Population, distribution Power

Tunable laser spectroscopic techniques such as laser-induced fluorescence (LIF) or resonantly enhanced multi-photon ionization (REMPI) are well-established mature fields in gas-phase spectroscopy and dynamics, and their application to gas-surface dynamics parallels their use elsewhere. The advantage of these techniques is that they can provide exceedingly sensitive detection, perhaps more so than mass spectrometers. In addition, they are detectors of individual quantum states and hence can measure nascent internal state population distributions produced via the gas-surface dynamics. The disadvantage of these techniques is that they are not completely general. Only some interesting molecules have spectroscopy amenable to be detected sensitively in this fashion, e.g., H2, N2, NO, CO, etc. Other interesting molecules, e.g. 02, CH4, etc., do not have suitable spectroscopy. However, when applicable, the laser spectroscopic techniques are very powerful. 

Now let s us have some fun by perturbing this equilibrium population distribution Selective saturation of the Ha transitions (aa —> Pa and ap —> PP) by low-power... 

A parametric test is one which makes particular assumptions about the mathematical nature of the population distribution from which the samples were taken. If these assumptions are not true, then the test is obviously invalid, even though it might give the answer we expect A non-parametric test does not assume that the data fit a particular pattern, but it may assume some things about the distributions. Used in appropriate circumstances, parametric tests are better able to distinguish between true but marginal differences between samples than their non-parametric equivalents (i.e. they have greater power ). 

The energy pump (e.g., flashlamps, gas discharges, or even other lasers) generates a population distribution N(E) in the laser medium, which strongly deviates from the Boltzmann distribution (2.18) that exists for thermal equilibrium. At sufficiently large pump powers the population density N Ek) of the specific level Ek may exceed that of the lower level / (Fig. 5.1b). 

Compared to discrete variables, ctmtinuous variables have a large information content so that small or moderate sample sizes are sufficient for a powerful test The probability distribution of the sample mean should be known and preferably normal, either because the population distribution is normal, or the sample is large enough to let the distribution of the sample mean approach normality (central limit theorem). 

INTERNATIONAL ATOMIC ENERGY AGENCY, Dispersion of Radioactive Material in Air and Water and Consideration of Population Distribution in Site Evaluation for Nuclear Power Plants, Safety Standards Series No. NS-G-3.2,... 

Application of an oscillating magnetic field at the resonance frequency induces transitions in both directions between the two levels of the spin system. The rate of the induced transitions depends on the MW power which is proportional to the square of oi = (the amplitude of the oscillating magnetic field) (see equation (bl.15.7)) and also depends on the number of spins in each level. Since the probabilities of upward ( P) a)) and downward ( a) p)) transitions are equal, resonance absorption can only be detected when there is a population difference between the two spin levels. This is the case at thennal equilibrium where there is a slight excess of spins in the energetically lower p)-state. The relative population of the two-level system in thennal equilibrium is given by the Boltzmaim distribution... 

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