Distance, fluctuations

The principal concern in radical pair theory is not which state is of lower energy but rather the energy difference and its variation as the length of the box or the inter-radical distance in the radical pair changes. Further, AEsi is time-dependent because the inter-radical distance fluctuates with time. As the separation gets larger, decreases... 

The magnetic field b(t) is, for instance, created by another spin (nuclear spin or the spin of an unpaired electron) in that case, it is proportional to 1/r (r distance between the two spins). Its time dependency arises from the orientation of r and/or from the distance fluctuation. However, in this section, we shall disregard the origin of b t) and we only rest on its general properties (assuming an isotropic medium) which arise from the random nature of molecular motions ... 

W AXS-pattern of a polymer melt if these Boltzmann-weighted distance fluctuations are not accounted for. They characterize a relevant feature of polymer melt structures. We treat this in terms of the Rotational Isomeric State Approximation (RISA) discussed in the next section. 

For our purposes we used a Gaussian distribution shifted in the ordinate direction towards lower values (Fig. 4). The standard deviation ct of this distribution is correlated somehow with the extent of distance fluctuations in the system. 

As a consequence of exclusion, the coordination number shows very peculiar behavior (Fig. 7). For example, six percent relative quadratic fluctuation yields to a bimodal distribution (Fig. 8). This indicates that every statistical homogeneous coordination needs larger distance fluctuations of segments lying in the... 

In the case of the PE melt, the largest part of the configuration entropy is included in the variety of chain conformations. In our model of the PE melt, these chain conformations cause the diameter of the correlation cylinders in which the chain segments are embedded to fluctuate. This leads necessarily to distance fluctuations of next neighbor segments because of steric hindrance of the local segment exclusion volume. Therefore, the inter- and intramolecular distance correlations cannot be discussed independently. 

Fig. 4. The dynamic scattering function < >g for a pair of elements (j, k) after averaging over all orientations and distance fluctuations in the hydrodynamic pre-average approximation, Eq. (B.49), and without this approximation, Eq. (B.45). The line labeled exact gives the exact deviation of the preaverage approximation, the dotted line represents the approximation of Eq. (B.50)R2)...

It is also worth noting that for the DMPC molecule, the distance-fluctuation criterion shows only one abrupt increase at T between 297 K and 301 K related to the main phase transition at T = 295 1.5 K [114, 115]. This confirms that C12 and C14 PC lipids have different dynamics at the molecular level. It is thus most likely to attribute the origins for the intrinsically different [123] gel to liquid phase transitions of PC bilayers with chains shorter than Cl3 to the substantially different dynamical behavior of the constituent lipid molecules. 

G.-B. Luo, M. Karpins, Determining the conformational change that accompanies donor-acceptor distance fluctuations an umbrella sampling analysis, J. Phys. Chem. B 115 (2011) 7991. 

The existence of large-distance fluctuations of the order parameter in the critical region leads also to the universality hypothesis, according to which the properties of thermodynamic functions of different physical systems are given by the space dimensionality d and the order parameter dimensionality n. The systems with equal d and n form a class of universality with the same critical indices. 

The stacking is subject to large paracrystalline distance fluctuations, therefore the stacking structure factor deviates significantly from 1 only for very small values of iQ < 0.025 A ). A detailed account on the structural properties is given in ref. [12]. 

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