Chirality interaction tensor

The chirality interaction tensor Wy is responsible for the interaction of the chiral guest, the chirality of which is described by the chirality tensor Cy, with the anisotropic host Wy = ikLkj- Ly covers the anisotropic host properties. W = Tr JT), is different from zero. The gyki are the orientational distribution coefficients of the guest in the molecular ensemble of the guest-host phase. From the two possible representations to avoid non-diagonal elements in (3.19), the representation in the system of principal axes of the order tensor is chosen instead of the principal axes of the chirality interaction tensor Wy. With Saupe s order parameters the HTP is also a sum of three terms... 

Equation (11) of Nordio et al [20] can be generalised to develop a theory with a non-traceless pseudotensor of second rank Wy, the chirality interaction tensor. Because the contribution of the interaction energy from the chiral/chiral potentials of the molecules is small in comparison to the chiral/achiral contribution, the helical twisting power is then given for a guest/host system as well as for a single component chiral nematic phase by ... 

To relate macroscopic properties, especially the results of chirality measurements, to mesoscopic and further to pseudoscalar molecular properties, experimental data should be available in order to develop and check structure-property relations, mechanisms, and models. A set of usable data for the chiral nematic phase consists of the composition of the phase, p, HTP, V.2, Ki, K2, and K3. On the microscopic scale the (HTP)i as well as the microscopic order paramet S, D, A, B, the helicity tensor Qy or the chirality interaction tensor W y, and a chirality tensor Cy or an equivalent quantity should be known for every component. At the moment, the coordinates W y can only be estimated because a variation of the order of the chiral dopant for a constant host order needs to be known for their measurement. Some data are collected in TABLE 1 in order to give a feeling for the size and sign of available quantities [25-33] but, as can be seen, no complete sets of data for a system have yet beoi given in the literature. 

If the chiral interaction of a fluid phase with a dopant molecule is described by an antisymmetric tensor of third rank, which can be reduced to a pseudotensor of rank 2, a description of the HTP can be obtained analogously to... 

One possible resolution of the disagreement which still remains is that the tensor component of the nucleon-nucleon interaction is weakened in the nuclear medium due to chiral Lagrangian scaling [12]. The effect of this weakening can be inferred from our comparison of the H7B and HBB core-polarization results. A more direct illustration of the effect of a weaker tensor force is shown in Fig. 6 which illustrates it for a particular transition. It is seen that a reduction of 35% in the tensor component of the H7B interaction combined with the soft-7t SmecUiJf) of Table 1 brings agreement for this transition. 

For future technology of spintronics and photonics, the interaction of chirality of electron spin with another particle, such as nucleus and photon, should play an important role. Furthermore, the general relativity has recently been of vital importance to our daily lives, particularly for ultra-high-precision communication with an artificial satellite (e.g., GPS). The intrinsic formulations of tlie quantum electron spin vorticity principle and the energy density concept presented in this paper should help us understand the importance of stress tensor in modeling of materials of technological importance and chemical reactions. 

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