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Two different approaches based on linear response theory are considered in this paper.
The open crack model based on linear response characteristics can identify the crack only at an advanced stage.
In addition, we develop a simplified model of the problem based on linear response theory that projects the dynamics into very few effective modes.
As discussed in Sect. 1, our approach presents some advantages when compared to other methods based on linear response theory [23 25], networks of stochastic binary neurons [26, 27], the linear noise approximation [28], the density functional approach [29], and large deviations theory [30 32].
Other EN Models such as backbone-enhanced elastic network model (BENM), β Gaussian Model (βGM), quantized elastic deformation model (QEDM), plastic network model (PNM), double-well elastic network model (DWNM) and models based on linear response theory, also to readers' great interest, are introduced in the supplementary material.
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The dynamics of the selective catalytic reduction (SCR) reaction over a commercial V2O5 WO3/TiO2 catalyst is investigated by concentration programmed surface reaction (CPSR), i.e. a modified transient response method based on linear temporal evolution of the reactant feed concentrations.
The wave-induced response was determined based on linear hydroelasticity, which involves linear potential theory for the fluid forces.
Calibration graphs were plotted based on linear regression analyses of the peak areas in response to concentrations of standards injected.
For continuous response variables, statistical analyses will be based on linear mixed models [ 79].
We processed the sensor responses, excluding the first exposure-purge cycles, by the pattern recognition technique based on Linear Discriminant Analysis (LDA 50.
The entire system is based on linear relationships between the individual and the state.
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