Cutoff length

Plot the shape of the contact line pinned to a defect using Eq. X-30 for water on polyethylene, stearic acid, and platinum. Assume that the upper cutoff length is 2 mm. How does the shape of the pinned contact line compare with your observations of raindrops on dirty windows ... 

Cutoff Length. The following factors should be considered in determining a cutoff length ... 

Recommended Cutoff Lengtha in Terms of Drum Lapa See Paragraph Titled Cutoff Length [11]... 

Equation (52) allows us to estimate the impact of viscoelastic braking on the capillary flow rate. As an example, we will consider that the liquid is tricresyl phosphate (TCP, 7 = 50 mN-m t = 0.07 Pa-s). The viscoelastic material is assumed to have elastic and viscoelastic properties similar to RTV 615 (General Electric, silicone rubber), i.e., a shear modulus of 0.7 MPa (E = 2.1 MPa), a cutoff length of 20 nm, and a characteristic speed, Uo, of 0.8 mm-s [30]. TCP has a contact angle at equilibrium of 47° on this rubber. 

The superstoichiometric zinc yielded as the reaction proceeds ionizes by giving an electron to the ZnO conduction band. Thus, the electrical conductivity of the semiconductor increases. A competing process that determines the beyond cutoff lengths of the curves in Fig. 5.3 is represented by the reaction... 

Here, the actual thickness of adsorbed molecule layers /ad is obtained by multiplying n by adsorbed molecule diameter a0. The actual thickness range in which the fractal geometry is satisfied represents the length-scale cutoff range of fractality.116,118 Here, the value of the lower (inner) cutoff length tadjmfa is equal to... 

Roughness parameters naturally depend on the length scale where they are defined. In dimensional metrology this scale is confined between the short-wavelength cutoff lengths... 

The existence of an inner cutoff length has important consequences with respect to the evaluation of the dimensions of natural fractals. All the dimensions described in Section 2.3, except the similarity dimension, require a passage to a limit (e.g. limit... 

With this simplification, the simulations become more tractable while still retaining a model with discrete solvent particles. Indeed, replacing such a model for solvent with a more realistic model, such as SPC/E, will improve the accuracy of the simulations however, the simplified model can stiU provide qualitative conclusions applicable to real systems, which has been proved in many previous researches for various areas [6, 7]. The L-J interaction is set to zero when molecules are separated by farther than the cutoff length Tf. = 2.5ff. 

Once the surface data have been filtered and the mean line (or plane in the case of three-dimensional measurements) has been determined, it is possible to quantify the surface features. Figure 1 shows a ground surface separated into the roughness and waviness components after applying a Gaussian filter and a 0.8 mm cutoff length. 

Processes in nature often result in fractal-like forms that differ from the mathematical fractals such as the Koch curve in two ways (a) the self-similarity is not exact but is a congruence in a statistical sense and (b) the number of repeated splittings is finite and random fractals have an upper and a lower cutoff length. A spatial example of a random fractal is the colloidal gold particle agglomerate shown earlier in Figure 7.4. 

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