Reverse mapping

Mapping and Reverse Mapping of Coarse-Grained RIS Chains. 81... 

Reverse mapping restores all of the missing atoms, and takes the system from the discrete space of the 2nnd lattice to a continuum. The starting point for reverse mapping depends on choices made in the performance of the second step. 

Fig. 4.5. Periodic cell for nine chains of Q00H202 at 0.75 g/cm3 and 443 K. a On the 2nnd lattice, with numbers denoting the locations of collapsed beads and b After completion of the reverse mapping in the third step. Adapted from [144]...

An intermolecular pair distribution function evaluated at the end of Step 2 would consist of delta functions at those distances allowed on the 2nnd lattice. After completion of reverse mapping, which moves the system from the discrete space of the lattice to a continuum, the carbon-carbon intermolecular pair distribution function becomes continuous, as depicted in Fig. 4.7 [144]. 

Fig. 4.10. A thin film of a melt of C100H202, with both surfaces presented to a vacuum, as represented a on the 2nnd lattice and b after reverse mapping. Adapted from [162]...

One of the important limitations of these methods, in their current state of development, is the necessity to conduct a new coarse-graining for each new type of polymer that is simulated. Major opportunities to increase the utility of this class of simulations lie in the development of methods, which make the mapping to the coarse-grained structure (and the reverse-mapping back to the structure expressed in fully atomistic detail) as general (and painless) as possible when new polymers are treated. This area is the subject of continuing work by all four groups. 

J We note that in some cases use of symmetry in the experiment allows what would seem to have irreversible equations of motion to be set in a reversible form or to use time-reversal mappings other than the standard (q, p) -> (q, —p). ... 

These buzz words include anything that connects one scale to the next, starting from a straight calculation of a constitutive equation parameter from molecular modelling to some more sophisticated schemes of mapping and reverse mapping of scales. The basic idea and attraction is depicted in Figure 2 ... 

In the above context, the perspective was one of how do we describe a molecule in terms of a graph however, it is the reverse mapping which leads to new molecular designs. So let us review quickly some basic features of graphs, specifically connected graphs, as molecular prototypes. 

This chapter will review the generation of free-standing thin films and fibers with a coarse-grained simulation method on a high coordination lattice,performed in a manner that allows accurate reverse-mapping of individual replicas to a fully atomistic representation in continuous space.4 After describing some of the properties of these films and fibers, we will present some new information about the limits on the stability of the models of these nanofibers. 

Construction of the thin films commences with an equilibrated model of the melt at bulk density, contained in a three-dimensional box of dimensions LxLyLz, measured along the three axes of the periodic cell. The angle between any two axes is 60°. Periodic boundary conditions are applied in all directions. The niunber and degree of polymerization of the parent chains are chosen so that the system will have bulk density, pbulk, at the temperature of the simulation. The construction, equilibration, analysis, and reverse mapping of these models of polyethylene melts have been reviewed recently, " and will receive no additional mention here. 

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