Statistical analysis, time-resolved

The instrument has been evaluated by Luster, Whitman, and Fauth (Ref 20). They selected atomized Al, AP and NGu as materials for study that would be representative of proplnt ingredients. They found that only 2000 particles could be counted in 2 hours, a time arbitrarily chosen as feasible for control work. This number is not considered sufficient, as 18,000 particles are required for a 95% confidence level. Statistical analysis of results obtained for AP was impossible because of discrepancies In the data resulting from crystal growth and particle agglomeration. The sample of NGu could not be handled by the instrument because it consisted of a mixt of needles and chunky particles. They concluded that for dimensionally stable materials such as Al or carborundum, excellent agreement was found with other methods such as the Micromerograph or visual microscopic count. But because of the properties peculiar to AP and NGu, the Flying Spot Particle Resolver was not believed suitable for process control of these materials... 

Besides improving classical electrochemical methods, newly employed techniques such as second harmonic-generation and time-resolved fluorometry, with either control of the potential drop across the interface or fluctuation analysis, are promising in this respect. Also indispensable are further advances in molecular dynamics and statistical-mechanical treatments of structure and charge transfer at the ITIES. 

There are several analytical procedures available for derivation of relaxation information from time-resolved anisotropy experiments, the merits of which have been discussed at length elsewhere [25,112,114]. The salient points are covered here direct analysis of r(t) using a function such as Equation 2.31 is the most straightforward method but can become particularly problematic if the motion under study is comparable to the width of the excitation pulse [25,112,114]. Furthermore, as r(t) can suffer contamination from the polarizing effects of stray excitation from the source, particularly in weakly fluorescent samples, other methods are required to overcome such artifacts. Impulse reconvolution [115] allows mathematical removal of the instrumental pulse from the experimental data and involves an analysis of s(t) by a statistically adequate model function (e.g., Eq. 2.8). The best fit to s(t) is... 

Fluorescence recovery after photobleaching (FRAP) and the measurement of the fluorescence resonance energy (FRET), which allow the diffu-sional mobility of cellular components and their interaction at the molecular level to be monitored are other varieties of time-resolved methods [30]. A novel method is fluorescence correlation spectroscopy (FCS), which measures the statistical fluctuations of fluorescence intensity within a con-focally illuminated volume. Correlation analysis allows the concentration of particles and their diffusion to be determined [31], [32], FCS has proved... 

In this chapter, we discussed the principle quantum mechanical effects inherent to the dynamics of unimolecular dissociation. The starting point of our analysis is the concept of discrete metastable states (resonances) in the dissociation continuum, introduced in Sect. 2 and then amply illustrated in Sects. 5 and 6. Resonances allow one to treat the spectroscopic and kinetic aspects of unimolecular dissociation on equal grounds — they are spectroscopically measurable states and, at the same time, the states in which a molecule can be temporally trapped so that it can be stabilized in collisions with bath particles. The main property of quantum state-resolved unimolecular dissociation is that the lifetimes and hence the dissociation rates strongly fluctuate from state to state — they are intimately related to the shape of the resonance wave functions in the potential well. These fluctuations are universal in that they are observed in mode-specific, statistical state-specific and mixed systems. Thus, the classical notion of an energy dependent reaction rate is not strictly valid in quantum mechanics Molecules activated with equal amounts of energy but in different resonance states can decay with drastically different rates. 

Analysis of this state is interesting from the point of view of the quantum measurement problem, an issue that has been debated since the inception of quantum theory by Einstein, Bohr, and others, and continues today [31]. One practical approach toward resolving this controversy is the introduction of quantum decoherence, or the environmentally induced reduction of quantum superpoations into clasacal statistical mbrtures [32], Decoherence provides a way to quantify the elusive boundary between classical and quantum worlds, and almost always precludes the existence of macroscopic Schrodinger-cat states, except for extremely short times. On the othm hand, the creation of mesoscopic Schrddinger-cat states like that of q. (10) may allow controlled studies of quantum decoherence and the quantum-classical boundary. This problem is directly relevant to quantum computation, as we discuss below. 

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