Interface divergence

The weighted mean curvature is the interface divergence of the evaluated on the unit sphere. The interface divergence is defined within the interface, and if the interface is not differentiable, subgradients must be used. The convex portion of is equivalent to the the Wulff shape, so the interface divergence is operating from one interface onto another. This form can get very complicated. 

Figure B3.6.3. Sketch of the coarse-grained description of a binary blend in contact with a wall, (a) Composition profile at the wall, (b) Effective interaction g(l) between the interface and the wall. The different potentials correspond to complete wettmg, a first-order wetting transition and the non-wet state (from above to below). In case of a second-order transition there is no double-well structure close to the transition, but g(l) exhibits a single minimum which moves to larger distances as the wetting transition temperature is approached from below, (c) Temperature dependence of the thickness / of the enriclnnent layer at the wall. The jump of the layer thickness indicates a first-order wetting transition. In the case of a conthuious transition the layer thickness would diverge continuously upon approaching from below.

We consider a finite space, which contains the NA sample and is in contact with a bath of water or water vapor. That allows one to maintain the r.h. in the experimental space at a constant level and change it when necessary. Such a scheme corresponds to the real experiments with wet NA samples. A NA molecule is simulated by a sequence of units of the same type. Thus, in the present study, we consider the case of a homogeneous NA or the case where averaging over the unit type is possible. Every unit can be found in the one of three conformational states unordered. A- or B- conformations. The units can reversibly change their conformational state. A unit corresponds to a nucleotide of a real NA. We assume that the NA strands do not diverge during conformational transitions in the wet NA samples [18]. The conformational transitions are considered as cooperative processes that are caused by the unfavorable appearance of an interface between the distinct conformations. 

Fig. 8. Microhardness profile across interfaces of two types of explosion clads that show widely divergent response resulting from the inherent cold-work hardening characteristics where Q represents the 3.2-mm type 304L stainless/28.6-mm, A 516-70 control (before cladding) ( ) = clad + flat ...

One now wonders whether these two phenomena are to be observed also for the whole two-dimensional surface of a crystal non-locking of the crystal surface in spite of lattice periodicity, and divergence of the fluctuation-induced thickening of the interface (or crystal surface), and in consequence the absence of facets. The last seems to contradict experience crystals almost by definition have their charm simply due to the beautifully shining facets which has made them jewelry objects since ancient times. 

According to the capillary wave approximation , a rough interface is characterized by a width that diverges logarithmically with its transverse dimensions ... 

We know that another interesting phenomenon occurs when the temperature increases up to the bulk transition Tj. Previous studies have shown that the APB is wetted by the disordered phase a large layer of disordered phase develops in between the two ordered domains. In other words, the APB is splitted into two order-disorder interfaces, whose separation diverges as In(T), - T). We display in Fig. 5 the 2-dlmensional maps for T=1687 K, i.e. very close to the first-order transition. As expected, we see that the APB separates into two order-disorder interfaces. Moreover, the width of the penetrating disordered layer varies along the APB. This means that each order-disorder interface develops its own transverse fluctuations and that the APB begins to behave as two separate objects. 

B-cell deficient mice are resistant to intraperitoneal inoculation with prions probably because of their involvement with FDC maturation and maintenance. The interface between FDCs and sympathetic nerves represents a critical site for the transfer of lymphoid prions into the nervous system however, the mechanism by which this is achieved remains unknown. Distinct forms of prion disease show differences in lymphoreticular involvement that may be related to the etiology of the disease or to divergent properties of distinct prion strains. For a review of prion disease peripheral pathogenesis see [18]. 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

The last terms in each of Eqn. (5.2-9) and Eqn. (5.2-10) represent the divergence of the deviatoric stress including viscosity and pseudo-turbulence. The quantities /n L and uG are effective viscosities of each phase including bulk and shear viscosities. Fl and Fg represent the volume-averaged forces exerted on the liquid-and gas-phase (respectively) by the other phases across the common interfaces. 

Recent studies indicate that the adsorption of metal ions is controlled only in part by the concentration of the free (aquo) metal ion of considerable importance is the ability of hydroxo and other complex ions and molecules to adsorb. There have been two apparently divergent approaches to describe the role played by hydroxo metal complexes in adsorption at solid-aqueous electrolyte interfaces. Matijevic et al. (9) have proposed that specific hydrolysis products—e.g., Al8(OH)2o4+ in the A1(III)-H20 system, are responsible for extensive coagulation and charge reversal of hydrophobic colloids. It has also been demonstrated by Matijevic that the free (aquo) species of transition and other metal ions... 

Vapor transport differs from surface diffusional transport, where the flux is always in the surface plane. For both surface diffusion and vapor transport, the diffusion potential at the surface is proportional to the local value of 7sk if the surface free energy is isotropic. For surface diffusion, the interface normal velocity is related to a derivative (i.e., the divergence of the flux). Also, the total volume is conserved during surface diffusion. For vapor transport, the interface normal velocity is directly proportional to the vapor flux, and the total number of atoms is not necessarily conserved. 

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