Cylindrical inclusion

Baumgartner and coworkers [145,146] study lipid-protein interactions in lipid bilayers. The lipids are modeled as chains of hard spheres with heads tethered to two virtual surfaces, representing the two sides of the bilayer. Within this model, Baumgartner [145] has investigated the influence of membrane curvature on the conformations of a long embedded chain (a protein ). He predicts that the protein spontaneously localizes on the inner side of the membrane, due to the larger fluctuations of lipid density there. Sintes and Baumgartner [146] have calculated the lipid-mediated interactions between cylindrical inclusions ( proteins ). Apart from the... 

In order now to define the radius r of the spherical layer corresponding to the mesophase, we express it as t = (rf + Ar) and we modify the respective relation given by Lipatov 11 for particulates to the appropriate relation for cylindrical inclusions. For the cases of particulate composites it was shown that the following relation holds ... 

Figure 18.3 Stress magnitudes in and around the cylindrical inclusion, in absence of diffusion. In (a) stress magnitudes are shown by means of profiles drawn on lines through the inclusion s centerline along the x-direction and the z-direction. In (b) stress states are shown by means of ellipses. As with the strain state, conditions are homogeneous inside the inclusion, and again homogeneous with different principal values at points remote from the inclusion.

Change of phase. It is to be recalled that in Chapters 13 through 16 the pattern has been to pose a question as follows Suppose that at an interface equilibrium exists at hydrostatic pressure P then is kept equal to P and equilibrium is disturbed by changing only what processes begin to run etc. A consequence of this approach is that we have not paid attention to processes brought on by making different from P except by references to 5p in part of Chapter 16. With a cylindrical inclusion, however, these processes must be considered, as follows. 

Jenner CE, Sanchez F, Nettleship SB, et al. The cylindrical inclusion gene of Turnip mosaic virus encodes a pathogenic determinant to the Brassica resistance gene TuRBOl. Mol. Plant Microbe Interact., 2000 13(10) 1102-1108. 

We have shown that, minimized with respect to the contact slope, the interaction between two insertions is repulsive. On the other hand, the interaction involving a larger numbers of insertions may become attractive. This has been observed in a model system of two interacting flat walls [129], which can approximate the interaction between two parallel arrays of insertions. Similarly, an attractive region is present in the interaction free energy for a two-dimensional array of cylindrical inclusions [90,94]. Clustering was also seen in... 

Nagy, P. B. and Nayfeh, A. H. (2000), On the thermoelectric magnetic field of spherical and cylindrical inclusions,/owmal of Applied Physics,91,1481-90. 

Goodier, J. N. (1933) Concentration of stress around spherical and cylindrical inclusions... 

Bohinc K, Kralj-Iglic V, May S (2003) Interaction between two cylindrical inclusions in a symmetric lipid bilayer. J Chem Phys 119 7435-7444... 

Kozlovsky Y, Zimmerberg J, Kozlov MM (2004) Orientation and interaction of oblique cylindrical inclusions embedded in a lipid monolayer a theoretical model for viral fusion peptides. Biophys J 87(2) 999-1012... 

The constraint matrix T depicts the effect of the constraining matrix on the inclusion and is a function of matrix material properties and ellipsoidal inclusion shape. It represents the piezoelectric analog to Eshelby s tensor in the elastic case, see Dunn and Taya [66]. Expressions for cylindrical inclusions to model fibrous composites are provided by Dunn and Taya [67] (this reference uses a different notation, T is called S). Equating Eqs. (5.12) and (5.13) and making use of Eq. (5.14) to replace the eigenfields Z and Eq. (5.11) to eliminate the perturbation fields Z after some manipulations, leads to... 

If we consider the element of filled polymer with cylindrical inclusions (reinforcing fibers), the expression for the modulus has the following form ... 

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