Taylor length

An additional length, intermediate in size between /0 and Zk, which often arises in formulations of equations for average quantities in turbulent flows is the Taylor length (A), which is representative of the dimension over which strain occurs in a particular viscous medium. The strain can be written as (U /l0). As before, the length that can be constructed between the strain and the viscous forces is... 

F H, O Kennard, D G Watson, L Brammer, A G Orpen and R Taylor 1987.1 ables of Bond Lengths determined by X-ray and Neutron Diffraction. 1. Bond Lengths in Organic Compounds. Journal of he Chemical Society Perkin Transactions 11 51-519. 

If we cany out a Taylor s expansion of the potential energy about the equilibrium length of an isolated chemical bond, we get... 

It is useful at this point if we examine the Taylor expansion for a general diatomic potential U R) about the equilibrium bond length R. ... 

Estr is the energy function for stretching a bond between two atom types A and B. In its simplest form, it is written as a Taylor expansion around a namral , or equilibrium , bond length Rq- Tenninating the expansion at second order gives the expression... 

There are two aspects in this. One is controlling the total length of the step, such that it does not exceed the region in which the second-order Taylor expansion is valid. The... 

Figure 10-91B. Steam and condensate temperatures versus condenser length. Temperature distribution curve for the same multizone condenser as in Figure 10-91 A. Points A, E, and F are the same. Point B is above C, which locates the start of the wet desuperheating zone on the tube surface. (Used by permission Rubin, F. L. Heat Transfer Engineering, V. 3, No. 1, p. 49, 1981. Taylor and Francis, Inc., Philadelphia, PA. All rights reserved.)...

Ohagen A, Devitt A, Kunstman KJ, Gorry PR, Rose PP, Korber B, Taylor J, Levy R, Murphy RL, Wolinsky SM, Gabuzda D (2003) Genetic and functional analysis of full-length human immunodeficiency virus type 1 env genes derived from brain and blood of patients with AIDS. J Virol 77(22) 12336-12345... 

Fig. 4. Tentative allocation of probe binding sites within the three-dimensional structure of Ca -ATPase derived from vanadate-induced E2-type crystals. The top picture is the projection view of the Ca -ATPase down the x-axis, revealing the pear-shaped contours of ATPase molecules. The maximum length of the cytoplasmic domain to the tip of the lobe is =r65A. In the middle and bottom pictures the same structure is viewed down the x-axis, revealing the gap between the bridge and the bilayer surface and the connections between ATPase molecules in neighboring dimer chains. The proposed binding sites for lAEDANS and FITC are indicated. The bottom right picture is the same structure viewed down the y-axis. Adapted from Taylor et al. [90].

To derive this result we only have to rely on Eq. (54) and the idea that the distribution of errors is a normal distribution. Of course, the error in the Taylor expansions is not just a function of distance, it is also a function of direction. Hence, a better model would assign each Taylor expansion confidence lengths for each direction in space. For various reasons, it is much simpler to associate a confidence length with each element of Z, and to define the weight function as... 

These length scales characterize the larger eddies in the flow (hence the name integral ). Other widely used length scales are the Taylor microscales, which are determined by the... 

Like the velocity spatial correlation function discussed in Section 2.1, the scalar spatial correlation function provides length-scale information about the underlying scalar field. For a homogeneous, isotropic scalar field, the spatial correlation function will depend only on r = r, i.e., R,p(r, t). The scalar integral scale L and the scalar Taylor microscale >-,p can then be computed based on the normalized scalar spatial correlation function fp, defined by... 

Taylor (1988) distinguished three types of fossil hydrothermal systems on the basis of varying water/rock ratios, temperatures, and the length of time that fluid/rock interaction proceeds ... 

---