Non-resonant domain

The analytic part is the following. In the domain Q of the actions we isolate a non-resonance domain V, characterized by a resonance module M, a real constant a and an integer N, where the following inequality holds true ... 

The conclusion is illustrated in Figure 4 until the orbit remains in the non-resonance domain V it lies in a small neighborhood of the plane of fast drift nx(po)- However, this is not enough to assure the long-time preservation of the actions, because the analytic theory does not assure that the orbit will be confined for a long time in V. The question is what happens if the orbit leaves the non-resonance domain ... 

Figure 4 The local dynamics in a non-resonance domain. The orbit lies in a neighborhood of the plane of fast drift.

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

While in the frequency domain all the spectroscopic information regarding vibrational frequencies and relaxation processes is obtained from the positions and widths of the Raman resonances, in the time domain this information is obtained from coherent oscillations and the decay of the time-dependent CARS signal, respectively. In principle, time- and frequency-domain experiments are related to each other by Fourier transform and carry the same information. However, in contrast to the driven motion of molecular vibrations in frequency-multiplexed CARS detection, time-resolved CARS allows recording the Raman free induction decay (RFID) with the decay time T2, i.e., the free evolution of the molecular system is observed. While the non-resonant contribution dephases instantaneously, the resonant contribution of RFID decays within hundreds of femtoseconds in the condensed phase. Time-resolved CARS with femtosecond excitation, therefore, allows the separation of nonresonant and vibrationally resonant signals [151]. 

The domain of oscillating orbits of the second type corresponds to the non-resonant orbits (Arnold tori) that satisfy ... 

ACCORD-ADEQUATE spectrum using a 500-MHz spectrometer equipped with a 5-mm cryoprobe. The data were acquired as 180 hypercomplex points in the second frequency domain using 256 transients/fi increment. The broad 14-vinyl methylene resonance was located in the structure based on correlations in the ACCORD-ADEQUATE spectrum from H14 to C13 and from H12 to both Cll and C13. The C18 aromatic methine resonance afforded ADEQUATE correlations to the flanking C17 and C19 non-protonated carbons and, finally, the C23 methine provided a correlation to the C22 non-protonated carbon. 

Most methods assume an exponential decay for the resonances in the time domain giving rise to Lorentzian lineshapes in the frequency domain. This assumption is only valid for ideal experimental conditions. Under real experimental circumstances multi-exponential relaxation, imperfect shimming, susceptibility variations and residual eddy current usually lead to non-ideal... 

Sets of truncated and non-truncated ID FIDs have been prepared to explore the advantage,s and limitations of LP in the following Check its. To speed up the calculations, the number of time domain data points and the number of resonance lines in the corresponding spectra have been deliberately reduced to a small number. Suitable 2D data sets have also been prepared for use with 2D WIN-NMR (see Table 5.3). 

Since enhanced electromagnetic fields in proximity to metal nanoparticles are the basis for the increased system absorption, various computational methods are available to predict the extent of the net system absorption and therefore potentially model the relative increase in singlet oxygen generation from photosensitizers. " In comparison to traditional Mie theory, more accurate computational methods, such as discrete dipole approximation (DDA/ or finite difference time domain (FDTD) methods, are often implemented to more accurately approximate field distributions for larger particles with quadruple plasmon resonances, plasmon frequencies of silver nanoparticles, or non-spherical nanoparticles in complex media or arrangements. ... 

Wigger, M. Eyler, J.R. Benner, S.A. Li, W. Marshall, A.G. Fourier Transform-Ion Cyclotron Resonance Mass Spectrometric Resolution, Identification, and Screening of Non-Covalent Complexes of Hck Src Homology 2 Domain Receptor and Ligands from a 324-Member Peptide Combinatorial Library, J. Am. Soc. Mass Spectrom. 13, 1162-1169 (2002). 

The field of electron spin resonance comprises a range of techniques. The types of experiment that can be carried out are either linear or non-linear, continuous wave (CW) or time-domain. 

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