Bridging the Length Scales

Therefore, an important objective in the theory branch of M/C interface research is to envisage new types of interatomic potentials suitable for modeling M/C interfaces to bridge the length scale gap between theory and experiments. In this context, ab initio studies are very useful firstly, for exploring the qualitative nature of M/C chemistry which must be captured by novel model interaction potentials secondly, to provide a broad database for testing new interaction potentials. 

D axisymmetric FEM models that can reduce computational time [59]. The multiscale RVE integrates nanomechanics and continuum mechanics, bridging the length scales from nanoscale to mesoscale. 

A fiirther theme is the development of teclmiques to bridge the length and time scales between truly molecular-scale simulations and more coarse-grained descriptions. Typical examples are dissipative particle dynamics [226] and the lattice-Boltzmaim method [227]. Part of the motivation for this is the recognition that... 

Understanding the effects of membrane structure, water content and water distribution on proton conductivity has to invoke additional theoretical tools. They have to bridge many length scales from molecular environments to random heterogeneous structure at macroscale. This involves phenomenological concepts and homogenization methods in order to average over microscopic details [65]. 

In between the aforementioned levels, in both length and timescales are hybrid (multiscale) simulation strategies that combine the theoretical approaches from the neighboring levels in different ways, thereby bridging the couesponding scales. Such coupled (e.g., quantum-to-atomistic or atomistic-to-continuum) approaches have been developed and employed in recent years. For each scale, we review the simulation techniques and tools, as well as discuss important recent contributions (see Box 2). 

D. N. Theodorou, in Challenges in Molecular Simulations Bridging the Time-Scale and Length-Scale Gap (SIMU) 19-40 (The European Science Foundation programme, 2002). 

Very recently, people who engage in computer simulation of crystals that contain dislocations have begun attempts to bridge the continuum/atomistic divide, now that extremely powerful computers have become available. It is now possible to model a variety of aspects of dislocation mechanics in terms of the atomic structure of the lattice around dislocations, instead of simply treating them as lines with macroscopic properties (Schiotz et al. 1998, Gumbsch 1998). What this amounts to is linking computational methods across different length scales (Bulatov et al. 1996). We will return to this briefly in Chapter 12. 

One of the apparent results of introducing couple stress is the size-dependent effect. If the problem scale approaches molecular dimension, this effect is obvious and can be characterized by the characteristic length 1. The size effect is a distinctive property while the film thickness of EHL is down to the nanometre scale, where the exponent index of the film thickness to the velocity does not remain constant, i.e., the film thickness, if plotted as a function of velocity in logarithmic scale, will not follow the straight line proposed by Ham-rock and Dowson. This bridges the gap between the lubrication theory and the experimental results. 

Because fully polymerized silicon species are more stable with respect to hydrolysis than weakly polymerized ones (24-36 ), the effect of restructuring at short length scales is manifested as the maximization of Q4 species at the expense of QJ-Q3 species. (Note In Q terminology, the superscript denotes the number of bridging oxygens (-0-Si) to which the silicon nucleus is bonded.) Conversely, under conditions where restructuring is inhibited, the pattern of condensation is more random in solution and less fully polymerized species are retained in the final gel. 

Clearly, there are two quite different types of models for a gas flow the continuum models and the molecular models. Although the molecular models can, in principle, be used to any length scale, it has been almost exclusively applied to the microscale because of the limitation of computing capacity at present. The continuum models present the main stream of engineering applications and are more flexible when applying to different macroscale gas flows however, they are not suited for microscale flows. The gap between the continuum and molecular models can be bridged by the kinetic theory that is based on the Boltzmann equation. 

Chapter 5 considers the connection between the universal large scale dynamics discussed first and the local specific dynamics discussed in the second step. The dynamics at intermediate length scales bridges the two and we will address the leading mechanism limiting the universal dynamics in flexible polymers. 

One of the most promising bottom-up approaches in nanoelectronics is to assemble 7i-conjugated molecules to build nano-sized electronic and opto-electronic devices in the 5-100 nm length scale. This field of research, called supramolecular electronics, bridges the gap between molecular electronics and bulk plastic electronics. In this contest, the design and preparation of nanowires are of considerable interest for the development of nano-electronic devices such as nanosized transistors, sensors, logic gates, LEDs, and photovoltaic devices. 

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