Over narrow boundaries

The significance of interlaminar stresses relative to laminate stiffness, strength, and life is determined by Classical Lamination Theory, i.e., CLT stresses are accurate over most of the laminate except in a very narrow boundary layer near the free edges. Thus, laminate stiffnesses are affected by global, not local, stresses, so laminate stiffnesses are essentially unaffected by interlaminar stresses. On the other hand, the details of locally high stresses dominate the failure process whereas lower global stresses are unimportant. Thus, laminate strength and life are dominated by interlaminar stresses. 

Fig. 1.13.1. Temperature profile near the junction between a system (left) at temperature T and a reservoir (right) at temperature Tq under QSI operating conditions. The change in temperature occurs over a narrow boundary region.

L/U) is much smaller than the diffusion time over a cell, that is L2/D. As a result of the dominant advective transport the concentration across a single cell is almost uniform and the concentration difference between two adjacent cells is restricted to a narrow boundary layer in the vicinity of the separatrix. In this region the dominant balance in the advection-diffusion equation is between advection along the separatrix and diffusion across the separatrix through the boundary layer... 

C with a water content of 0.075 kg/kg. Although heat and mass transfer rates were relatively insensitive to the choice of the model, the amount of fog formation was not. The models neglect the effects of condensation within the boundary layer, thus underestimating fog formation by a factor of up to three. The amount of fog formed in flue-gas washing plants increased up to a maximum value with decreasing feed-water temperature over a narrow band of liquid-to-gas ratios. 

Fig. 1. The H — T phase diagrams for different S/F systems, (a) Structure with narrow domains. The solid (dashed) line corresponds to an isolated superconducting nucleus at the domain boundary (far from the domain boundary), (b) Isolated superconducting nucleus in a structure with wide domains BoD2/To = 25). (c) Periodic domain structure for ttBow2/To = 5 (solid line) and -nBow2 /To = 1 (dashed line), (d) Ferromagnetic dot over the superconducting film (N = 10).

Typical domain walls are smooth and extend over many interatomic distances. However, deviations from this continuum picture occur in very hard materials (narrow walls), at grain boundaries and in the case of geometrical constraints. Narrow-wall phenomena, which have been studied for example in rare-earth cobalt permanent magnets [189] and at grain boundaries [95, 96], involve individual atoms and atomic planes and lead to comparatively small corrections to the extrinsic behavior. 

Quantum phenomena at the vacuum interface have been postulated in analogy with known effects at physico-chemical interfaces. To be consistent, special properties of the latter are therefore implied. A physical interface is the boundary surface that separates two phases in contact. These phases could be two solid phases, two liquid phases, solid-liquid, solid-gas or liquid-gas phases. What they all have in common is a potential difference between the two bulk phases. In order to establish equilibrium at the interface it is necessary that rearrangement occurs on both sides of the interface over a narrow region. Chemical effects within the interfacial zone are unique and responsible for the importance of surfaces in chemical systems. At the most fundamental level the special properties of surfaces relate to the difference between isolated elementary entities and the same entities in a bulk medium, or condensed phase. 

---