Fluctuation rate

The temperature-dependent fluctuation rates a>i2 of the EFG, which result from this simultaneous fit, were interpreted in terms of low-temperature tunneling plus a temperature-dependent activation of the terminal O-atom from position 1 to 2 and vice versa, described by the expression... 

When electrically insulated strip or spot electrodes are embedded in a large electrode, and turbulent flow is fully developed, the steady mass-transfer rate gives information about the eddy diffusivity in the viscous sublayer very close to the electrode (see Section VI,C below). The fluctuating rate does not give information about velocity variations, and is markedly affected by the size of the electrode. The longitudinal, circumferential, and time scales of the mass-transfer fluctuations led Hanratty (H2) to postulate a surface renewal model with fixed time intervals based on the median energy frequency. 

The turbulent energy dissipation rate can be expressed in terms of the fluctuating rate-of-strain tensor ... 

The second-order fluctuating rate-of-strain tensor is real and symmetric. Thus, its three eigenvalues are real and, due to continuity, sum to zero. The latter implies that one eigenvalue (a) is always positive, and one eigenvalue (y) is always negative. In the turbulence literature (Pope 2000), y is referred to as the most compressive strain rate. 

As shown above, the intrinsic fluorescence spectra of proteins as well as coenzyme groups and probes shift within very wide ranges depending on their environment. Since the main contribution to spectral shifts is from relaxational properties of the environment, the analysis of relaxation is the necessary first step in establishing correlations of protein structure with fluorescence spectra. Furthermore, the study of relaxation dynamics is a very important approach to the analysis of the fluctuation rates of the electrostatic field in proteins, which is of importance for the understanding of biocatalytic processes and charge transport. Here we will discuss briefly the most illustrative results obtained by the methods of molecular relaxation spectroscopy. 

Exercise. A population grows with a fluctuating rate coefficient... 

Fluctuation Rate and Molecular Displacements in the Direction of External Stress... 

It is interesting to compare the fluctuation rate vn for mobile conformations characterized by two or more positions with the molecular dislocations taking place in the... 

However, in reality, all macromolecules in solution are undergoing constant Brownian motion, and this fact leads to fluctuation in I(t). The fluctuation rate can be related to the translational diffusion of the macromolecules. The faster the diffusion, the faster the fluctuation will be. 

The calculation of severance payments in equations (3.16) and (3.17) considers the natural fluctuation rate and personnel requirements as specified in equation (3.49). Again, non-negativity constraint (3.72) ensures that in case of personnel increases no negative severance payments are calculated. The same type of formulation could also be used to model training costs for newly hired employees but this was considered to be of minor relevance in the application cases pursued so far. 

CeCu6 and CeRu2Si2 show neither superconductivity nor magnetic order down to 20 mK. Therefore, the behaviour of 1/7) in these compounds presents a fundamental property of heavy fermion material. As seen in Fig. 3,11,12 1/7) is temperature independent above the Kondo temperature, / , corresponding to a localized state of the 4/ electron. At higher temperatures 1/7) is expected to decrease due to the increase in the fluctuation rate of the localized 4f spin. Below 7k, 1/7) shows a 7) T= constant behaviour corresponding to the Fermi liquid state. 

The collapse of a six-line hyperfine spectrum with decreasing relaxation time is illustrated by the calculated spectra in Fig. 3.8 [44] for a " Fe nucleus in a fluctuating magnetic field and a fixed electric field gradient for different values of the electronic relaxation time. If the fluctuation rate is very slow compared to the precession frequency of the nucleus in the field H, the full six-line hyperfine pattern is observed. If the fluctuation rate is extremely rapid the nucleus will see only the time-averaged field which is zero and a symmetric quadrupolar pattern will be seen. At intermediate frequencies the spectra reflect the fact that the 2> -> transitions which make up the low-velocity component of the quadrupole doublet relax at higher frequencies than do the I I i> and -]-> -> transitions which... 

We investigate the overall effect of the bath fluctuation on the photon statistics for the steady-state case as the fluctuation rate R is varied from slow to fast modulation regime. To characterize the overall fluctuation behavior of the photon statistics, we define an order parameter q. 

First, we discuss the strong modulation regime, v F, shown in Figure 4.14 with v/F = 100 in this case. Depending on the fluctuation rate, there are three distinct regimes ... 

Table IV.2 summarizes various expressions for the line shape and Q found in the limiting cases of the two-state jump model investigated in this work. For simplicity, we have set fj = 1. We see that although the fluctuation model itself is a simple one, rich behaviors are found. We believe that these behaviors are generic (although we do not have a mathematical proof). In the weak modulation cases, both and Q can be described by a single expression, irrespective of the fluctuation rate R. However, in the strong modulation cases, and Q change their qualitative features as R changes.

Fig. 1. Time scales of various techniques to study magnetism. 1/t is the fluctuation rate of the field sensed hy the nuclear prohes or the rate of spin fluctuations.

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