Elastic energy terms, calculation

The total energy is calculated in terms of the ratio y of the thermal part of the pressure to the elastic part, and other variables. Isentropic processes are discussed, and the initial conditions of a Landau-Stanyukovich-Zel dovich-Kompaneets (LSZK) detonation are obtained in terms of y... 

A possibly important eflect of the linear dependence of on eurvature for Cq 0 is a lowering of the elFeetive bending rigidity. Let us calculate it in terms of the neutral surfaee. For eylindrieal curvature the total elastic energy density referring to this surface may be expressed by... 

The two terms in the square brackets of Eq. (94) can be identified as a temperature independent internal energy term, and a temperature dependent entropy term resulting from the hard particle pair distribution function. From this equation it can be seen that the calculation of the principal elastic constants of a nematic liquid crystal depends on the first and second derivatives with respect to the angle 9 of the single particle orientational distribution function. Any appropriate angular function may be used for/(f2i, 9(R)), but the usual approach is to use an expansion in terms of spherical harmonics. The necessary mathematical manipulations are complicated, but give relatively compact results. Thus the ingredients of a molecular calculation of torsional elastic constants within the van der Waals... 

The field terms may stabilize or destabilize the intrinsic thermodynamic order of a mesophase, and hence increase or decrease the temperature of its transition to a less ordered phase. The shift in the transition temperature is calculated by comparing the electric (magnetic) energy with the transition enthalpy or some other competing thermodynamic quantity (e.g. elastic energy). Below we consider examles. 

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