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Article

Power Spectral Density Analysis of Nanowire-Anchored Fluctuating Microbead Reveals a Double Lorentzian Distribution

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Department of Biophysics, Faculty of Science, P. J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
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Institute of Experimental Physics SAS, Department of Biophysics, Watsonova 47, 040 01 Košice, Slovakia
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Department of Chemistry, Biochemistry and Biophysics, University of Veterinary Medicine and Pharmacy, Komenského 73, 041 81 Košice, Slovakia
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Faculty of Science and Informatics, University of Szeged, Dugonics Square 13, 6720 Szeged, Hungary
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Biological Research Centre, Institute of Biophysics, Eötvös Loránd Research Network (ELKH), Temesvári krt. 62, 6726 Szeged, Hungary
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Center for Interdisciplinary Biosciences, Technology and Innovation Park, P. J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
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Author to whom correspondence should be addressed.
Academic Editors: Maria Luminita Scutaru and Junseok Kim
Mathematics 2021, 9(15), 1748; https://doi.org/10.3390/math9151748
Received: 26 May 2021 / Revised: 9 July 2021 / Accepted: 21 July 2021 / Published: 24 July 2021
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems)
In this work, we investigate the properties of a stochastic model, in which two coupled degrees of freedom are subordinated to viscous, elastic, and also additive random forces. Our model, which builds on previous progress in Brownian motion theory, is designed to describe water-immersed microparticles connected to a cantilever nanowire prepared by polymerization using two-photon direct laser writing (TPP-DLW). The model focuses on insights into nanowires exhibiting viscoelastic behavior, which defines the specific conditions of the microbead. The nanowire bending is described by a three-parameter linear model. The theoretical model is studied from the point of view of the power spectrum density of Brownian fluctuations. Our approach also focuses on the potential energy equipartition, which determines random forcing parametrization. Analytical calculations are provided that result in a double-Lorentzian power density spectrum with two corner frequencies. The proposed model explained our preliminary experimental findings as a result of the use of regression analysis. Furthermore, an a posteriori form of regression efficiency evaluation was designed and applied to three typical spectral regions. The agreement of respective moments obtained by integration of regressed dependences as well as by summing experimental data was confirmed. View Full-Text
Keywords: nanowire cantilever; stochastic model; double Lorentzian spectrum nanowire cantilever; stochastic model; double Lorentzian spectrum
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MDPI and ACS Style

Bánó, G.; Kubacková, J.; Hovan, A.; Strejčková, A.; Iványi, G.T.; Vizsnyiczai, G.; Kelemen, L.; Žoldák, G.; Tomori, Z.; Horvath, D. Power Spectral Density Analysis of Nanowire-Anchored Fluctuating Microbead Reveals a Double Lorentzian Distribution. Mathematics 2021, 9, 1748. https://doi.org/10.3390/math9151748

AMA Style

Bánó G, Kubacková J, Hovan A, Strejčková A, Iványi GT, Vizsnyiczai G, Kelemen L, Žoldák G, Tomori Z, Horvath D. Power Spectral Density Analysis of Nanowire-Anchored Fluctuating Microbead Reveals a Double Lorentzian Distribution. Mathematics. 2021; 9(15):1748. https://doi.org/10.3390/math9151748

Chicago/Turabian Style

Bánó, Gregor, Jana Kubacková, Andrej Hovan, Alena Strejčková, Gergely T. Iványi, Gaszton Vizsnyiczai, Lóránd Kelemen, Gabriel Žoldák, Zoltán Tomori, and Denis Horvath. 2021. "Power Spectral Density Analysis of Nanowire-Anchored Fluctuating Microbead Reveals a Double Lorentzian Distribution" Mathematics 9, no. 15: 1748. https://doi.org/10.3390/math9151748

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