Static criticality factor

The multiplication constant and perturbation. The new eigenvalue quantity, here called the multiplication constant k, is often called the effective multiplication constant and is called the static criticality factor, (7, by Weinberg and Wigner. It is the largest real eigenvalue of the criticality equation... 

The formal description of thermodiffusion in the critical region has been discussed in detail by Luettmer-Strathmann [79], The diffusion coefficient of a critical mixture in the long wavelength limit contains a mobility factor, the Onsager coefficient a = ab + Aa, and a thermodynamic contribution, the static structure factor S(0) [7, 79] ... 

Fig. 6 Left Soret coefficient. S j for a number of PDMS/PEMS blends. The red bullets correspond to the critical blend with a critical temperature of Tc = 38.6 °C. Right Same data as left normalized to mean field static structure factor S(0). The legends give the PDMS and PEMS molar masses in kg mor1 [97]...

For materials that exhibit classical active-passive behavior, passivation is more conducive under static rather than dynamic conditions. For the latter, the frequency of cyclic loading is often one of the critical factors that influences CF in corrosive environments. Cathodic protection generally mitigates CF and SCC, but increases the probability of HEC of susceptible materials. 

Typical results are shown in Fig. 6 for U-methane in graphite pores of H =7.5 at T=114 K. At p/ps=l the system is solid-like at this temperature, but a discrete change in density occurs around p ps ca.0.5. The self diffiisivity along axial direction also shows drastic change at this point. Further examination of various characteristics of molecular state such as snapshots, in-plane pair correlations and static structure factors confirmed that this change in density is the result of a phase transition from solid-like state to liquid-like one, or melting. Since the critical condensation condition for this pore is far lower than this transition point to stay around p ps= ca.0.2, the liquid-like state is not on metastable branch but thermodynamically stable. Thus a solid-liquid coexistence point is found for this temperature. 

The two parameters A and in (22a) are determined by the static structure factor at the transition point, and take values around A 0.73 and w 0.7 for the PY Sq for hard spheres. The transition point then lies at packing fraction 0c = 0.52 (index c for critical), and the separation parameter measures... 

In contrast, static SIMS measurements are performed with a number of incident ions (<10 ions/cm ) about one order of magnitude less than the number of atoms at the surface of the sample (one monolayer of Si contains 10 atoms/cm ). In this case, the damage to the sample surface is minimized and ions are mainly emitted from the first atomic layers, also promoting desorption of large fragments. However, count rates are low and information is restricted to relatively abundant species from the very superficial layers of the target. In both cases, instrumental parameters need to be selected according to the most critical factors in the analysis (e.g., lateral resolution, depth resolution, or sensitivity), and the optimal conditions represent a compromise between those different factors. 

Service failures in plastics can be caused by fatigue. When time is the critical factor, this type of failure is called static fatigue or creep rupture. If mechanical load reversal... 

In melt intercalation, the polymer and layered silicate mixture is annealed above the Jg in either static or flow conditions. Modified layered silicates are usually employed to promote intercalation. The polymer chains spread from the molten mass into the silicate galleries to form either intercalated or delaminated hybrids according to the degree of penetration. The critical factor that determines which type is obtained is probably linked to thermodynamic factors. This method is environmentally benign due to the absence of organic solvents. Furthermore, it is compatible with current industrial processes such as extrusion and injection molding. However, very careful attention has to be paid to finely tune the processing conditions to increase the compatibility of the clay layer surfaces with the polymer matrix. 

III.2 In another article on bone cements [Vallo, C, Influence of filler content on static properties of glass-reinforced bone cement, J. Biomed. Mater. Res., 53(6), 717 (2000)], the following data for the critical intensity factor in these same glass-bead-fllled PMMA composites as was used in Problem 5.III.1 are given ... 

The filter bank is the deciding factor for the basic structure of a perceptual coding system. Figure 2.6 shows the basic block diagram of an static n-channel analysis/synthesis filter bank with downsampling by k. If k = n, it is called a filter bank with critical sampling. A number of basic parameters can be used to describe filter banks used for audio coding ... 

In considering the vibronic side-bands to be expected in the optical spectra when we augment the static crystal field model by including the electron-phonon interaction, we must know the frequencies and symmetries of the lattice phonons at various critical points in the phonon density of states. We shall be particularly interested in those critical points which occur at the symmetry points T, A and at the A line in the Brillouin zone. Using the method of factor group for crystals we have ... 

---