โ Scribed by Dan Nily
No coin nor oath required. For personal study only.
The goal of multiscale models is to enable translation of system characteristics on one length or time scale to another. Traditionally, multiscale models utilize characteristics determined on the molecular scale in meso-and macro (or continuum) models of the macro-system. Such hierarchical approaches enable, presumably, control of the bulk system through manipulation of the molecular component. This approach may be used, for example, in the design on nanostructured materials.
Recent development in multiscale modeling are enabling another approach, where the information from different size or time scales can travel in the opposite direction, namely, utilization of the macro-scale system properties in the understanding of the underlying meso and molecular organization. This approach is of special interest in the study of biological systems, where the complexity of the nano-scale assembly may prohibit effective molecular modeling. In this issue we present reviews of recent developments in several aspects of multiscale modeling.
The potential of mean force (PMF) is a cornerstone of multiscale simulations. Dahirel and Jardat review recent simulation studies of the PMF between charged nano-particles in solution. The review clearly summarizes the advantages and limits of the classic DLVO theory in nano-scale systems, and defines the conditions in which the DLVO potential can be used for the PMF.
Fujita and Yamaguchi explore the consequences of the potential of mean force in colloidal systems, namely, self organization. Colloidal self organization into ordered structures on length scales that are orders of magnitude larger than the particle dimensions. Successful computation of colloidal assembly requires, therefore, the ability to cross from the nano/ molecular length scale, where interactions such as van der Waals and electrostatics dominate, through the meso-scale where hydrodynamics are important, to yield the macro-scale material characteristics of the ordered array. Fujita and Yamaguchi discuss recent continuum models that treat the combined motion of the particles and fluid through a hydrodynamic interaction that is introduced into the conservation equation of momentum through constitutive equations. This approach allows
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## Abstract We consider a multiscale network of natural gas pipelines. Different arcs of the network are to be modeled by possibly different models depending on the requisite qualitative detail required: an isothermal Euler system of equations; linearized model derived from the isothermal Euler sys