Topological surface

Surface-relief grating (SRG, regular topological surface modification) formed via irradiation with an interference pattern of coherent light has been demonstrated only recently/ " and is perhaps the most attractive target in the current research of azo polymers (Chapters 13 and 14 of this book focus on this subject). It is still unclear whether there are any common mechanisms involved between SRG formation and the photomechanical response observed in monolayers described in Section 15.4.1. Nevertheless, with regard to photoinduced motions in Az polymers, it is quite important to proceed with SRG experiments. 

The pattern of state transitions is mapped, often onto a topological surface. A topological surface (called a manifold) can suggest canonical equations possessing coefficients that can be assigned mechanistic meaning. 

Surface topology Surface topology dictates cellular infiltration, adhesion, and differentiation. Considering the complex interactions between cells and the extracellular matrix (ECM), hiomimetic TE approaches are becoming increasingly popular. The use of natural polymer and the introduction of specific cell adhesion motifs in synthetic biomaterials have been demonstrated to improve cell adhesion, minimize immune response, and favor tissue-specific cell differentiation. ... 

Fig. 4.1 Different topological surfaces (a) has genus zero (b) has genus one (c) has genus two (d) has genus three.

The compaction process may be defined as a process whereby the elastomer comes in contact with the topological surface of carbon black. The question is how to express the degree of compaction quantitatively. If carbon black were a porous material, whose pores were as depicted in Figure 3.12a, the degree of compaction might be expressed as a percentage of pore-volume occupied with rubber. 

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