Morphological characteristics of self-assembled aggregate textures using multifractal analysis: Interpretation of Multifractal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e611" altimg="si4.svg"><mml:mi>τ</mml:mi></mml:math>(q) Using Simulations

Sato, Yoshihito; Munakata, Fumio

doi:10.1016/j.physa.2022.127771

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…This is because when estimating the interaction energy (E int. ) between particle groups using multifractal analysis, [7,10,26,27] E int. between the SN particle groups [10] tends to increase with the addition amount; however, E int.…”

Section: Resultsmentioning

confidence: 99%

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Munakata,

Ogiya,

Sato

2024

Appl. Phys. A

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To investigate the relationship between histological properties and thermal conductivities of binary self-assembled/self-organized fractal materials fabricated by the mixed diffusion of filler particles, the particle group distribution of the filler particles was analyzed. Unlike conventional research on particle size distribution, we performed an analysis that focuses on interactions and connectivity between particles from the perspective of the Barabasi-Albert model. In three complex network systems of β-Si3N4 (SN)/austenitic stainless steel (SUS), SN/piezoelectric polyvinylidene fluoride (PVDF), and BaTiO3 (BT)/PVDF, the size distribution of secondary particles was a power-law distribution until the particle group grew relatively large. In the SN/SUS and SN/PVDF systems, a crossover phenomenon was observed in which the order distribution exhibited a power-law in the region where the particle group area was small, and as the particle group became larger, the order distribution became exponential distribution. On the other hand, the BT/PVDF system deviated from the power law distribution as the particle group area increased but did not exhibit an exponential distribution. The characteristics of the particle group distribution of these filler particles were closely related to thermal conductivity, indicating that the connection of particle groups was important. Furthermore, the relationship between the multifractal capacitance dimension, which is strongly correlated with the distance between the particle groups, and the total number of filler particle groups suggests that the texture of these composite material systems may have both small-world and scale-free properties. We also focused on the relationship between the multifractal and complex network properties of the three particle groups. As a result, a correlation was found between the slope γ, which reflects the characteristics of the power distribution, and the thermodynamic parameter α (corresponding to internal energy change) obtained from multifractals. In particular, the smaller the change in γ relative to the change in α, the more pronounced the bonding of particles and particle groups, while the larger change in γ suggested the dispersion of particle groups.

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Section: Resultsmentioning

confidence: 99%

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Munakata,

Ogiya,

Sato

2024

Appl. Phys. A

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“…At the spatial level, the spectra under positive moment orders correspond to central or high-density areas in a city, while those under negative moment orders correspond to marginal or low-density areas [ 17 ]. It has been observed that the spectra under positive moment orders exhibit similarities across different cities, while the spectra under negative moment orders display significant variations between cities [ 28 , 29 ]. This distinct growth pattern of spectra suggests that central areas represent stable zones for urban development, while marginal areas are the most dynamic regions for urban growth.…”

Section: Introductionmentioning

confidence: 99%

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra

Chen

2023

Entropy

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Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time, while during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectra alone. By integrating this index with multifractal spectra, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

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“…moment orders correspond to central or high-density areas in a city, which are stable areas for urban development and are similar across different cities; The spectrums under negative moment orders, on the other hand, correspond to marginal or low-density areas in a city, which are the most dynamic areas for urban growth and exhibit significant differences between cities [16,17]. At the temporal level, the multifractal parameters in the mathematical world are continuous and stable.…”

Section: Introductionmentioning

confidence: 99%

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectrums

Fu¹

2023

Preprint

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Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about cen-tral areas with relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas with more active growth. However, effectively utilizing mul-tifractal spectrums to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator, and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time. While during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectrums alone. By integrating this index with multifractal spectrums, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

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Morphological characteristics of self-assembled aggregate textures using multifractal analysis: Interpretation of Multifractal τ(q) Using Simulations

Cited by 6 publications

References 23 publications

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Thermal conductivities and complex network properties of fractal self-assembled/self-organized texture in binary composite materials

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectrums

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