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Fractal dimensions in the Gromov–Hausdorff space [PDF]
Bulletin of the Polish Academy of Sciences Mathematics, 2023 In this paper, we first show that for all four non-negative real numbers, there exists a Cantor ultrametric space whose Hausdorff dimension, packing dimension, upper box dimension, and Assouad dimension are equal to given four numbers, respectively. Next, by constructing topological embeddings of an arbitrary compact metrizable space into the Gromov ...
Yoshito Ishiki
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Fractal memory structure in the spatiotemporal learning rule [PDF]
Frontiers in Computational NeuroscienceThe spatiotemporal learning rule (STLR) can reproduce synaptic plasticity in the hippocampus. Analysis of the synaptic weights in the network with the STLR is challenging. Consequently, our previous research only focused on the network's outputs. However,
Takemori Orima +4 more
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Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves [PDF]
Journal of Applied and Computational Mechanics, 2020 The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives.
Ji-Huan He
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Fractal Operators and Fractional-Order Mechanics of Bone
Fractal and Fractional, 2023 In recent years, the concept of physical fractal space has been abstracted from muscle/ligament fibers, nerve fibers and blood flows. In the physical fractal space, bio-fractal mechanics may be set up.
Zhimo Jian +3 more
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DYNAMICS IN FRACTAL SPACES [PDF]
Fractals, 2021 We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm. We use the mathematical concept of fiber bundle to characterize the multivalued nature of geodesic trajectories ...
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Fractal Description of Rock Fracture Networks Based on the Space Syntax Metric
Fractal and Fractional, 2022 Fractal characteristics and the fractal dimension are widely used in the description and characterization of rock fracture networks. They are important tools for coal mining, oil and gas transportation, and other engineering problems. However, due to the
Lili Sui +6 more
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Crystallization of space: Space-time fractals from fractal arithmetic [PDF]
Chaos, Solitons & Fractals, 2016 version accepted in Chaos, Solitons & ...
Aerts, Diederik +2 more
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Buildings, 2023 Land resources in cities are limited, and the cost of green space construction is high. Compared with increasing the amount of green space, maximizing the cooling effect of limited green space has important theoretical and practical significance.
Yilu Gong, Xueming Li, He Liu, Yu Li
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Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus
Entropy, 2023 This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry.
Airton Deppman +2 more
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Fractal Variational Theory for Chaplygin-He Gas in a Microgravity Condition [PDF]
Journal of Applied and Computational Mechanics, 2021 On the microgravity condition, gravity affects the motion of objects and the flow of fluids, and the continuum assumption is not valid, therefore, a fractal Chaplygin-He gas model is developed by a new fractal derivative in microgravity space.
KangLe Wang, ShaoWen Yao
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