Tensors for Physics

210 12 Integral Formulae and Distribution Functions in the ordered and the isotropic state is sa=−kB ∫ fln(f/f 0 )d^2 u=−kB〈ln(f ...

12.2 Orientational Distribution Function 211 HereLμLμ, with Lμ=εμνλuν ∂ ∂uλ , is the Laplace operator on the unit sphere. The pr ...

212 12 Integral Formulae and Distribution Functions In the presence of an external torqueT, which can be derived from a potentia ...

12.3 Averages Over Velocity Distributions 213 Kinetic Theory of Gasesare presented. Physical phenomena associated with the veloc ...

214 12 Integral Formulae and Distribution Functions In thermal equilibrium,Fis equal to the absolute MaxwellianF 0 , which is th ...

12.3 Averages Over Velocity Distributions 215 tensors constructed from the components of the velocity variableV. However, addi- ...

216 12 Integral Formulae and Distribution Functions These functions are orthogonal and normalized according to〈Φ(s)Φ(s ′) 〉 0 =δ ...

12.3 Averages Over Velocity Distributions 217 expression, used for the dynamics of colloidal Brownian particles, is − ( δF δt ) ...

218 12 Integral Formulae and Distribution Functions with the relaxation frequencyν 1 =ν 0. Clearly, the flow term couples the mo ...

12.3 Averages Over Velocity Distributions 219 In local thermal equilibrium, at temperatures and densities, where quantum effects ...

220 12 Integral Formulae and Distribution Functions nowΦhas to be orthogonal to the moments associated with the conserved quanti ...

12.3 Averages Over Velocity Distributions 221 Thethirteen moments approximationof kinetic gas theory [45] employs just these 3 p ...

222 12 Integral Formulae and Distribution Functions quantities become anisotropic. The basics and examples for the use of tensor ...

12.4 Anisotropic Pair Correlation Function and Static Structure Factor 223 is not an ordinary position vector but it is the diff ...

224 12 Integral Formulae and Distribution Functions The factor^12 stems from the fact that the interaction between two particles ...

12.4 Anisotropic Pair Correlation Function and Static Structure Factor 225 Fig. 12.1Schematic scattering geometry with wave vect ...

226 12 Integral Formulae and Distribution Functions where it is understood, that the “spherical” partgsof the pair correlation f ...

12.4 Anisotropic Pair Correlation Function and Static Structure Factor 227 It depends on the geometry of applications whether an ...

228 12 Integral Formulae and Distribution Functions approach ofgto its equilibrium valuegeq=geq(r)when the flow is switched off. ...

12.4 Anisotropic Pair Correlation Function and Static Structure Factor 229 The term involving the productLμνLκσgives contributio ...