Longitudinal correlation length

In the same paper Picken et al [13] also describe a more general two-dimensional lattice model to deal with this additional aspect. In this model only splay and bend deformations are allowed to occur. The longitudinal relaxation (i.e. the band spacing) will be determined mainly by the bend elastic constant K, as used in the one-dimensional model, and the lateral relaxation is driven by the splay modulus K, They find the result of this model to be not completely satisfactory.. .. it is clear that from the present model the aspect ratio of the bands Lj /L l is expected to be a constant (and equal to (iC /K ) ). This is not in agreement with the experimental results where the lateral correlation length seems to depend on the applied preshear rate, (and the longitudinal correlation length does not). They speculate that Possibly, the applied shear rate influences the details of the initial texture that is formed upon cessation of flow. ... 

Similarly the longitudinal correlation length in molecular position can be measured from the meridional spread of the small-angle scattering maximum arising from smectic-like fluctuations (FIGURE 5). The position Qo of such a peak has been used to estimate the apparent molecular length. 

Figure 7. Isometric map of iujectant cor centratiou tor a case with large correlation lengths and no diffusioii. The longitudinal direction (parallel to flow) is x the transverse direction (perpendicular to flow) is y. Concentration gives the appearance of layering even though there are none present. (Reproduced from Refo. )...

T — Tmf, while the expansion of this energy in terms of q — x determines4) the longitudinal and transverse correlation length, f0 and f ox, respectively. 

The symmetric limit corresponds very probably to the BCS superconductivity in the conducting polymer24 (SN)X. It seems that there the ratio of the longitudinal and transverse correlation lengths is temperature independent, as in Equ. (45). 

Correlation length, longitudinal (parallel to n) (Jn = transverse (perpendicular to n) ... 

Figure 4. Longitudinal ( n) and transverse (ijj correlation lengths as a function of the reduced temperature for 8CB (n-octylcyanobiphenyl). The solid lines are least-squares fits to single power laws corresponding to V =0.67 0.02 and Vj =0.51 0.04 (after [39]).

The auto-correlation functions can be used to define two characteristic length scales of an isotropic turbulent flow. The longitudinal integral scale is defined by... 

Since the variance contributions a1 (in length units) of longitudinal diffusion, injection, and detection are not correlated, their variances can be added... 

If the inner tube is longitudinally finned on the outside surface, the equivalent diameter is used as the characteristic length in both the Reynolds-number and the heat-transfer correlations. The fin effi-... 

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