The growth mechanism of fractal islands on a two-dimensional nonlattice substrate with periodic boundary conditions has been investigated by using Monte Carlo technique. Results show that the fractal dimension of the final
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The growth mechanism of fractal islands on a two-dimensional nonlattice substrate with periodic boundary conditions has been investigated by using Monte Carlo technique. Results show that the fractal dimension df
of the final
ramified islands is almost independent of the diffusion step length, mobility and rigid rotation of the islands. The
characteristics of the size distribution of the discs in an island do not change the dimension df
of the island. However,
we find that df
increases linearly with the surface coverage ρ of the system and its slope decreases with the increase of
the mean diameter of the discs.
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Certainly, when it comes to academic writing, integrity is paramount. Selecting a meaningful topic is crucial; it should align with one's interests, contribute to existing knowledge, and address a relevant research gap. Establishing a logical structure involves outlining key arguments, organizing evidence coherently, and ensuring a clear progression of ideas. By upholding these principles, academic writing not only fosters intellectual growth but also maintains the integrity of scholarly discourse.
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Certainly, when it comes to academic writing, integrity is paramount. Selecting a meaningful topic is crucial; it should align with one's interests, contribute to existing knowledge, and address a relevant research gap. Establishing a logical structure involves outlining key arguments, organizing evidence coherently, and ensuring a clear progression of ideas. By upholding these principles, academic writing not only fosters intellectual growth but also maintains the integrity of scholarly discourse.
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The key findings of the study are that the fractal dimension (df) of the final ramified islands is largely unaffected by factors such as the diffusion step length, mobility, and rigid rotation of the islands. Furthermore, the characteristics of the size distribution of the discs within an island do not alter the fractal dimension (df) of the island. However, a significant observation is that df increases linearly with the surface coverage (ρ) of the system, and the slope of this increase decreases with the mean diameter of the discs.
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The study found that the fractal dimension (df) of the islands increases linearly with the surface coverage (ρ) of the system. This indicates that as more discs are placed on the substrate, the complexity or fine structure of the islands increases. Additionally, the slope of this increase decreases with the increase in the mean diameter of the discs. This means that when larger discs are used, even with increasing surface coverage, the fractal dimension (df) of the islands grows relatively slower.
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Urban development must always focus on social equity, ensuring equal distribution of public service facilities in urban planning and construction, and ensuring that all sectors of society can enjoy basic public services, such as parks, libraries, medical institutions, and other public facilities. It is necessary to reasonably layout and cover different areas of the city, facilitate residents in various communities, and strengthen care and protection for vulnerable groups. More preferential and supportive policies should be given to them to ensure that they are not marginalized in urban development.
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