Multiscale phenomenon

The phase equilibrium of materials is an inherently multiscale phenomenon which spans from the functional group (or atomic) scale through the morphological-structure scale to the macroscopic scale. Two texts presented in this volume are devoted to this problem. 

For each phenomenon, there are also many elements involved which determine the behaviour of each phenomenon. These phenomena are described by a wide range of characteristic time and length values. For the case of CVI fabrication of fibre-reinforced ceramic-matrix composites, the diameter of a molecule and the thickness of the interfacial phase are about 10 1 run and 102nm respectively, whilst the sizes of the substrate/component and the reaction are around 1 m. In addition, elementary chemical reactions occur in a time range of 10 " to 10 4 s, the time for heat transfer and mass transfer is around 1 s to 10 min. By contrast, the total densification time for one CVI run is as long as approximately 102 h. In such cases, it is necessary to establish multiscale models to understand and optimise a CVD process. 

A second major problem involves the consequences of the multiscale nature of superplastidty, notably the correlation between the individual behavior of one grain under shear and normal stresses, and the average collective behavior of these grains. This is a very difficult task, as plastidty is a nonequilibrium phenomenon, and grain motion cannot be completely treated as being thermal in nature. Rather, it implies that the usual methods of thermodynamics and statistical physics cannot be applied -or perhaps they can, but under certain restrictions. 

Two important challenges exist for multiscale systems. The first is multiple time scales, a problem that is familiar in chemical engineering where it is called stiffness, and we have good solutions to it. In the stochastic world there doesn t seem to be much knowledge of this phenomenon, but I believe that we recently have found a solution to this problem. The second challenge—one that is even more difficult—arises when an exceedingly large number of molecules must be accounted for in stochastic simulation. I think the solution will be multiscale simulation. We will need to treat some reactions at a deterministic scale, maybe even with differential equations, and treat other reactions by a discrete stochastic method. This is not an easy task in a simulation. 

Vibrational spectroscopy is an important tool to obtain information about the secondary structure of proteins [827]. The ability to relate protein conformations to infrared vibrational bands was established very early in the pioneering work of Elhot and Ambrose before any detailed X-ray results were available [828]. Vibrational circular dichroism (VCD) provides sensitive data about the main chain conformation [829, 830]. The Raman optical activity (ROA) signal results from sampling of different modes but is especially sensitive to aromatic side chains [831, 832]. A theoretical prediction for the ROA phenomenon was developed by Barron and Buckingham [833, 834], and the first ROA spectra were measured by Barron, Bogaard and Buckingham [835, 836]. First ab initio predictions were provided by Polavarapu [837]. In 2003, Jalkanen et al. showed that DPT approaches in combination with explicit water molecules and a continuum model reproduce the experimental spectra much better [838]. DFT-based approaches to VCD spectra were, for example, pioneered by Stephens et al. [839]. To extract the local structural information provided by ROA, Hudecova et al. [721] developed multiscale QM/MM simulation techniques. 

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