Lindemann length

Fluorescence sensors have been used since 1957 to measure cell internal NAD(P)H at 450 nm. Later on they were applied for in situ determination of the cell concentration. However, the culture fluorescence intensity is not only influenced by the cell concentration, but also by the physiological state of the cells [56] and, in addition to that, there are several other compounds that participate in the fluorescence emission besides NAD(P)H. To identify the fluorophores in the cells and cultivation medium, the excitation and the emission wave lengths are varied in a broad range [57,58]. Two instruments were applied for the 2D-fluorescence spectroscopy Model F-4500 (Hitachi) and the BioView Sensor (Delta light Optics). Each of them uses an excitation range of 250-560 nm,an emission range of 260/300-600 nm and the measuring time of 1 min [59,60]. The application of this technique for CPC production was performed by Lindemann [61]. 

Between temperatures of 28 and 29 K the rms bond length fluctuations of the 13-particle system increase dramatically. Similar results have been obtained for all the other clusters N = 5, 6, and 7) for which S(T) is cal-culated. - The curves of S T) for these systems are similar to those occurring with first-order phase transitions of macroscopic systems.Lindemann s criterion states that melting occurs for such systems when rms fluctuations reach 10%.For the small clusters studied, the rise in this function occurs at values of S slightly below 10%—an effect that can be attributed to the large ratio of surface to core atoms. 

The microcanonical analog of the macroscopic phases is quite often defined by means of the energy dependence of Lindemann index. This quantity is designed to detect the stiffness of a molecule by measuring the deviation of the bond lengths from their averaged values as... 

In this section the results obtained from AIMD-B-LYP simulations by energizing three isomers of Li9" clusters will be analyzed [39]. For this purpose three types of quantities will be used. One of them is the root-mean-square (RMS) bond-length fluctuation 8 [25], which is calculated at the end of trajectories. A sharp increase of the 8 value is known as the Lindemann criterion for bulk melting, while in the context of finite-size clusters it can be taken as an indication of transition from solid-like to liquid-like state. We find it particularly instructive to analyze the trajectories in terms of atomic equivalence indexes ,... 

Fig. 4. Averaged relative root mean square bond length fluctuations for the Ar-Ar and Ar-SF distances for certain SF -(Ax) clusters. The shaded band identifies the 8 values chosen to define the Lindemann criterion for melting.

FIGURE 4.14 (a) Result of the scaling procedure described in the text, (b) Volume fraction dependence of the localization length in units of mean interparticle distances. Dashed horizontal line corresponds to the Lindemann criterion, = 0.1. 

The two glass states differ in their local packing and consequently stiffness. While repulsion localizes particles according to Lindemann criterion, bond formation allows particles less local free volume. Figure 7.8 shows the localization lengths (left panel), calculated from the MSD at infinite time, along the transition lines in Figure 7.7. 

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