Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide

C. Ganesa Moorthy; G. Udhaya Sankar

doi:10.54559/amesia.1878486

Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide

Abstract

Evaluation of Hausdorff Besicovitch Dimension (𝐷𝐻𝐵) provides a technique for evaluating structural density and space filling behavior in complex nanostructured systems where conventional Euclidean descriptors fail. In the present work, 𝐷𝐻𝐵 analysis is employed to investigate the morphological complexity and structural density of copper oxide (CuO) nanotubes and nanostructures using transmission electron microscopy (TEM) images. A MATLAB based box-counting algorithm was implemented to extract scaling behavior across multiple length scales, enabling the correlation between image derived mass distribution and geometric occupancy. TEM observations reveal a wide range of morphologies, including isolated nanotubes, dendritic nanostructures, aggregated clusters, and near space filling networks. The calculated 𝐷𝐻𝐵 values span from ~1.73, a characteristic of diffusion limited aggregation and highly porous architectures, to values approaching 2.0, an indication of dense, compact, and nearly space filling structures. Structural density maps derived from distance transform analysis further corroborate 𝐷𝐻𝐵 results by variations in local clustering and thickness of nanotubes and nanostructures.

Keywords

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Details

Primary Language

English

Subjects

Experimental Mathematics, Pure Mathematics (Other), Material Design and Behaviors

Journal Section

Research Article

Authors

C. Ganesa Moorthy ^*
0000-0003-3119-7531
India

G. Udhaya Sankar
0000-0002-1416-9590
India

Publication Date

June 30, 2026

Submission Date

January 31, 2026

Acceptance Date

May 25, 2026

Published in Issue

Year 2026 Volume: 7 Number: 1

DOI

https://doi.org/10.54559/amesia.1878486

IZ

https://izlik.org/JA66SX95BF

Cite

RIS / Bibtex

APA

Moorthy, C. G., & Sankar, G. U. (2026). Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide. Amesia, 7(1), 11-24. https://doi.org/10.54559/amesia.1878486

AMA

1.Moorthy CG, Sankar GU. Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide. Amesia. 2026;7(1):11-24. doi:10.54559/amesia.1878486

Chicago

Moorthy, C. Ganesa, and G. Udhaya Sankar. 2026. “Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide”. Amesia 7 (1): 11-24. https://doi.org/10.54559/amesia.1878486.

EndNote

Moorthy CG, Sankar GU (June 1, 2026) Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide. Amesia 7 1 11–24.

IEEE

[1]C. G. Moorthy and G. U. Sankar, “Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide”, Amesia, vol. 7, no. 1, pp. 11–24, June 2026, doi: 10.54559/amesia.1878486.

ISNAD

Moorthy, C. Ganesa - Sankar, G. Udhaya. “Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide”. Amesia 7/1 (June 1, 2026): 11-24. https://doi.org/10.54559/amesia.1878486.

JAMA

1.Moorthy CG, Sankar GU. Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide. Amesia. 2026;7:11–24.

MLA

Moorthy, C. Ganesa, and G. Udhaya Sankar. “Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide”. Amesia, vol. 7, no. 1, June 2026, pp. 11-24, doi:10.54559/amesia.1878486.

Vancouver

1.C. Ganesa Moorthy, G. Udhaya Sankar. Hausdorff Besicovitch Dimension Technique to Determine Structural Density of Nanotubes and Nanostructures of Copper Oxide. Amesia. 2026 Jun. 1;7(1):11-24. doi:10.54559/amesia.1878486

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