Spatial expansion

Summarizing, it can be seen that the reaction rate of a given number of atoms of a micro component decreases drastically with the spatial expansion of the system in which they are contained (i.e. the number of atoms per volume unit). Therefore, at critical concentrations, micro-microcomponent kinetics prevails largely over thermodynamics in a reaction. 

Figure 23. Dynamics of spatial expansions of optical molasses of Rb adapted from Pmvost et al. (data from Ref. 79). (a) A photograph of the irradiated cloud at r = 0. (b) Excited atom distribution in the irradiated cloud at r = 0. (c) Time dependence of the cloud radius, (d) Time dependence of the volume of the irradiated cloud, (e) Time dependence of the density of the expanding cloud.

Reduced to its ultimate essence, the substance of these long pages can be summed up in this simple affirmation that if the universe, regarded sidereally, is in process of spatial expansion (...), in the same way and still more clearly it presents itself to us.physico-chemically [underlined by me - auth., as in process of orgsmc involution upon itself (...)... 

Structurally, the bent 6-substituted ligands have structural similarities to banana LCs. However, no mesomorphism was detected. The corresponding lanthanide complexes have the shape of calamitic LCs, but they decompose at temperatures between 180 and 200 °C, without evidence for mesomorphism. The absence of mesomorphism was attributed to the spatial expansion brought by the bulky R(N03)3 groups (Nozary et al., 2002). Two of the three bound bidentate nitrate anions are located on opposite sides of the planar aromatic core, so that they strongly disturb the intermolecular interactions between the rigid cores and reduce the molecular anisotropy. Also a ligand with four terminal chains (L21) did not lead to liquid-crystalline lanthanide complexes (Nozary et al., 2000). 

Measurements on a series of sterols have supplied very informative data on the dimensions of the unit cells (see Table 67) and made it possible to calculate the thickness of the molecules and their spatial expansion in the molecular plane. The result is that the formula preferred by organic... 

Generally, a homogeneous wall temperature over the entire mold surface is desirable. Different wall temperatures are justified if certain areas of the part must be higher or lower tempered, for example in mass accumulations or warpage compensation. A completely homogeneous wall temperature, particularly in complex molded parts with spatial expansion, is practically not achievable, but this should always be the desired goal. Impacts from an increased cavity temperature are ... 

The spatial expansion of the system under study must also be considered. For instance, Guillaumont and Adloff, considering disproportionation of Pu(V) from a theoretical point of view, have shown that for 100 atoms of Pu, assuming a very... 

The first issue is the problem of uncertainty of the model, which arises from the situation that the chemical accuracy of the model is not fully validated in the actual ambient atmosphere. The second problem is the temporal and spatial expanse of photochemical air pollution, i.e. the relationship between the O3 and the initial concentrations of NOx and VOC in the source area and down-wind area where O3 is reached after a few hours of transport is quite different. As for the chemical accuracy of the model, in the case of chamber experiments where the reactant VOC is well defined, the isopleths based on the model which can reproduce the experiment are recognized as accurate within the limit of validation, and they are useful for understanding the relationships between O3 and initial concentrations of NOx and VOC conceptually and quantitatively. However, in the actual ambient... 

---