Tensor gradient-energy coefficient

Coefficients aij T) depend explicitly on temperature T. Coefficients afj, aijki, are supposed to be temperature independent, constants giju and Vijkimn determine the magnitude of the gradient energy. Tensors gijki, Oijki and positively defined. Tensor is the surface excess elastic moduli, p, p is the surface stress tensor [81,82], is the surface piezoelectric or piezomagnetic tensor [67], qijki are the bulk striction coefficients Ciju are components of elastic stiffness tensor [83]. 

In addition to the fluxes, also the flux jg depends on the gradients most simply (neglecting minor effects) only on the temperature gradient by Fourier s law of heat conduction. Finally the tensor F depends on the velocity gradients with viscosity as the coefficient of proportionality. Taking into account these relations, Eq. (C.6) represents the energy transport equation. 

In this expression, the coefficients d, C, C2,P, and y are constants, while a = a T — T ) changes sign when T = T. The three terms with coefficients a, P, and y are just those terms which appear in the nematic free energy the Cl and C2 terms are order parameter gradients ( , ,/ = dEy/dxi) which are also allowed for nematics. The chiral term with coefficient d is forbidden in nematics—it contains the antisymmetric tensor Cyi and lacks nematic mirror symmetry. 

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