Elastic molecular skeleton

As rubber concrete has long-term strength that is distinct from zero and creep damped out at compression, it is necessary to enter element E representing an elastic molecular skeleton of a material into the rheological material circuit (Figure 2.43). 

Using differential geometry, a curve can be reconstructed from the knowledge of its curvature and torsional functions (the Frenet-Serret formulas). Therefore, these two functions give a concise shape description, provided one associates an everywhere-differentiable curve to the molecular skeleton. This approach has been employed in the analysis of protein shape. Moreover, this technique allows one to represent the dynamics of molecular chains or loops in terms of the deformation of elastic bodies. We return to this point when we discuss a number of purely topological descriptors of molecular curves. 

The step-potential model allows us to calculate the bond lengths in 7r-electron systems. Bond length and 7r-elec-tron density in a bond are related the 7r-electron cloud attracts the nuclei. Thus assuming first a (r-bonded molecular skeleton with uniform bond length a, the skeleton is elastically deformed in the field of the 7r-electron cloud and the cloud is deformed in the changed potential. This iterative process is repeated until self-consistency between bond length (or bond potential V,) and ir-electron density p, in the middle of bond i is reached for each bond. We find... 

Fibrous proteins represent a substantial subset of the human proteome. They include the filamentous structures found in animal hair that act as a protective and thermoregulatory outer material. They are responsible for specifying much of an animal s skeleton, and connective tissues such as tendon, skin, bone, cornea and cartilage all play an important role in this regard. Fibrous proteins are frequently crucial in locomotion and are epitomised by the muscle proteins myosin and tropomyosin and by elastic structures like titin. Yet again the fibrous proteins include filamentous assemblies, such as actin filaments and microtubules, where these provide supporting structures and tracks for the action of a variety of molecular motors. 

When fluids can seep through pores, interacting mechanically with the solid skeleton, the material is composed of more than one constituent thus we need to use a mixture theory in which we could clearly make out each part filled by different constituents on a scale which is rather large in comparison with molecular dimensions so we put forward a new continuum theory of an immiscible mixture consisting both of a continuum with ellipsoidal microstructure (the porous elastic solid) and of two classical media (see, also, the conservative case examined by Giovine (2000)). In accordance with Biot (1956), we consider virtual mass effects due to diffusion we also introduce the microinertia associated with the rates of change of the constituents local densities, as well as the one due to the deformation of the pores close to their boundaries. 

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