Spectral intensities, fluctuations calculations

One of the shortcomings of LIBS, particularly in relation to quantitative elemental analysis, arises from the instability of the laser-induced plasma emission resulting from laser intensity fluctuations (1-5%) the amount of scattered light present depends on local matrix effects and on physical and chemical properties of the target material. The most common way of compensating for signal fluctuations in LIBS is by calculating the ratio of the spectral peak intensity to that of a reference intensity. However, this internal calibration method provides relative rather than absolute concentrations. 

The liquid phase cage model accounts for appearance in the spectrum of resolved rotational components by effective isotropization of the rapidly fluctuating interaction. This interpretation of the gas-like spectral manifestations seems to be more adequate to the nature of the liquid phase, than the impact description or the hypothesis of over-barrier rotation. Whether it is possible to obtain in the liquid cage model triplet IR spectra of linear rotators with sufficiently intense Q-branch and gas-like smoothed P-R structure has not yet been investigated. This investigation requires numerical calculations for spectra at an arbitrary value of parameter Vtv. 

Thus they were able to calculate the velocity intensity from the mass-transfer intensity and the spectral distribution function of mass-transfer fluctuations. By measuring and correlating mass-transfer fluctuations at strip electrodes in longitudinal and circumferential arrays, information was obtained about the structure of turbulent flow very close to the wall, where hot wire anemometer techniques become unreliable. A concise review of this work has been given by Hanratty (H2). 

The fluctuations are often caused by atomic motion e.g. Brownian motion in liquids, ionic hopping, molecular rotations, librations and atomic vibrations. These motions are often complex and it is the range of frequencies that are present in the motions that determine relaxation. The spectral density function describes the relative intensities of different frequencies in the motions and can be used to calculate relaxation rates. 

To get deeper insight into the effect noise has on the time scales and coherence of the system we determine the interval between two consecutive excitations and calculate the mean interspike-interval (T). In Fig. 5.11(b) (top) the decrease of (T) as a function of D is shown thus demonstrating that the mean interspike-interval is strongly controlled by the noise intensity especially at lower values of the latter. This is very important in terms of experiments, where noise can induce oscillations by forcing stationary fronts to move. The corresponding spectral peak frequency / shows a linear scaling for small D. As a measure for coherence we use the normalized fluctuations of pulse duration [10]... 

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