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The lengths of both (8,0) and (5,5) BNNTs after the relaxation by the DFT method are defined as the referenced lengths at strain of 0, where the axial stresses are 0 after calculation by Equation 1.
The second type of phase jump when is a real phase jump, which also occurs in the calculation by equation (20).
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Solid black lines are calculations by Equation 7; red circles mark the simulated points.
The frequency is shown within the current range of the stable vortex steady-state orbit, Jc 1 < J < Jc 2. Solid black lines are calculations by Equation 5; red squares mark the simulated points.
We estimated u(0) after the pulse as u(0) = 0.1 and plotted the solid lines without any fitting except using the simulated value of the critical current Jc 1. Overall agreement of the calculations by Equation 8 and simulations is quite good, especially for large times t ≥ 3τ+, although the calculated relaxation time τ+ is smaller than the simulated one due to overestimation of ω 0 ′ within TVA.
The deformation distribution profiles of ε III (z) used for XDP calculation were defined by Equation 3 and are shown in the inset.
The normal approximation used in the calculations is given by equation 3.2.7 of Lawless [ 80].
At the point where the phase angle is zero (or close to zero), the impedance is pure ohmic and the resistance of the membrane can directly be determined and used for the ionic conductivity calculation, by the following equation (2): σ = L / Rb.A (2).
For confirmation of validation of this calculation, the τSiNW obtained by Equation 5 was compared to the simulation results of PC1D in Figure 7.
Ignoring the calculation deviations generated by Equations 4, 5, and 6 and tube size, the uncertainty of these experimental results can be expressed as follows: (10).
Ignoring the calculation deviations generated by Equations 4, 5. and 6, the uncertainty of these experimental results can be expressed as follows: (11).
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