Mean length

All definitions of the mean given (eqs. 1—4) are based on the number of particles being measured. As opposed to number-based means, length, surface-area, and mass-based means have also been defined. The linear, or length mean (Lm) diameter,dj, is defined by the foUowiag equation ... 

PAN fibers were purehased from AKZO Fortafil Fibers, Rockwood, Term., under the designation F3-0. Fibers with a mean length of 100,am and 200,am have been utilized. 

Assuming that we are comparing different materials on the basis that the mean length, width and loading is fixed but the beam depth is variable then equation (1.1) may be written as... 

The relaxation time r of the mean length, = 2A Loo, gives a measure of the microscopic breaking rate k. In Fig. 16 the relaxation of the average length (L) with time after a quench from initial temperature Lq = 1.0 to a series of lower temperatures (those shown on the plot are = 0.35,0.37, and 0.40) is compared to the analytical result, Eq. (24). Despite some statistical fluctuations at late times after the quench it is evident from Fig. 16 that predictions (Eq. (24)) and measurements practically coincide. In the inset is also shown the reverse L-jump from Tq = 0.35 to = 1.00. Clearly, the relaxation in this case is much ( 20 times) faster and is also well reproduced by the non-exponential law, Eq. (24). In the absence of laboratory investigations so far, this appears the only unambiguous confirmation for the nonlinear relaxation of GM after a T-quench. 

FIG. 18 Scaling plot of L t) from the numerical solution of the rate equations for quenches to different equilibrium states [64] from an initial exponential MWD with L = 2. The final mean lengths are given in the legend. The inset shows the original L t) vs t data. Here = (0.33Lqo). ... 

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

Recrystallization of 76 (R=H) from CH2CI2 provided crystals adequate for X-ray structural determination. The molecule was found to be saddle shaped with a phenyl ring at each vertex and nadir. The alkynyl bonds were found to be essentially linear and to possess a mean length of 1.194 A, typical for the length of triple bonds in free butadiyne. Although 76 is a dehydrobenzoannulene possessing a 4n TT-electron circuit, the nonplanarity of the macrocycle alleviated much of the strain associated with a flat structure and thus precluded the possibility of anti-aromatic ring currents. 

Fibre means length >5pm, average diameter <3pm and length dia ratio >3 1. 

Fig. 5.8. Comparison of chemically realistic input for the optimization procedure and results for the corresponding lattice model, using the two-bond and four-bond optimization procedure a mean length (L) (in lattice units), b mean angle (0), and c the mean reduced barrier (W)/kBT. From [32]...

The immediate treatment outcome resulted in less than half (47 percent) of the PCP abusers completing the treatment program. The mean length of stay was just under 4 weeks. 

The plant has a spare kettle reboiler available with the following specification. U-tube bundle, 50 tubes, mean length 4.8 m, end to end. 

A mean length diameter or arithmetic mean diameter may also be defined by ... 

Having obtained a measure of surface area, a mean pore size may be calculated by simplifying the pore system into np cylindrical pores per unit mass of adsorbent, of mean length Lp and mean pore radius rp. 

If the aim of an investigator is to determine equilibrium concentrations in samplers, then the residence time (tm) is a logical parameter to compare among samplers. The tm is the mean length of time that a molecule spends in a passive sampling device, where solute exchange follows first-order kinetics. Residence time is given by... 

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