Tensors for Physics

292 15 Liquid Crystals and Other Anisotropic Fluids 15.4.2 Landau Theory for the Isotropic-Cubatic Phase Transition A phenomenol ...

15.4 Cubatics and Tetradics 293 By analogy with the description of the alignment tensor elasticity, cf. Sect.15.3.3, the potenti ...

294 15 Liquid Crystals and Other Anisotropic Fluids Fig. 15.7Tetrahedron embedded within a cube. Thelinesconnecting the center w ...

15.5 Energetic Coupling of Order Parameter Tensors 295 or the molecular alignment and the anisotropy of the pair-correlation fun ...

296 15 Liquid Crystals and Other Anisotropic Fluids 15.5.2 Second-Rank Tensor and Vector. Letd∼〈e〉anda∼〈uu〉>be a polar vector ...

15.5 Energetic Coupling of Order Parameter Tensors 297 the number density and to the permanent electric dipole moment of the mol ...

298 15 Liquid Crystals and Other Anisotropic Fluids In thermal equilibrium, these derivatives are equal to zero. In connection w ...

Chapter 16 Constitutive Relations Abstract In this chapter is devoted to constitutive laws describing equilibrium and non-equili ...

300 16 Constitutive Relations 16.1 General Principles. 16.1.1 Curie Principle Constitutive relations are laws of physics where, ...

16.1 General Principles 301 1,parity invarianceof the relation (16.1) requires that the parity of the coefficient tensorChas to ...

302 16 Constitutive Relations 16.1.2 Energy Principle Consider a constitutive relation (16.1) where=kapplies and where the scal ...

16.1 General Principles 303 where the tensorsJ(..)andF(..)are referred to asthermodynamic fluxesandther- modynamic forces, respe ...

304 16 Constitutive Relations 16.2 Elasticity A property typical for a solid body is its elastic response to a small deformation ...

16.2 Elasticity 305 is determined by the trace of the deformation tensor. The symmetric traceless part is associated with volume ...

306 16 Constitutive Relations purpose, an appropriate Cartesian coordinate system is chosen and the components ofσμνanduμνare re ...

16.2 Elasticity 307 The Voigt coefficients are c 11 =c 22 =c 33 =B+ 4 3 G, c 12 =c 23 =c 31 =B− 2 3 G, c 44 =c 55 =c 66 =G, othe ...

308 16 Constitutive Relations In addition to the bulk and shear moduliBandG, which already occur for isotropic systems, a third ...

16.2 Elasticity 309 16.2.5 Microscopic Expressions for Elasticity Coefficients. Consider a system ofNparticles, located at the p ...

310 16 Constitutive Relations represents the deformation-induced variation ofΦμν. The second term on the right hand side of (16. ...

16.2 Elasticity 311 remarkable, since the computation ofGfluctinvolves not only two-particle, but also three- and four-particle ...