Structural Analysis of Phononic Crystals and Propagation of Elastic Waves in Cubic Solids in Fractal Dimensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12310%2F25%3A43910085" target="_blank" >RIV/60076658:12310/25:43910085 - isvavai.cz</a>
Result on the web
<a href="http://chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://link.springer.com/content/pdf/10.1007/s10659-025-10117-9.pdf?utm_source=clarivate&getft_integrator=clarivate" target="_blank" >http://chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://link.springer.com/content/pdf/10.1007/s10659-025-10117-9.pdf?utm_source=clarivate&getft_integrator=clarivate</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10659-025-10117-9" target="_blank" >10.1007/s10659-025-10117-9</a>

Result language
angličtina
Original language name
Structural Analysis of Phononic Crystals and Propagation of Elastic Waves in Cubic Solids in Fractal Dimensions
Original language description
We generalize the classical lattice dynamics model to a fractal setting by writing the basic equations of crystal dynamics according to a so-called LOSA model based on the "product-like fractal measure" concept. The fractal model is used to investigate the solutions to the dynamics of a Bravais lattice. The key role is played by so-called fractal elastic waves, where the mathematical solutions to wave equations have been obtained and analyzed, accounting for the underlying fractal geometry. By comparing the theoretical results with available experimental data graphically, we obtain a good match, say, for a diamond. Our numerical analysis estimates the fractal dimension of the order of D approximate to 2.52documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$D approx 2.52$end{document} which is in agreement with research studies on fractal phononic crystals. Attenuation of waves in cubic solids for small fractal dimensions has been observed. Such results justify the naming of this study as an estimation of the fractal dimension of phononic crystals.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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