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We use a Hamiltonian of quantum harmonic oscillator H m = ℏ ω m b + b with the frequency ω m and the annihilation operator b of the resonator mode to describe the eigenmode.
In addition, the model was utilized in a predictive mode to describe the performance of a FTCMR employing another membrane from the same batch and catalytically activated under the same procedure, but operating under different operating conditions (0% stage-cut).
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Much of the literature of friction-induced vibration focusses on highly simplified models that may include three or fewer modes to describe the independent subsystems.
Then the Green matrix is constructed analytically as a linear combination of normal modes to describe the response of a plate and an acoustic medium to the point loading by a force or a moment.
By using the method of assumed modes to describe the deformations of the three sub-layer beams, with the longitudinal shrinking caused by transverse deformation included and all the high-order terms retained, the high-order approximate coupling (HOAC) dynamic equations of a hub-ACLD beam system are derived.
The key enablers are the extension of the POD basis functions to the pressure data, the use of calibration methods for the POD ROM and the addition in the POD expansion of several non-equilibrium modes to describe various operating conditions.
We proposed a multi-mode absorption model to describe the effect of melamine absorption on the LSPR peak shifts of Ag-decorated SiO2NPs.
We also develop a two-mode coarse grained model to describe diffusion and reaction accurately in such systems and develop criteria under which the pore and crystallite scale gradients can be neglected.
The pseudo-ductile behaviour is explained by adapting the Damage Mode Map to describe the failure process of interlaminated hybrid specimens with different low elongation material strength.
But nostalgia aside, those battle lines were real and Nilsen quickly transformed into warrior mode order to describe the landscape when he first joined Sega.
Meanwhile, the number of s-modes required to describe the total sound power radiation is found to be the same as that of a-modes.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com