Periodic surfaces volume fraction

In the latter the surfactant monolayer (in oil and water mixture) or bilayer (in water only) forms a periodic surface. A periodic surface is one that repeats itself under a unit translation in one, two, or three coordinate directions similarly to the periodic arrangement of atoms in regular crystals. It is still not clear, however, whether the transition between the bicontinuous microemulsion and the ordered bicontinuous cubic phases occurs in nature. When the volume fractions of oil and water are equal, one finds the cubic phases in a narrow window of surfactant concentration around 0.5 weight fraction. However, it is not known whether these phases are bicontinuous. No experimental evidence has been published that there exist bicontinuous cubic phases with the ordered surfactant monolayer, rather than bilayer, forming the periodic surface. 

The relationship of the thermal conductivities of fabrics and volume fractions of water in the interfiber spaces was expressed by a quadratic curve when the heat flow was normal to the fabric surface and by a straight line when the flow was parallel to the warp yarns. Except for hairy wool fabrics, the thermal conductivity of various wet fabrics may be calculated from the equations of Naka and Kamata (J3). An earlier investigation used an environmentally controlled room as a periodic heat source, and observed conductivities of 1-2 x 10 l cal/cm-sec °C for cotton, linen, and wool fabrics, and changes to 2-10 x 10 when the water content of these fabrics were increased ( ). After correcting for anisotropic effects, good agreement between actual conductivity measurements of wool fabrics and those calculated from a mathematical model of a random arrangement of fibers was observed. 

The examined C/C composite was fabricated via. preformed yam method[6]. The reinforcing fiber, fiber volume fraction, stacking sequence, and dimensions of specimens of it are Toray M40, 50%, 0790°, and 30mm x 30mm x 3mm, respectively. In the laminated C/C composite, periodical cracks along the fiber axis direction, transverse cracks (TCs), frequently appear as shown in Fig. 1. The surface layers of the TCs especially affect characteristics of the coating on C/C composites. 

The computational domain was divided into 1,401 elements, for 186 nodes. With this coarse grid, errors in area determinations were on the order of 0.5% (volume fraction errors were about 0.2%). With s set equal to unit, / was chosen to be sinusoidal with period 2 f(y) = a. sin n y — ). Thus the unit cell is actually homeomorphic to two unit cells of the P surface, so that b — 2. The amplitude a was varied up to a value of 0.6, and the result for 0.6 is shown in Fig. 8 (see color insert) two unit cells are shown side by side. 

The I-WP and F-RD minimal surfaces have been shown to provide two counterexamples to a conjecture that has previously been made (Meeks 1978, p. 81, Conjecture 6) A triply periodic minimal surface disconnects into two regions with asymptotically the same volume. The volume fraction of the labyrinth containing the symmetric skeletal graph is 0.5360 0.0002 for the I-WP minimal surface and 0.5319 0.0001 for F-RD. 

Since analytical expressions for only a few continuous triply periodic CMC surfaces are known (e.g. the Enneper-Weierstrass parameterization of the single-gyroid minimal surface with H = 0 and a volume fraction of 50 % [9]), these surfaces are typically modeled with the help of level surfaces. 

Current understanding of the erosion of polymer laminates has come chiefly from rain erosion studies of composite aircraft materials. Analogies have been drawn between cavitation and liquid impingement processes on metallic materials both involve extensive structural damage early in the incubation period as a result of short-term shock pulses. Furthermore, the deformed surfaces of materials which are subjected to both processes are very similar, and so are the methods used to improve their performance [99]. Attempts have been made to prioritize the factors affecting erosion of FRP by liquid impingement, with more or less predictable results [100] in respect of resin composition, fiber volume fraction and orientation, porosity and thermal conductivity. All these factors were found to affect performance. 

Not unexpectedly, Figure 1 shows that the behavior of p near the surface of the filler particles is qualitatively similar to that found for polymer melts near planar solid surfaces [22-24], i.e. it is characterized in all cases by a series of maxima and minima of progressively decreasing intensity with a periodicity approximately 0.8<7. This is true in particular for system Mg,10, in which p reaches its bulk value within approximately 2a from the surface of the particles, as found near planar solid surfaces. The behavior is quite different in the other two cases. In fact, the curve for system Mi6,36 shows a monotonous decrease following the initial series of maxima and minima, and the value of p for r = 20less than unity, while the curve for system Mg,50 shows a complex behavior characterized by the superposition of the series of maxima and minima with periodicity 0.8a with a second series of broad maxima and minima with a periodicity approximately 4complex behavior is observed for the other systems studied, such that intrinsically different p curves are obtained for different systems. In particular, the complexity of the curves is found to increase with increasing size and volume fraction of the filler. 

---