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Research Highlights

Novel Equations Developed Across
Selected Publications

Concise, website-ready summaries of original analytical and predictive models

Six publications  |  One verified equation from each  |  Plain-language impact statement
Prepared 7 August 2026

Editorial note

The equations below were selected because they represent the principal model, extension or design rule developed in each paper. Standard background relations were deliberately excluded. Equation numbering follows the published article. For website use, the equations are presented in a compact linear form while retaining the symbols and scientific meaning of the source publication.

Publication 1
Unraveling the Liquid Gliding on Vibrating Solid–Liquid Interfaces with Dynamic Nanoslip Enactment
Payam et al., Nature Communications 13, 6608 (2022) https://doi.org/10.1038/s41467-022-34319-0
Equation (4)
\[\frac{b}{\delta} = \frac{(1+i)\!\left[Z^{L_s} - Z^{L_{ns}} - i\omega\varrho_f \ell_a\right]}{2\!\left[Z^{L_{ns}} + i\omega\varrho_f \ell_a\right]}\]
One-line summary. This dynamic-nanoslip model extracts the normalized slip length from QCM load impedance while explicitly including interfacial liquid inertia.
Key terms. b, slip length; δ, viscous penetration depth; ZLs and ZLns, load impedances with slip and no slip; ω, angular frequency; ϱf, fluid density; ℓa, interfacial inertia length.
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Publication 2
Ion-Induced Hydrophilic Switching Enables Nanostructure Morphology Control for Superior Nanoplasmonic Sensing
Bhalla et al., Journal Name, Year Add DOI link here
Equation (X)
\[\text{Add equation here}\]
One-line summary. Add one-line summary here.
Key terms. Add key terms here.
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Publication 3
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Authors, Journal, Year Add DOI
Equation (X)
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One-line summary. Add summary here.
Key terms. Add key terms here.
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Publication 4
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Authors, Journal, Year Add DOI
Equation (X)
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One-line summary. Add summary here.
Key terms. Add key terms here.
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Publication 5
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Authors, Journal, Year Add DOI
Equation (X)
\[\text{Add equation here}\]
One-line summary. Add summary here.
Key terms. Add key terms here.
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Publication 6
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Authors, Journal, Year Add DOI
Equation (X)
\[\text{Add equation here}\]
One-line summary. Add summary here.
Key terms. Add key terms here.