tourism – more than 30% of the GDP and the increased urbanization is another factor creating ecological problems to the local population. The relationships between the fractal nature and the possible ways to avoid the pollution are also in the focus of this research.

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Application of Fractal Theory in Aggregate Gradation Research

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.204-208.1923 ◽

2012 ◽

Vol 204-208 ◽

pp. 1923-1928

Author(s):

Bo Tan ◽

Rui Hua Yang ◽

Yan Ting Lai

Keyword(s):

Fractal Dimension ◽

Fractal Theory ◽

Asphalt Mixture ◽

Fractal Dimensions ◽

Aggregate Gradation ◽

Structure Characteristics ◽

Aggregate Distribution ◽

Dimension Formula ◽

Mass Fractal ◽

Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

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Roughness and fractality of fracture surfaces as indicators of mechanical quantities of porous solids

Open Physics ◽

10.2478/s11534-011-0061-0 ◽

2011 ◽

Vol 9 (6) ◽

Cited By ~ 2

Author(s):

Tomáš Ficker ◽

Dalibor Martišek

Keyword(s):

Mechanical Properties ◽

Fractal Dimension ◽

Fractal Dimensions ◽

Point Of View ◽

Porous Solids ◽

Surface Parameter ◽

Cement Pastes ◽

Fracture Surfaces ◽

Profile Parameter ◽

3D Profile

AbstractThe 3D profile surface parameter H q and fractal dimension D were tested as indicators of mechanical properties inferred from fracture surfaces of porous solids. High porous hydrated cement pastes were used as prototypes of porous materials. Both the profile parameter H q and the fractal dimension D showed capability to assess compressive strength from the fracture surfaces of hydrated pastes. From a practical point of view the 3D profile parameter H q seems to be more convenient as an indicator of mechanical properties, as its values suffer much less from statistical scatter than those of fractal dimensions.

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Influence of the nature of active surface sites of highly disperse oxides on adsorption of heavy metal ions

Surface Chemistry in Biomedical and Environmental Science ◽

10.1007/1-4020-4741-x_39 ◽

2006 ◽

pp. 429-438

Author(s):

V. I. Zarko ◽

V. M. Gun'ko ◽

L. S. Andriyko ◽

E. V. Goncharuk ◽

M. Matysek ◽

...

Keyword(s):

Heavy Metal ◽

Metal Ions ◽

Heavy Metal Ions ◽

Active Surface ◽

Surface Sites ◽

Active Surface Sites

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Etching-Assisted Route to Heterophase Au Nanowires with Multiple Types of Active Surface Sites for Silane Oxidation

Nano Letters ◽

10.1021/acs.nanolett.9b02532 ◽

2019 ◽

Vol 19 (9) ◽

pp. 6363-6369 ◽

Cited By ~ 4

Author(s):

Chaoqi Wang ◽

Xiang Li ◽

Lei Jin ◽

Peng-Han Lu ◽

Catherine Dejoie ◽

...

Keyword(s):

Active Surface ◽

Surface Sites ◽

Active Surface Sites ◽

Au Nanowires

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Complexity-Based Analysis of the Relation between Human Muscle Reaction and Walking Path

Fluctuation and Noise Letters ◽

10.1142/s021947752050025x ◽

2020 ◽

Vol 19 (03) ◽

pp. 2050025 ◽

Cited By ~ 12

Author(s):

Shahul Mujib Kamal ◽

Sue Sim ◽

Rui Tee ◽

Visvamba Nathan ◽

Hamidreza Namazi

Keyword(s):

Fractal Dimension ◽

Statistical Analysis ◽

Fractal Theory ◽

Contact Point ◽

Fractal Dimensions ◽

Human Muscle ◽

Physiological Signals ◽

Eeg Signal ◽

Leg Muscles ◽

Emg Signal

Legs are the contact point of humans during walking. In fact, leg muscles react when we walk in different conditions (such as different speeds and paths). In this research, we analyze how walking path affects leg muscles’ reaction. In fact, we investigate how the complexity of muscle reaction is related to the complexity of path of movement. For this purpose, we employ fractal theory. In the experiment, subjects walk on different paths that have different fractal dimensions and then we calculate the fractal dimension of Electromyography (EMG) signals obtained from both legs. The result of our analysis showed that the complexity of EMG signal increases with the increment of complexity of path of movement. The conducted statistical analysis also supported the result of analysis. The method of analysis used in this research can be further applied to find the relation between complexity of path of movement and other physiological signals of humans such as respiration and Electroencephalography (EEG) signal.

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