Resonance condition model components

The term has two components a resonant contribution from the adsorbate vibrations x (incorporating the resonance condition (ffliR-m )) and a nonres-onant contribution Xnr from the surface itself. In many cases, the applied light frequencies are far from resonances of the surface, and the response of the surface is therefore usually modeled by a frequency-independent nonresonant susceptibility... 

Figure 2.6. The laboratory and rotating frame representations. In the laboratory frame the co-ordinate system is viewed as being static, whereas in the rotating frame it rotates at a rate equal to the applied rf frequency, vq. In this representation the motion of one component of the applied rf is frozen whereas the other is far from the resonance condition and may be ignored. This provides a simplified model for the description of pulsed NMR experiments.

Proteins crosslinked by formaldehyde are important in photography, the leather industry and in bio-medical sciences. Due to the complex structure of the gelatin molecules (consisting of approximately 20 Afferent kinds of amino acids) and the very low crosslink density, it is not possible to detect crosslink resonances under normal conditions. In order to overcome this problem a 13C enriched formaldehyde is used. By comparison with the chemical shifts of model crosslink compounds it is concluded that the predominant crosslink is formed between the lysine and arginine components in gelatin. A possible mechanism for the reaction between these two amino acid components and the formaldehyde has been proposed 154>. 

This can be verified by substituting the expression for v t) into the differential equation model and performing the indicated operations. The fact that v t) can be shown to have this form indicates that it is possible for this circuit to sustain oscillatory voltage and current waveforms indefinitely. When the parametric expression for v(t) is substituted into the differential equation model the value of co that is compatible with the solution of the equation is revealed to be ct) = l/.-/(LC). This is an example of the important fact that the frequency at which an electrical circuit exhibits resonance is determined by the physical value of its components. The remaining parameters ofv(t), K, and (p are determined by the initial energy stored in the circuit (i.e., the boundary conditions for the solution to the differential equation model of the behavior of the circuit s voltage). 

For enclosed bodies of water the probable maximum storm surge should be derived by using validated one or two dimensional mathematical models. The critical portion of the wind field, after being adjusted for any overland effects, is used as input for this analysis. The selection of coefficients and boundary conditions should be based on conservative assumptions. When one dimensional models are used, the transverse or crosswind set-up or a transverse seiche component is calculated separately and added to the longitudinal wind set-up. If the water body is sensitive to resonance, the transient responses should also be considered separately in a one dimensional model. If the water body is considered to be relatively insensitive to resonance, an analysis should be performed to substantiate this. The two dimensional transient mathematical models automatically take into account the transverse components and resonance effects. Components of the probable maximum still water levels are the longitudinal wind set-up, the transverse or cross-wind set-up and the reference water level. 

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