Structure continuous

The SCLl structure. Fig. 8(a), is triply continuous, the GLl, SCL2, Fig. 8(b,c), are quadruply continuous, and GL2, Fig. 8(d) is sextuply continuous. For bigger sizes of the unit cell one is able to generate the structures -tuply continuous. It is remarkable that the volume fraction of oil and water is 0.5 for all these structures. The genus for every surface in a given -tuply continuous structure is the same. 

The GL2 structure suggests that one can generate arbitrary n-tuply continuous structures. It is only necessary to set the cell length sufficiently large. We have not attempted to generate such structures because, due to the limits imposed by computer memory and processor speed, the lattice spacing would be too big for a given size of the lattice to obtain a reasonable accuracy. 

W. Gozdz, R. Hotyst. Triply periodic surfaces and multiply continuous structures from the Landau model of microemulsions. Phys Rev E 54 5012-5027, 1996. 

The essential property of a cementitious material is that it is cohesive. Cohesion is characteristic of a continuous structure, which in the case of a cement implies an isotropic three-dimensional network. Moreover, the network bonds must be attributed to attractions on the molecular level. Increasingly, recent research tends to show that cements are not bonded by interlocking crystallites and that the formation of crystallites is incidental (Steinke et al., 1988 Crisp et al., 1978). The reason is that it is difficult to form rapidly a mass which is both cohesive and highly ordered. 

Cement formation requires a continuous structure to be formed in situ from a large number of nuclei. Moreover, this structure must be maintained despite changes in the character of the bonds. These criteria are, obviously, more easily satisfied by a flexible random structure than by one which is highly-ordered and rigid. Crystallinity implies well-satisfied and rigidly-directed chemical bonds, exact stoichiometry and a highly ordered structure. So unless crystal growth is very slow a continuous molecular structure cannot be formed. 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

Garud, R. Nayyar, P. 1994. Transformative capacity continual structuring by inter-temporal technology transfer. Strategic Management journal, 15 265-385. 

In polymeric materials, the morphology development upon spinodal decomposition proceeds through various stages [92,93]. In the early stage of decomposition a co-continuous structure develops. A dispersed two-phase structure results only in the late stage of phase separation and the shape of the domains is not uniform. The morphology development upon spinodal decomposition is presented in Fig. 6. 

Various diverse systems qualify as gels if one assumes that in these systems the common features are the solid-like behavior and the presence of a continuous structure of macroscopic nature (6,7). For the purpose of the discussion in this paper, we describe a gel as a colloidal system comprised of a dispersed component and a dispersion medium both of which the junction points are formed by covalent bonds, secondary valence bonds, or long range attractive forces that cause association between segments of polymer chains or formation of crystalline regions which have essentially infinite life time (8). 

Obviously, we ve picked the inputs for this example so that they would partition easily into small collections of paired intervals and probabilities. When the input p-boxes are smooth or complicated continuous structures, the partitions are discretizations that will often need to be much finer. The precision of the result depends on the fineness of these partitions, which can be arbitrarily increased to achieve whatever precision is required. 

Silica sol is a stable dispersion of fine particles, while gel has a three-dimensional continuous structure. Si02 content in sol range between 10-50%, while that in dry sdica gels is between 96.5 to 99.6%. Density of dry gels is 2.22 g/cm3 and sols 2.20 to 2.30 g/cm. Weight loss in sols at 105°C is between... 

In the unstable region, the concentration fluctuations are delocalized and there is no thermodynamic barrier to phase growth. Thus, separations that take place spontaneously lead to long range phase separation. This process is called spinodal decomposition (SD). In this mechanism, decomposition starts with a co-continuous structure and gradually shifts to a droplet morphology because of the breakdown of the continuous structure [41]. 

---