Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group

The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte

Site symmetry and crystal symmetry: a spherical tensor analysis

The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet.Comment: 27 pages, 3 figure

On the conveyance of angular momentum in electronic energy transfer

When electronic excitation transfer occurs, it is of considerable interest to establish whether angular momentum can also be conveyed in the process. The question is prompted by a consideration that when the participating chromophores are atoms, ions, or molecular systems having high local symmetry, the electronic excited states that are involved are generally characterized not only by energy, but by angular momentum properties. Moreover, it is known that electron spin can be communicated between quantum dot exciton states. Resolving the general issue entails an electrodynamic representation exploiting irreducible tensor methods, the analysis being illustrated by application to energy transfer associated with a variety of multipolar transitions. The results exhibit novel connections between an angular momentum content of the electromagnetic coupling and a strongly varying distance dependence. It is concluded that the communication of angular momentum does not in general map unambiguously between a donor and energy acceptor