Advanced time domain

Rizos, D.C. 1993. An Advanced Time Domain Boundary Element Method for General 3-D Elastodynamic Problems. Ph.D. Dissertation, University of South Carolina. 

Many of the fiindamental physical and chemical processes at surfaces and interfaces occur on extremely fast time scales. For example, atomic and molecular motions take place on time scales as short as 100 fs, while surface electronic states may have lifetimes as short as 10 fs. With the dramatic recent advances in laser tecluiology, however, such time scales have become increasingly accessible. Surface nonlinear optics provides an attractive approach to capture such events directly in the time domain. Some examples of application of the method include probing the dynamics of melting on the time scale of phonon vibrations [82], photoisomerization of molecules [88], molecular dynamics of adsorbates [89, 90], interfacial solvent dynamics [91], transient band-flattening in semiconductors [92] and laser-induced desorption [93]. A review article discussing such time-resolved studies in metals can be found in... 

In the one-dimensional NMR experiments discussed earlier, the FID was recorded immediately after the pulse, and the only time domain involved (ij) was the one in which the FID was obtained. If, however, the signal is not recorded immediately after the pulse but a certain time interval (time interval (the evolution period) the nuclei can be made to interact with each other in various ways, depending on the pulse sequences applied. Introduction of this second dimension in NMR spectroscopy, triggered byjeener s original experiment, has resulted in tremendous advances in NMR spectroscopy and in the development of a multitude of powerful NMR techniques for structure elucidation of complex organic molecules. 

From the last example, we may see why the primary mathematical tools in modem control are based on linear system theories and time domain analysis. Part of the confusion in learning these more advanced techniques is that the umbilical cord to Laplace transform is not entirely severed, and we need to appreciate the link between the two approaches. On the bright side, if we can convert a state space model to transfer function form, we can still make use of classical control techniques. A couple of examples in Chapter 9 will illustrate how classical and state space techniques can work together. 

The fourth chapter by James McGuinty et al. describes the more advanced forms of time-domain FLIM. While not immediately available on commercial instruments this chapter should give the reader an idea what the current state-of-the-art is in terms of FLIM instrumentation, and perhaps what to expect on future commercial instruments. Real-time FLIM, combined FLIM-spectral imaging, hyperspectral FLIM-imaging, combined lifetime-anisotropy imaging and some of their applications are covered here. 

K. L. Shlager, and J. B. Schneider, A survey of the finite-difference time domain literature, in A. Taflove (Ed,), Advances in computational electrodynamics the finite difference time domain method (Artech House, 1998), pp. 1- 62. 

G. Guthausen, H. Todt, W. Burk, D. Schmalbein, and A. Kamlowski, Time-domain NMR in quality control more advanced methods, in Modem Magnetic Resonance, G.A. Webb (ed.). Springer, Netherlands, 2006. 

Recent advances in ultrashort laser technology has enabled us to investigate dynamics of molecules in a time domain, and furthermore, the success of a theoretical interpretation of the results of time-domain experiments by a moving wavepacket on a potential energy surface (PES) impressively demonstrated the importance of time-domain experiments [1]. On the other hand, it is well-known that a spectrum in a frequency domain and an autocorrelation function in the time domain can be transferred with each other via a Fourier transformation [2]. Therefore, it can be said that the spectrum... 

The best approach, adapted from an earlier proposal by Tomlinson and Hill (19), is to specify the desired frequency-domain excitation profile in advance, and then syntheize its corresponding time-domain representation directly via inverse Fourier transformation. The result of the Tomlinson and Hill procedure is shown at the bottom of Figure 2, in which a perfectly flat, perfectly selective frequency-domain excitation is produced by the time-domain waveform obtained via inverse Fourier transformation of the desired spectrum. 

As has been described, CD is one of the few spectroscopic techniques sensitive to the structural parameters that define and guide the three-dimensional shape of a biologically active entity. This important structural information, obtained on a time-resolved basis in the same time domain as the biological event under study, is an extremely important advance that will have wide application in biophysical studies of proteins, polypeptides and other biologically significant species. 

Recent advances, for example, replacement of the Pockels cell with a PEM system, has provided an improvement in the experimental SNR of an order-of-magnitude [44]. Further, the authors suggest that with their experimental approach, the picosecond laser system now in use could be replaced by one operating with femtosecond pulses. If successful, this would allow extension of CD measurements into a time domain where the initial structural changes which determine the outcome of a sequence of complicated events can be probed. 

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